Die doppelte Kontingenz von Elfmeterschüssen.

Transcription

Die doppelte Kontingenz von Elfmeterschüssen.
Eine empirische Analyse
Von Roger Berger und Rupert Hammer!
Zusammenfassung: Beim Elfmeterschuss bilden Torwart und Schütze zeitgleich und wechselseitig Erwartungen zur Sprung- bzw. Schussrichtung ihres Gegners und handeln entsprechend. Strafstöße sind damit ein ideales Beispiel fUr doppelte Kontingenz und eignen sich auf Grund ihres
standardisierten Ablaufs für einen empirisch fundierten Vergleich der einschlägigen Ansätze Parsons, Luhmanns und der Spieltheorie. Dieser Vergleich zeigt, dass sich nur aus der Spieltheorie
empirisch gehaltvolle Aussagen zu Handlungsmustern der Spieler ableiten lassen. Diese folgen
aus der Minimax-Lösung und besagen, dass die Spieler ihre Entscheidungen mit vorhersagbaren
Wahrscheinlichkeiten randomisieren. Parsons Ansatz dagegen ist nicht auf die Elfmetersituation
anwendbar. Da die Interessen der Spieler hier vollständig komplementär sind, können sich keine
geteilten stabilen Muster bilden, an denen die Akteure ihre Seitenwahl ausrichten. Denn jedes
Muster würde vom Gegner sofort zum eigenen Vorteil unterlaufen werden. Aus Luhmanns Ansatz
folgt, dass die Spieler beim Elfmeter handlungsunfähig sind, weil sie den infiniten Regress von
Erwartungen wegen der Gleichzeitigkeit der Entscheidungen und der fehlenden Möglichkeit kommunikativer Aushandlungsprozesse nicht durchbrechen können. Für die empirische Analyse benutzen wir einen Datensatz, der alle 1043 Elfmeterschiisse aus elf Spielzeiten der Bundesliga
umfasst. Sie bestätigt weitgehend die spieltheoretischen Hypothesen. Die beobachteten professionellen Fußballspieler lösen die doppelte Kontingenz »Elfmeterschuss« wie vorhergesagt. Dies
trifft insbesondere auf die Torhüter zu, die im spieltheoretischen Sinne fast optimal handeln.
1. Einleitung
Ana7sen rund um das Fußballspiel erfreuen sich in der Soziologie einer gewissen Beliebtheit. Allerdings finden sich - abgesehen von dem bekannten Artikel von Esser (1991) - keine Arbeiten, die sich mit einzelnen Spielsituationen befassen. Dies ist insofern erstaunlich,
als soziale Interaktion bei Spielen wie Fußball quasi wie im Reagenzglas stattfindet. Die
Interaktionen sind real und es steht (fast) immer buchstäblich etwas auf dem Spiel. Gleichzeitig ist die soziale Situation örtlich und zeitlich eingeschränkt und gut beobachtbar. Auch
die Zahl der Akteure und ihre Handlungsalternativen sind vorgegeben, was die theoretische
und empirische Analyse vereinfacht.
Dies ist bei der im Folgenden betrachteten sozialen Interaktion - der Elfmetersituation ebenfalls der Fall. Der Schütze versucht dabei, den Ball aus einer Distanz von 11 Metern mit
einem Schuss im Tor unterzubringen. 3 Der Torhüter, auf der Torlinie stehend, probiert eben
dies zu verhindern. Beide Spieler stehen dabei vor demselben Problem: Auf welche Seite des
1) Roger Berger ist Stipendiat des Schweizerischen Nationalfonds (Stipendium Nr. PA-108952 I 1) an
der Universität Leipzig. Rupert Hammer ist Absolvent des Diplomstudiengangs am Institut für Soziologie der LMU München.
Wir danken Thomas Voss und einem anonymen Gutachter für Verbesserungsvorschläge. Holger
Rablfs und Jöm Wendland von der IMP AG München danken wir für die kostenlose Bereitstellung
des verwendeten Datenmaterials. Angela Fabry danken wir für die sprachliche Überarbeitung. Für
alle verbleibenden Fehler sind die Autoren verantwortlich.
2) Vgl. exemplarisch die Internetseite für sozialwissenschaftliche Fußballforschung (www.ruhr-uni-bochum.de/fussball) oder Kalter (1999).
3) Ein Elfmeter wird vom Schiedsrichter ausgesprochen, wenn ein Spieler im eigenen Sechzehnmeterraum eine von zehn möglichen Regelübertretungen - normalerweise Foul- oder Handspiel- begeht.
Soziale Welt 58 (2007), S. 397 - 418
398
Roger Berger und Rupert Hammer
Tors soll der Ball geschossen werden bzw. der Torhüter springen. Die Schussgeschwindigkeit
des Balles und die Ausmaße des Tors (7,11 m breit und 2,44 m hoch) machen es nämlich
zwingend erforderlich, dass der Torhüter sich für eine Ecke entscheidet, bevor er eindeutig sehen kann, wohin der Ball fliegt. Der Schütze wiederum weiß, dass der Torwart nicht vor dem
Moment der Schussabgabe in eine Ecke springen wird, da er sich sonst sämtlicher Abwehrchancen berauben würde. Ein Schuss in die jeweils andere Ecke würde dann den sicheren
Torerfolg bedeuten. Die Elfmetersituation erfordert deswegen eine simultane Entscheidung der
beteiligten Spieler und das Ergebnis - Tor oder nicht - hängt immer von der Entscheidung beider Akteure ab. Bei einern erfolgreichen Torschuss würde sich der Torhüter im Nachhinein
wünschen, in die andere Ecke gesprungen zu sein, ebenso wie der Schütze bei einern Misserfolg lieber die andere Ecke gewählt hätte, wenn er gewusst hätte, dass der Torwart sich in diese
wirft. Das erzielte bzw. nicht erzielte Tor ist also ein emergentes soziales Phänomen, das von
einem Akteur alleine nicht erzeugt werden kann, sondern sich erst aus der Interaktion ergibt.
Die Elfmetersituation ist damit als soziologischer Untersuchungsgegenstand prädestiniert.
Dies gilt umso mehr, als die Struktur dieser Interaktion ein idealtypisches Beispiel für eine
Situation doppelter Kontingenz ist. Denn Ego, das in seinen Aktionen prinzipiell frei ist,
trifft auf Alter, für den das ebenfalls gilt und beide Akteure wissen, dass beide dies wissen,
etc. Die soziologische Bedeutung dieser Interaktionsstruktur zeigt sich auch daran, dass sich
verschiedene theoretische Ansätze prominent mit dieser Frage beschäftigen. Folgt man
Ganssmann (2006), so sind dies insbesondere die Spieltheorie und die Ansätze von Parsons
und Luhmann. Diese werden in diesem Aufsatz einander gegenilbergestellt und daraufhin
untersucht, ob und wenn ja, welche stabilen Verhaltensmuster der beiden Spieler sie für
Strafstöße (nämlich die in der ersten Bundesliga ausgeführten) vorhersagen, und ob sich diese theoretisch fundierten Prognosen empirisch bestätigen lassen.
Dazu werden im nächsten Abschnitt 2 die fußballerischen Grundlagen des Problems dargelegt. In Abschnitt 3 werden erst die aus der Spieltheorie folgenden Vorhersagen zur Elfmetersituation entwickelt. Anschließend wird analog für die Ansätze von Parsons und Luhmann verfahren. Im 4. Abschnitt wird der Stand der empirischen Forschung berichtet und im
5. die theoretischen Vorhersagen an einem Datensatz überprüft, der alle Elfmetersituationen
der ersten Bundesliga der Spielzeiten von 1992 bis 2004 umfasst. Im letzen Abschnitt werden die Ergebnisse diskutiert.
2. Die Interaktion zwischen Schütze und Torwart
Im Folgenden werden die fußballerischen Grundlagen der Strafstoßsituation dargestellt. Mittels der zentralen Regeln der zuständigen Organisation FIFA kann der Ablauf beschrieben
werden: »Der Ball wird auf die Strafstossmarke [11 m vom Mittelpunkt der Torlinie zwischen den Pfosten und gleich weit von beiden Pfosten entfernt] gelegt. Der ausführende
Spieler muss klar identifiziert sein. Der Torwart der verteidigenden Mannschaft muss mit
Blick zum Schützen auf seiner Torlinie zwischen den Pfosten bleiben, bis der Ball mit dem
Fuß gestossen ist. Der ausführende Spieler muss den Ball mit dem Fuss nach vorne stossen.«
(FIFA 2005, Auszug Regel 14). Obschon dies nicht zwingend vorgeschrieben ist, wird der
Ball vorn Elfmeterschützen direkt auf das Tor geschossen, da sich durch einen Pass auf einen
Mitspieler kein Vorteil erzielen lässt. 4
4) Tatsächlich kommt ein Passspiel fast nie vor. Berühmt geworden ist allerdings ein Strafstoß von
Cruyffund Dlsen von Ajax Amsterdam aus dem Jahre 1982, in dem sich die beiden Spieler vor dem
(erfolgreichen) Torschuss sogar zweimal zupassten. Im letzten bekannten Beispiel gelang es 2005
Henry und Pires von Arsenal FC im Spiel gegen Manchester City allerdings nicht, ein Tor aus dem
gepassten Strafstoß zu erzielen.
Die doppelte Kontingenz von Elfmeterschüssen
399
Der Schütze kann nun relativ sicher sein, dass der Ball ins Tor geht, wenn er den Ball in
eine vom Torwart möglichst entfernte Zone des Tors schießt. Dann führt in der Regel auch
ein nicht mit maximaler Präzision und Wucht ausgeführter Schuss zum Tor. Dazu stehen
dem Schützen nun zwei Optionen offen. Er kann den Ball nach links schießen, wenn er erwartet, dass der Torwart nach rechts springt und vice versa. Der Torhüter ist umgekehrt
ebenso gezwungen, sich »schon vor dem Anlauf des Schützen eine bestimmte Ecke auszuwählen. Sobald der Elfmeterschütze den Ball berührt, springt er in die von ihm spekulierte
Ecke. Wird der Ball in die andere Ecke geschossen, ist der Torerfolg des Gegners nicht mehr
zu verhindern. Wird er in die von ihm ausgewählte Ecke geschossen, erhöhen sich seine
Chancen, den Ball zu halten ... [, d]enn so fällt die Reaktionszeit von 0,25 s weg« (Johanni /
Tschachner 2005, S. 28). Würde der Torwart erst nach der Schussabgabe springen, könnte er
einen ausreichend hart getretenen BallS nie halten, da dazu die menschliche Reaktionszeit
und Sprungkraft nicht ausreicht (vgl. Johanni / Tschachner 2005). Der Torhüter muss also
eine Erwartung über die vorn Schützen gewählte Ecke bilden. Das Problem besteht nun offensichtlich darin, dass der hier betrachtete professionelle Elfmeterschütze seine Erwartungen wiederum entsprechend anpassen wird, worauf der Torwart wiederum die andere Seite
wählen wird usw. usf. Da die beiden Spieler aber nun beim Elfmeterschuss offensichtlich
nicht wie Buridans Esel stehen bleiben, stellt sich die Frage, wie eine Auflösung dieses Zirkels sich potentiell gegenseitig blockierender Erwartungen, wie er typisch ist für eine doppelte Kontingenz, aus theoretischer Sicht aussehen kann.
3. Theoretische Lösungsmöglichkeiten der doppelten Kontingenz beim Elfmeterschuss
Die theoretische Darstellung beginnt mit der spieltheoretischen Analyse. Anschließend erfolgt die Darstellung der entsprechenden Ansätze von Parsons und Luhmann.
3.1 Elfmeterschüsse aus spieltheoretischer Sicht
Die Spieltheorie ist der Zweig der Theorie rationalen Handels, welcher sich mit SituationeI1
strategischer Interdependenz befasst. Die Annahmen, von denen die Theorie rationalen Handelns ausgeht, gelten daher auch für die Spieltheorie (und einige mehr dazu). Hier wird allerdings darauf verzichtet, alle diese Annahmen darzulegen. Stattdessen wird nur auf die für die:
vorgenommene Analyse entscheidenden Prämissen eingegangen, welche im Folgender
aufgeführt werden. 6 Die beiden Spieler haben eine stabile Präferenzordnung. Jedem mögli
chen Ausgang des Spiels ist für jeden Spieler ein bestimmter Nutzen zugeordnet, der die
Präferenzordnung des Spielers vollständig abbildet.? Für die hier vorgenommene Analyse
muss dieser Nutzen außerdem kardinal sein (vgl. Varian 1992). Beide Spieler kennen dil
Struktur des Spiels und insbesondere ihre eigenen Auszahlungen, sowie die Payoffs des an
deren Spielers. Zudem wissen beide Spieler, dass beide Spieler dies wissen, dass beide Spie
ler dies wissen, etc. Diese letzte Annahme wird als »common knowledge« bezeichnet. AU
. diese Bedingungen sind beim Elfmeterschuss erfüllt. Das Spiel hat zwei unterschiedlich
5) Die größere Herausforderung für den Schützen stellt dabei die Schussgenauigkeit dar. Selbst schlecl
te Amateurspieler können dem Ball die erforderliche Geschwindigkeit geben. Professionelle Spiel(
können den Ball beim Strafstoß mit einer Geschwindigkeit von mehr als 27 mls schießen. Dem TOJ
wart bleibt damit kaum eine halbe Sekunde, um den Ball zu erreichen, bevor er im Tor liegt (Joham
I Tschachner 2005, S. 26).
6) Eine aktuelle Einführung in die Theorie rationalen Verhaltens geben z.B. Diekmann I Voss (2004)
7) Dabei müssen diese Präferenzen nicht zwingend eigennutzorientiert sein. Die - hier selbstverstän(
liche - Annahme egoistischer Präferenzen macht allerdings die unabdingbare »common knov
ledge«-Annahme (siehe unten) plausibler.
400
Ausgänge: »Tor« oder »kein Tor«. Dies ist beiden Spielern bekannt. Ebenso bekannt ist der
kardinale Nutzen, den die beiden Ausgänge für beide Spieler haben und der genau ein Tor
(erzielt oder verhindert) beträgt. Und offensichtlich wissen auch beide Spieler, dass dies beide Spieler wissen, usw. usf.
Das Elfmeterschießen selbst ist, in spieltheoretischen Termini ausgedrückt, ein einfach gespieltes Nullsummenspiel mit vollständiger, aber nicht perfekter Information und simultanen
Zügen. Bereits 1928 hat von Neumann mit seiner »Theorie der Gesellschaftsspiele« alle formalen Grundlagen für die hier benötigte Analyse gelegt. 8 Grafisch wird das Spiel am einfachsten in strategischer Form dargestellt. In der Literatur wird es in Anlehnung an ein
Kinderspiel als »matching pennies« bezeichnet.
Abbildung 1: Auszahlungsmatrix des Elfmeterschusses, mit den beiden Handlungsoptionen
»Links« und »Rechts«
Torhüter
4U1
Spieler. 9 Keiner der beiden Spieler kann seinen erwarteten Nutzen erhöhen, indem er von
dieser Entscheidung abweicht, solange der andere Spieler ebenfalls nicht davon abweicht.
Die theoretische Analyse könnte damit abgeschlossen werden. Eine zu prüfende Hypothese würde dann lauten, dass beide Seiten sowohl vom Schützen als auch vom Torwart gleich
häufig gewählt werden. Für die empirische Überprüfung der Vorhersagen zum Spiel »matching pennies« wäre dies auch genügend. Aber beim Elfmeterschuss ergeben sich trotz seiner strukturellen Einfachheit doch einige zusätzliche Fragen: Beispielsweise besteht für den
Schützen auch die Möglichkeit in die Mitte des Tores zu schießen, weshalb der Torwart in
der Mitte des Tors stehen bleiben und einen derart geschossenen Ball mit Leichtigkeit abwehren könnte. Weiterhin ist bekannt, dass die Schützen ihren »starken« Fuß für den Schuss
bevorzugen, wenn sie, wie beim Strafstoß, frei wählen können. Außerdem kann ein Strafstoß
auch dann ins Tor gehen, wenn der Torwart in die richtige Ecke springt. Umgekehrt besteht
auch die Möglichkeit, dass der Schuss an die Torumrandung oder gänzlich daneben geht,
selbst dann, wenn der Torwart in die falsche Ecke gesprungen ist. Insgesamt erscheint daher
eine verfeinerte Analyse sinnvoll:
Fehlschüsse an die Torumrandung bzw. Treffer trotz richtiger Torwartentscheidung
Links
Rechts
Links
-1,1
1, -1
Rechts
1, -1
-1, 1
Schütze
Uie doppelte Kontingenz von tJjmeterschüssen
Die erste Zahl in jeder Zelle bezeichnet jeweils die Auszahlung des Schützen, die zweite
diejenige des Torhüters.
Die Lösung des Spiels ist nun diejenige Kombination der Strategien der beiden Spieler,
von denen keiner abweichen will, solange der jeweils andere seine Wahl beibehält. Eine
Strategie besteht dabei aus einer eindeutigen Anweisung, was an jedem Punkt, an den das
Spiel kommen kann, zu tun ist. Die möglichen Handlungen sind nach links oder rechts zu
schießen bzw. zu springen. Die Lösung ist ein gemischtes Nash-Gleichgewicht, d.h. eine
Strategienkombination, die darin besteht, dass beide Spieler zwischen den beiden
Handlungsmöglichkeiten »Links« und »Rechts« mischen. Die Strategien der beiden Spieler
geben ihnen vor, aus welcher Wahrscheinlichkeitsverteilung sie ihre Handlung zufallig wählen sollen. Die Randomisierung geschieht dabei unter Einberechnung des Nutzens, den der
Gegenspieler aus einer bestimmten Auszahlung bezieht. Die Wahrscheinlichkeiten für die
eigene Entscheidung werden dann genau so gewählt, dass sie die eigene Auszahlung maximieren, also so, dass die Erfolgswahrscheinlichkeit für den Torschuss bzw. die Abwehr am
größten ist. Dies geschieht unter der Annahme, dass der Gegner gleichfalls maximiert. D.h.
das aus dieser simultanen Maximierung resultierende Nash-Gleichgewicht ist (immer) ein
Gleichgewicht, sowohl in Erwartungen als auch in Handlungen (vgl. Varian 1992, S. 265).
Es lässt sich intuitiv erahnen, dass die entsprechenden Wahrscheinlichkeiten bei der ModelIierung des Elfmeterschusses als »matching pennies« genau 0,5 für beide Seiten betragen
(für eine formale Herleitung siehe verschiedene Lehrbücher, z.B. Dixit / Skeath 2004 für
eine Illustration mit Sport). Der erwartete Nutzen beträgt damit Null für jeden der beiden
8) Die Ausführungen von Neumanns sind als so genanntes Minimax-Theorem in die Literatur eingegangen. Weil in dem Aufsatz theoretisch eine breitere Perspektive eingenommen wird, wird hier vom allgemeineren Konzept des Nash-Gleichgewichts ausgegangen. Für Nullsummenspiele fallen allerdings
das Nash-Gleichgewicht und die Minimax-Lösung zusammen, so dass dieses Vorgehen keine theoretischen Auswirkungen hat.
Im Spiel »matching pennies« sind die Auszahlungen vorgegeben und werden mit Sicherheit
ausbezahlt, wenn eine bestimmte Strategienkombination auftritt. Beim Strafstoß ist dies
nicht zwingend der Fall. So gilt ein Schuss genau in eine der oberen Torecken allgemein als
unhaltbar. Allerdings ist bei dieser Entscheidung auch das Risiko recht groß, dass der Schuss
neben das Tor oder an die Torumrandung geht. Dies kann berücksichtigt werden, indem für
die deterministischen Auszahlungen [1, -1] aus dem Spiel »matching pennies« die
Trefferwahrscheinlichkeiten [Qi' Pj ] eingesetzt werden, wie sie in Abbildung 2 dargestellt
sind. (Die unterschiedlichen Wahrscheinlichkeiten für die linke und rechte Seite sowie die
Mitte bzw. deren Gegenwahrscheinlichkeiten ergeben sich aus weiteren Überlegungen (siehe
unten).) Die Wahrscheinlichkeiten entsprechen im Betrag gleichzeitig den erwarteten Payoffs kardinalen Nutzens von 1 (Tor).
Schuss in die Mitte
Schützen wählen in wenigen Fällen keine der beiden Seiten, sondern zielen in die Mitte.
Noch seltener kommt es vor, dass der Torwart in der Erwartung eines solchen Schusses in
der Mitte stehen bleibt. Im Gegensatz zu den Sprüngen auf die Seiten hat diese Strategie für
den Torwart den Vorteil, dass der Ball fast sicher abgewehrt werden kann, wenn er tatsächlich in die Mitte kommt. Ebenso sicher resultiert aber ein Tor, wenn dies nicht geschieht und
der Schuss auf eine der beiden Seiten geht. Da insbesondere die Schüsse in die Mitte empirisch nicht zu vernachlässigen sind, wird im Folgenden in Anlehnung an Chiappori et al.
(2002) der Elfmeterschuss mit dem Strategienraum {Links, Mitte, Rechts} modelliert.
Mit Palacios-Huerta (2003) ist es auch denkbar, den Strategienraum mit einem technischen Argument auf den Strategienraum {Links, Rechts} zu reduzieren. Dabei wird angenommen, dass Schüsse in die Mitte mit denselben Kosten verbunden sind wie diejenigen auf
die rechte Seite (vom Torwart aus gesehen für Rechtsfüßer und vice versa, vgl. unten), weil
sie mit derselben Schusstechnik ausgeführt werden. In diesem Fall werden die Schüsse in die
Mitte zur rechten Seite gezählt. Bei der empirischen Analyse wird in einzelnen Fällen auf
dieses Argument zurückgegriffen und es werden nur zwei Schussrichtungen betrachtet, wenn
die Analyse ansonsten nicht sinnvoll durchführ- oder darstellbar ist.
9) Im Gegensatz zu dieser Gleichgewichtsauszahlung bedingt die Definition eines Nullsummenspiels
nur, dass die erwartete Auszahlung des gesamten Spiels Null beträgt.
402
Es muss betont werden, dass es sich bei der Frage, ob die Elfmetersituation mit zwei oder
drei Strategien modelliert werden soll, um ein rein empirisches Problem handelt.
Spieltheoretisch betrachtet ist nur entscheidend, dass die Spieler ihre Schuss- bzw. Sprungrichtungen derart mischen, dass für jeden Punkt des Tores die gleiche Treffer- bzw.
Abwehrwahrscheinlichkeit besteht. Wenn entsprechend präzise Daten zur Verfügung stehen
würden, könnte die empirische Analyse deshalb auch auf einen noch größeren Strategienraum ausgedehnt werden. Für die hier verwendeten Daten ist dies jedoch nicht sinnvoll.
mit »rechts« bezeichnet. Für mit dem linken Fuß schießende Schützen ist die natürliche Seite
dagegen vom Torwart aus gesehen links. Diese wird dann ebenfalls mit »rechts« (weil natürliche Seite) bezeichnet (und vice versa). Dies ermöglicht es, alle Elfmetersituationen für
Rechts- und Linksfüßer sowie für die Torhüter in einer einheitlichen Notation zu analysieren. Damit stellt sich das Spiel »Elfmeterschuss« wie folgt dar (vgl. Abb. 2):
Abbildung 2: Matrixdarstellung des Elfmeterschusses, mit den Treffer- bzw. Abwehrwahrscheinlichkeitenfür die Handlungsalternativen »Links«, »Mitte« und »Rechts«
Gleichheit des Spiels in jeder Spielsituation undfür beide Spieler bzw. Schussfüße
Es ist denkbar, dass die Treffer- bzw. Abwehrwahrscheinlichkeit nicht bei jedem Strafstoß
und bei jedem Spieler bzw. jeder Spielerkombination gleich ist. Möglicherweise sind z.B.
die Schützen mehr unter Druck, wenn ihr Team im Rückstand liegt, wenn das Spiel fast zu
Ende ist, so dass ein Tor wahrscheinlich das letzte im Spiel sein würde, oder wenn der
Schütze ein Heimspiel hat. Weiterhin ist bekannt, dass die Schützen jeweils einen »starken«
Fuß haben, mit dem sie besser schießen können als mit dem »schwachen« Fuß. Rechtsfüßer
schießen aus anatomischen Gründen einfacher in die linke Ecke und Linksfüßer umgekehrt
in die rechte Ecke. Auch hier ist denkbar, dass Linksfüßer z.B. eine höhere
Trefferwahrscheinlichkeit haben als Rechtsfüßer, weil die Torhüter z.B. weniger Übung darin haben, die selteneren Schüsse von Linksfüßern abzuwehren.
Allgemeiner ausgedrückt muss untersucht werden, ob die Kosten der beiden Spieler bei jedem Elfmeter in jeder Spielsituation gleich sind. IO Für das Spiel »matching pennies« ist dies
tatsächlich so. Der kardinale Nettonutzen ist im Betrag genau 1. Sollte dies beim Elfmeterschuss nicht zutreffen, so würden die Auszahlungen bzw. Trefferwahrscheinlichkeiten für
die Wahl der drei Handlungsoptionen dadurch verändert werden und damit auch die optimale Strategie.
Dies bedeutet gleichzeitig, dass sich, je nachdem welche Annahmen über das tatsächlich
gespielte Spiel zu Grunde gelegt werden, auch die resultierende Hypothesenmenge ändert.
Aus Übersichtlichkeitsgründen wird diese Analyse hier nicht vollständig vorgeführt (siehe
dafür Chiappori et al. 2002). Vielmehr wird hier ein Resultat der empirischen Analyse schon
vorgezogen und nur diejenige Hypothesenmenge betrachtet, die zu den tatsächlich beobachteten empirischen Gegebenheiten passt. Dadurch wird nicht der Anwendungsbereich der
spieltheoretischen Überlegungen eingeschränkt, sondern nur der für diese Anwendung empirisch testbare Bereich. Die theoretischen Überlegungen gelten unabhängig davon für jeden
einzelnen Elfmeterschuss. Diese Einschränkungen sind allerdings nicht gravierend, da die
Spielsituation des Elfmeters im verwendeten Datensatz in jeder Minute des Spiels und bei jedem Spielstand gleich ist. Für die Torhüter unterscheidet sich das Spiel nicht, egal ob sie einem Rechts- oder einem Linksfüßer gegenüber stehen. Allerdings unterscheidet sich die
Trefferwahrscheinlichkeit für den Schützen in Abhängigkeit von seinem Schussfuß. Tatsächlich schießen Rechtsfüßer, wie vermutet, leichter in die linke Ecke und für Linksfüßer verhält es sich umgekehrt. In der Folge wird diese Seite als »natürliche« Seite bezeichnet (also
bei Rechtsfüßern die linke und bei Linksfüßem die rechte). Da die Torhüter den Schussfuß
der Schützen und demzufolge auch die natürliche Ecke kennen 11, kann jeder Strafstoß dadurch beschrieben werden, ob der Schütze in die natürliche Ecke schießt und der Torwart in
die natürliche Ecke springt. In der Folge wird bei rechts schießenden Schützen die vom Torwart aus gesehen rechte Seite als natürliche Seite für Schützen und Torwart betrachtet und
10) Für den Nutzen gibt es hierzu keine Zweifel. Dieser ist im Betrag für beide Spieler genau gleich groß.
11) Der starke bzw. Schussfuß ist einfach am Anlauf des Schützen erkennbar (von links, um mit rechts
zu schießen und umgekehrt).
403
Torhüter
I
Schütze
Links
Mitte
Rechts
Links
PL, I-P L
QL,I-QL
QL,I-QL
Mitte
M,l-M
0, I
M,I-M
Rechts
QR,I-QR
QR,I-QR
PR' I-PR
Der erste Ausdruck in jeder Zelle bezeichnet jeweils die Wahrscheinlichkeit, dass der
Strafstoß in einem Tor resultiert (die erwartete Auszahlung für den Schützen). Entsprechend
gibt die Gegenwahrscheinlichkeit die erwartete Auszahlung für den Torwart an, dass kein
Tor resultiert.
Für die Reihenfolge der Torerfolgswahrscheinlichkeiten ergeben sich dadurch die aus den
obigen Ausführungen unmittelbar einsichtigen Annahmen:
1. QR> PL
2. QR>M
3. QR ~ QL
4. QL -PL
und
und
und
QL>PR
QL>M
~
QR-PR
PR~PL
Für den Schützen heißt dies: Die Wahrscheinlichkeit des Torerfolgs ist höher, wenn der
Torwart in die falsche Ecke springt, als wenn dieser die richtige Ecke wählt (Annahme 1).
Ein solcher Schuss in die entgegensetzte Ecke des Torwarts hat dabei eine höhere
Trefferwahrscheinlichkeit, als wenn der Schütze in die Mitte schießt (Annahme 2). Wenn der
Torwart in die falsche Ecke springt, ist die Chance, ein Tor zu erzielen, bei einem Schuss auf
die natürliche Seite mindestens so groß wie oder größer als bei einem Schuss auf die unnatürliche Seite (Annahme 3). Das Risiko, dass der Torwart den Ball hält, wenn er sich richtig
entscheidet, ist auf der natürlichen Seite kleiner als auf der unnatürlichen (Annahme 4). Für
den Torwart gelten dieselben Annahmen jeweils umgekehrt. Auch hier wird davon ausgegangen, dass diese Annahmen »common knowledge« für beide Spieler sind (vgl. oben).
Aus diesen Annahmen lassen sich eine Reihe von testbaren Hypothesen ableiten (für die
Herleitung siehe Chiappori et al. 2002).12
12) Die hier dargestellten Hypothesen beziehen sich allesamt auf das Aggregat der Schützen und der Torhüter. Aus soziologischer Sicht stellen diese den zentralen Prüfstein für die hier verfolgte Anwendung
der Spieltheorie dar. D.h., dass die Spieltheorie hier als eine Theorie betrachtet wird, die mittels verallgemeinernden Annahmen über individuelles Verhalten empirisch prüfbare Aussagen zu Zuständen
auf der sozialen Aggregatebene macht (vgl. z.B. Coleman 1986; 1990).
Allerdings können mittels der vorgeführten spieltheoretischen Analyse auch Hypothesen formuliert
werden, die sich auf individuelle Spieler beziehen, die mehrere Elfmeter geschossen haben bzw. dabei im Tor standen. Auf die Darstellung dieser Hypothesen wird hier verzichtet, da sie für die soziologische Untersuchung des Gegenstands nicht entscheidend sind. Eine entsprechende Analyse findet
sich in Berger / Hammer (2007).
404
Roger Berger und Rupert Hanlmer
H1: Die Randomisiemngen durch den Schützen und den Torwart sind unabhängig voneinander.
H2: Der Schütze hat eine höhere Wahrscheinlichkeit, in die Mitte zu schießen, als der Torwart, dort stehen zu bleiben.
H3a: Die Wahrscheinlichkeit des Torerfolgs ist gleich groß, egal ob der Schütze nach
»Links«, »Rechts« oder in die »Mitte« schießt.
H3b: Die Wahrscheinlichkeit ein Tor zu verhindern ist gleich groß, egal ob der Torwart
nach »Links« oder »Rechts« springt oder in der »Mitte« stehen bleibt.
H4a: Der Schütze hat eine größere Wahrscheinlichkeit, seine natürliche Seite (»Rechts«)
zu wählen.
H4b: Der Torwart hat eine größere Wahrscheinlichkeit, die natürliche Seite des Schützen
(»Rechts«) zu wählen.
H5: Der Torwart hat eine größere Wahrscheinlichkeit, die natürliche Seite des Schützen
(»Rechts«) zu wählen, als dass der Schütze dorthin schießt.
H6: Die Kombination (»Rechts«, »Rechts«) ist wahrscheinlicher als die beiden Kombination (»Links«, »Rechts«) und (»Rechts«, »Links") und diese wiederum sind wahrscheinlicher als die Kombination (»Links«, »Links«).
Es ist zu erkennen, dass jeder der heiden Spieler seine Entscheidung jeweils an den Auszahlungen des Gegners orientiert. Es wird so gewählt, dass beide Spieler indifferent zwischen ihren reinen Strategien sind und sich nur noch an den Wahrscheinlichkeitsverteilungen
für die Aktionen des Gegners orientieren, wodurch sich ein gemischtes Gleichgewicht ergibt.
So liegt der Grund dafür, dass der Torwart seltener die Mitte wählt, als der Schütze dorthin
schießt, in den Kosten eines Schusses in die Mitte für den Schützen. Wählt der Torwart dann
nämlich auch die Mitte, so ist die Trefferwahrscheinlichkeit sehr gering (vgl. Abb. 2). Für
den Torwart sind die erwarteten Kosten eines Schusses in die Mitte dagegen immerhin geringer als diejenigen eines Schusses in die gegenüberliegende Ecke (vgl. Annahme 2). Da
sich der Schütze an diesen Kosten für den Torwart orientiert, ist die Gleichgewichtswahrscheinlichkeit für Schüsse in die Mitte für den Schützen höher, denn erwartet »teure« Aktionen werden selten gewählt, erwartet »billige« dagegen häufig.
Wäre dies nicht der Fall, so wären die Spieler füreinander berechenbar und sie könnten
sich jeweils verbessern, wenn sie ihre Entscheidung in Richtung der Hypothese verschieben
würden. Dies kann veranschaulicht werden, wenn man sich die Elfmetersituation für einen
einarmigen Torwart vorstellt. Würde dieser gehandicapte Spieler gleich häufig nach links
und rechts springen, würde der Schütze ausschließlich auf die Seite mit dem fehlenden Arm
schießen, weil die Trefferwahrscheinlichkeit dort offensichtlich höher ist. Deshalb würde
sich der Torwart an dieser Auszahlung orientieren und entsprechend häufiger auf die Seite
mit dem fehlenden Ann springen, bis die Erfolgswahrscheinlichkeit für den Schützen auf
beide Seiten gleich hoch wäre.
Für die empirische Überprüfung der Hypothesen muss beachtet werden, dass sich dabei jeweils ein statistisches Aggregationsproblem ergibt. Erstens können Häufigkeiten und Wahrscheinlichkeiten nicht bei einzelnen Elfmetersituationen beobachtet werden, sondern nur im
Aggregat aller Spieler und Situationen. Zweitens bildet die empirisch gemessene Häufigkeit
nur dann die theoretisch erwartete Wahrscheinlichkeit ab, wenn alle Spieler und
Elfmetersituationen homogen sind, wenn also alle Spieler immer da~selbe Spiel spielen.
Sollte dagegen in der Population aller Elfmetersituationen Heterogenität existieren, wäre die
Wahrscheinlichkeitsmessung verzerrt. Nun können zumindest einige mögliche Heterogenitätsvermutungen ausgeschlossen werden. Es besteht Gleichheit der Elfmetersituation unab-
hängig vom Spielstand, Spielzeit, vom Torwart und vom Schussfuß des Spielers.
Heterogenität (die theoretisch schon einbezogen wurde) besteht allerdings bei der Schussrichtung des Spielers in Abhängigkeit vom Schussfuß. Die Zahl der potentiellen Heterogenitätsquellen ist jedoch größer und potentiell unbekannt. Zwar erlaubt gerade die hoch
standardisierte Elfmetersituation im Verbund mit einigen Fußballkenntnissen die plausible
Annahme, dass für die zentralen Quellen von Heterogenität bereits kontrolliert wird. Mit Sicherheit festgestellt werden kann dies jedoch nicht. Dies liegt schon daran, dass zu einer statistischen Kontrolle nur die verfügbaren Variablen herangezogen werden können. Begegnet
werden kann der Problematik allerdings, indem die Hypothesen als Häufigkeits- statt als
Wahrscheinlichkeitsaussagen formuliert werden. Damit wird zwar ihr Informationsgehalt
verringert, jedoch sind sie robuster und sollten auch dann noch zutreffen, wenn in den Daten
selektive Verzerrungen auftauchen (vgl. Chiappori et al. 2002, S. 1143f).
3.2 Parsans und die doppelte Kontingenz beim Elfmeterschuss
Von der Spieltheorie beeinflusst war Parsons, als er das Konzept der doppelten Kontingenz
in die Soziologie einführte (vgl. Ganssmann 2006, S. 152). Dies ist erkennbar an seiner
entsprechenden Definition, deren Grundelemente mit derjenigen der Spieltheorie vereinbar
sind, nämlich, dass die Akteure »ego« und »alter« (Parsons et al. 2001, S. 16) »among available alternatives« (ebd.) eine auswählen, nachdem sie komplementäre »expectations« (ebd.)
gebildet haben. Die Auszahlungen (»gratifications« (ebd.» von Ego hängen dabei auch von
der Auswahl von Alter ab und umgekehrt. Die Auflösung der doppelten Kontingenz hat dann
die folgenden Eigenschaften. »[ ... ] since the outcome of ego's action (e.g. success in the attainment of a goal) is contingent on alters reaction to what ego does, ego becomes oriented
not only to alter's probable overt behavior but also to what ego interprets to be alter's expectations relative to ego's behavior, since ego expects that alter's expectations will influence
alter's behavior.« (Parsons I Shils 1951, S. 105, Hervorhebungen im Original). Weiter wird
festgestellt, dass diese Erwartungen reziprok oder komplementär sein müssen. Es ist schwierig, darin nicht die Umschreibung eines Gleichgewichts in Erwartungen und Handlungen zu
sehen, dessen prinzipielle Existenz Nash (1950) für alle real zu erwartenden Situationen strategischer Interaktionen bewiesen hat (vgl. oben).
Allerdings gibt Parsons die spieltheoretische Annahme auf, dass die Akteure jeweils
Spielausgänge mit hohem Nutzen solchen mit niedrigem Nutzen vorziehen. Stattdessen geht
er davon aus, dass die doppelte Kontingenz erst durch geteilte und stabile kulturelle Muster
(Bedeutungen, Werte und Normen) aufgelöst werden kann. Damit kann er auch auf die Annahme des »common knowledge« verzichten. Ego braucht keine Erwartungen über Alter zu
bilden. Er orientiert sich einfach an dem geteilten kulturellen Muster. Falls dieses wirklich
von beiden Akteuren geteilt wird (und nur dann kann die doppelte Kontingenz aufgelöst
werden), wird sich auch Alter daran orientieren, so dass die wechselseitigen Erwartungen erfüllt werden. Das eigentliche Problem eines Akteurs im Sinne von Parsons besteht dann darin, eine Erwartung darüber zu bilden, ob der andere Akteur das kulturelle Muster tatsächlich
stabil mit ihm teilt. In den Medienberichten zum Elfmeterschießen mit dem deutschen Torwart Lehmann bei der WM 2006 wurde häufig davon ausgegangen, dass dies tatsächlich
möglich ist. Lehmann wurde nämlich vom Trainerstab auf einem Zettel mitgeteilt, dass z.B.
der Schütze Ayala rechts schießen werde. Tatsächlich tat er dies auch und Lehmann konnte
den Ball dort abwehren. 13 Eine tiefere Betrachtung zeigt jedoch, dass ein solches Muster weder geteilt noch stabil sein kann. Denn wenn Ayala tatsächlich wüsste, dass Lehmann seine
Schussrichtung »rechts« kennen würde, und Lehmann wüsste dies auch, usw. usf. (was das
13) Lehmann wehrte noch einen weiteren Strafstoß ab und Deutschland gewann das Viertelfinale gegen
Argentinien mit 4:2. Dies bescherte dem Torwart und seinem ominösen Zettel einige Medienpräsenz.
406
Muster zu einem geteilten machen würde), würde Ayala nicht dorthin schießen. Oder er würde gerade diese Richtung wählen, weil Lehmann in Antizipation dessen die Seite gewechselt
hat, etc. Die doppelte Kontingenz kehrt damit auf einer zweiten Ebene zurück und destabilisiert jedes evtl. vorhandene Verhaltensmuster. 14 Obschon diese Frage offensichtlich Analogien mit der hier geteilten aufweist, soll sie hier nicht weiter analysiert werden. Denn das
Beispiel des Elfmeterschusses zeigt schon, dass der Ansatz durch diesen Wechsel der Handlungstheorie an Reichweite verliert.
Das Problem des Parsons'schen Ansatzes wird auch deutlich, wenn man sich vergegenwärtigt, welche Art von doppelter Kontingenz dadurch in idealer Weise gelöst werden kann.
Dies sind Koordinationsprobleme, bei denen die Interessen der Beteiligten vollständig deckungsgleich sind. 15 Diese weisen - in spieltheoretischen Termini ausgedrückt - mehrere
gleichwertige Gleichgewichte auf. Die Auswahl eines Gleichgewichtspunktes ist dann tatsächlich durch kulturelle l\1uster oder »conventions« (Parsons et al. 2001, S. 16) gewährleistet (wie das Beispiel des Links- oder Rechtsverkehrs anschaulich zeigt). Sollte in einer bestimmten Situation jedoch keine Konvention bestehen, so bedingt Parsons Modell
Aushandlungsprozesse, in denen es zu einer »reaction« (ebd., Hervorhebung RB I RH) von
Alter auf Egos Aktion kommt. D.h. dieser Aushandlungsprozess läuft zeitlich gestaffelt im
Schema »Aktion, Reaktion, Reaktion auf die Reaktion, etc.« ab.
Damit ergeben sich drei Gründe, wieso Parsons Ansatz in der Elfmetersituation nicht anwendbar ist. Erstens handelt es sich hierbei ohne Zweifel um eine Situation, in der die Akteure vollständig eigennutzorientiert sind. Es wäre unsinnig diese Annahme aufzuheben.
Selbst wenn die Akteure diese Präferenzen nicht hätten, würde sie ihnen durch die Spielstruktur aufgezwungen. Denn es handelt sich beim Elfmeterschuss um ein Nullsummenspiel,
in dem der Gewinn von Ego genau der Verlust von Alter ist und umgekehrt. Solange ein
Spieler also nicht vollständig altruistisch ist, muss er egoistisch sein. Der Ansatz von Parsons
ist damit (mindestens) auf Nicht-Nullsummen-Interaktionen beschränkt, in denen sich
Kooperationsgewinne erzielen lassen. 16
Zweitens ist die Suche nach geteilten kulturellen Mustern o.Ä. hier sinnlos, weil beide
Spieler sich gerade nicht verstehen und auf ein entsprechendes Muster zurückgreifen wollen.
Jede solche geteilte Regelmäßigkeit (falls sie tatsächlich existieren sollte) wird von beiden
Spielern sofort unterlaufen werden, um den Gegner zu täuschen und Instabilität in der Interaktion zu erzeugen und damit die von Parsons als notwendig erachtete Bedingung für die
Auflösung der doppelten Kontingenz zu untergraben (Parsons et al. 2001, S. 16). Nur ein
einziges Muster kann von den beiden Spielern nicht zerstört werden, ohne sich selbst zu
schaden und dies ist dasjenige, das sich durch die gemischten Strategien im Gleichgewicht
ergibt. Man könnte nun einwenden, dass das gemeinsame kulturelle Muster hier z.B. die Ak14) Der »Zettel« selbst belegt diese These übrigens auch empirisch. Von den vier argentinischen SchUtzen (der letzte trat nicht an, da die Entscheidung schon gefallen war) waren nur zwei darauf aufgeführt. Beide schossen auch wirklich in die vorhergesagte Richtung. Einen Schuss davon konnte
Lehmann parieren. Eine Bilanz, die auch ohne Zettel durchaus im Bereich des Wahrscheinlichen
liegt. Lehmann bestätigte dies auch indirekt, indem er später angab, er habe die Informationen sowieso nicht entziffern konnte, weil die Schrift verschmiert gewesen sei.
15) Das einfachste Beispiel für eine solche Koordinationssituation ist die doppelte Kontingenz, die zwei
kreuzende Autofahrer zu lösen haben: nämlich, ob beide links oder rechts fahren. Dies stellt die Fahrer normalerweise vor keinerlei Probleme, da eines der beiden (reinen) Gleichgewichte [links, links]
oder [rechts, rechts] eindeutig durch die jeweilige Straßenverkehrsordnung vorgegeben ist und keiner
der Fahrer einen Anreiz hat, von dieser Norm abzuweichen.
16) Dazu gehören auch Interaktionssituationen, in denen sich die Interessen der Beteiligten nur partiell
überlappen, wie etwa das bekannte Gefangenendilemma.
4U7
zeptanz der Spielregeln sei. Dies ist aus zwei Gründen falsch. Zum einen ist das Explanandum hier die Elfmetersituation bzw. die empirische Verteilung der daraus folgenden Handlungen und nicht z.B. die Einwilligung in Spiel und Regeln o.Ä. Zum anderen besteht
Fußball- und jedes andere (sportliche) Spiel- (auch) aus einer Menge von gleich oder ähnlich strukturierten Nullsummenspielen, die theoretisch analog gelöst werden können. 17 Das
Regelwerk des Elfmeters macht diese Lösung nur für die empirische Analyse einfacher zugänglich als andere Spielsituationen, die keiner Spielregel unterworfen sind. Dies zeigt z.B.
die Analyse des Schusses aufs Tor aus dem Halbfeld (vgl. unten, Moschini 2004). Damit ist
gezeigt, dass die bei der Elfmetersituation resultierenden Regelmäßigkeiten nicht auf geteilten kulturellen Mustern beruhen.
Da nun aber kein kulturell geteiltes Deutungsmuster der Elfmetersituation zwischen den
beiden Spielern vorliegen kann, das über die spieltheoretisch erklärbaren Regelmäßigkeiten
hinausgeht, müsste dieses drittens gemäß Parsons Ansatz in einem zeitlich gestaffelten Prozess ausgehandelt werden. Dies ist nun allerdings empirisch offensichtlich nicht Fall, da
beim Elfmeterschuss simultane Aktionen vorliegen. Entsprechende Prozesse müssten dann
vor dem Strafstoß stattfinden und sind schon deshalb unmöglich, weil die beiden Kontrahenten bis kurz vor der Interaktion nicht wissen können, dass sie aufeinandertreffen.
Zusammenfassend kann deshalb festgehalten werden, dass dem Ansatz von Parsons zwar
verschiedene Formen der doppelten Kontingenz theoretisch zugänglich sind. Die Menge der
doppelten Kontingenzen, die nach Parsons lösbar sind, umschließt aber nur eine Teilmenge
der spieltheoretisch fassbaren. Weil die Situation des Elfmeterschusses nicht dazu gehört, erübrigt sich eine entsprechende empirische Analyse.
3.3 Luhmann und die doppelte Kontingenz beim Elfmeterschuss
Ein ähnliches Bild zeigt sich, wenn man die Ausführungen Luhmanns zur doppelten Kontingenz betrachtet. Luhmann lässt die Eigennutzannahme ebenfalls nicht zu. Im Gegensatz zu
Parsons ersetzt er sie aber nicht durch eine anders geartete Handlungstheorie (bei Parsons:
Orientierung an kulturellen Mustern), sondern lässt die damit verknüpften Fragen weitgehend offen. Damit kann mit Luhmann vorerst nichts empirisch Gehaltvolles zur Strafstoßsituation gesagt werden. Konsequenterweise stellt er deshalb auch fest, dass in Situationen
doppelter Kontingenz apriori keine Handlungen stattfinden, bzw. dass alle Ansätze, die auf
Handlung abstellen, hier nicht greifen können (vgl. z.B. Ganssmann 2006, S. 153; Vanderstraeten 2002, S. 85). Luhmann geht sogar noch einen Schritt weiter und behauptet, dass sogar schon »[d]er Versuch, [in einer Situation doppelter Kontingenz] den anderen zu berechnen, [ ] zwangsläufig scheitern [müsse]« (Luhmann 1988, S. 156). Es sind also nicht nur
keine Handlungen denkbar, sondern auch die Bildung von Erwartungen ist unmöglich. 18 Geschweige denn können Vorhersagen über zu erwartende soziale Muster oder Regelmäßigkeiten getroffen werden. Diese Ansicht ist nun spätestens seit Nash (1950) eindeutig widerlegt,
und oben wird eine entsprechende konkrete Umsetzung vorgeführt. Zudem ist offenbar auch
noch kein Elfmeterschuss daran gescheitert, dass sich der Schütze nicht für eine Schussrichtung entscheiden konnte.
Deshalb wird nun die einschlägige Lösung von Luhmann betrachtet. Er schlägt vor auf das
Konzept von Kommunikation zurückzugreifen. Diese kann hier etwa aus der Körpersprache
17) Der probabilistische Charakter der entsprechenden Lösungen macht ja den Reiz dieser Spiele aus.
Denn ob schon im Durchschnitt klar ist, wie eine entsprechende Situation ausgeht (z.B. landen etwa
75% aller Elfmeterschüsse im Tor), muss dies im Einzelfall durchaus zutreffen.
18) Vgl. ähnlich auch Vanderstraeten (2002, S. 85): «The participants are opaque and incalculable to one
another«.
408
des Schützen bei der Vorbereitung des Strafstoßes, beim Anlauf oder aus Finten des Torwarts u.Ä. bestehen. 19 Allerdings wird diese Kommunikation - genauso wie die geteilten
Deutungsmuster in Parsons Ansatz - ausschließlich darauf ausgerichtet sein, den Gegner zu
täuschen. Das Antäuschen einer Schussrichtung beim Anlauf kann dann bedeuten, dass der
Schütze dorthin schießt, oder eben gerade nicht. Die doppelte Kontingenz setzt sich also auf
der Ebene von Kommunikation fort und wird dadurch nicht gelöst. Auch eine Auflösung des
Zirkels der wechselseitigen Erwartungen durch eine Sequenzialisierung der Erwartungen
und den daraus folgenden Aktionen ist nicht möglich. Wie oben dargestellt wird der Torwart
sich nie für eine Aktion entscheiden, bevor der Schütze dies nicht tut, und umgekehrt. Denn
eine entsprechende Aktion würde dem Gegner tatsächlich eindeutig und glaubwürdig kommunizieren, wie die doppelte Kontingenz zu seinen Gunsten gelöst werden kann.
Es kann auch angeführt werden, dass das Zustandekommen einer Elfmetersituation an sich
schon die Folge von Kommunikation und anschließender Systembildung ist. Der Strafstoß
ist dann schon eine strukturierte doppelte Kontingenz und weist nicht mehr die prinzipielle
Offenheit einer reinen doppelten Kontingenz auf. Auch dieser Einwand führt allerdings nicht
weiter. Denn erstens ist, wie oben schon aufgeführt, auch hier das Explanandum das Verhaltensmuster beim Strafstoß und nicht z.B. dessen konstituierende Regeln. Unterstellt man
zweitens dennoch, dass die doppelte Kontingenz der Elfmetersituation durch vorgängige
Systembildung bereits strukturiert ist, so müsste deren Auflösung dadurch gegenüber einer
völlig offenen Situation sogar erleichtert sein. Dies ist jedoch nicht der Fall. Vielmehr kreiert
die Elfmeterregel ja erst die doppelte Kontingenz. Und offenbar müssen die Spieler beim
Elfmeter genauso den Zirkel von wechselseitigen Erwartungen lösen wie die Akteure in unstrukturierten Situationen, wie sie z.B. unten in der Diskussion beschrieben werden. Definitorische Umdeutungen geben der Analyse hier also keinen empirischen Gehalt.
Luhmann gibt jedoch einen Hinweis, wie dies geschehen kann. Falls nämlich ein (oder
wie im hier untersuchten Fall: mehrere) Beobachter feststellt, dass er bei einem Strafstoß auf
zwei psychische Systeme zuschreibbare Handlungen beobachtet (vgl. Vanderstraeten 2002,
S. 85), ergibt sich daraus, dass das System in »Gang gesetzt« wird und sich die Partner an
der Frage orientieren, »ob eine Handlung ihm nützen oder schaden wird« (Luhmann 1988, S.
160, Hervorhebung im Original). Damit landet man auch mit Luhmann letztlich bei der
Spieltheorie.
Man kann sich deshalb fragen, ob Luhmanns Ansatz allgemeiner ist und die spieltheoretische Analyse als eine Art Spezialfall enthält. 20 Diese Frage ist zu verneinen, wie eine weitere Betrachtung zeigt. Erstens hat Luhmann für die in der Spieltheorie übliche Annahme der
Eigennutzorientierung wenig übrig und weist sie als viel zu »anspruchsvoll« ab, »als dass
man sie allgemein voraussetzen könnte« (Luhmann 1988, S. 160). Abgesehen davon, dass
diese Vermutung empirisch belegt und nicht apriori behauptet werden sollte, erweist sich
die Annahme eigennützigen Verhaltens gerade in der Elfmetersituation als die einzig vernünftige Prämisse. Dennoch könnte man davon ausgehen, dass Luhmann die hier untersuchte Form der doppelten Kontingenz zwar etwas stiefmütterlich behandelt, die spieltheoretische Lösung aber durchaus gelten lässt. Dies ist jedoch falsch, denn Luhmann lehnt die
Idee, dass es in einem System von wechselseitig aufeinander bezogenen Erwartungen und
daraus resultierenden Handlungen ein Gleichgewicht geben kann - also die Konzeption des
19) Allerdings werden solchen Aktionen durch die Regeln Grenzen gesetzt. Z.B. darf der Torhüter die
Torlinie während der Ausführung des Elfmeters nicht verlassen und der Schütze darf den Anlauf
nicht unterbrechen.
20) Immerhin hat Luhmann die Entwicklung der Spieltheorie durchaus zur Kenntnis genommen (vgl.
Luhmann 1973).
409
Nash-Gleichgewichts - explizit ab, wenn er behauptet: »Dies [die Antizipation von Alter
durch Ego und umgekehrt, RB / RH] kann nicht in Form von verleinerter Voraussicht geschehen, weil dies das Problem nur neu ins Spiel bringen würde« (Luhmann 1988, S. 171;
ähnlich z.B. Vanderstraeten 2002, S. 86). Damit geht Luhmann einen Schritt weiter als Parsons. Bei diesem ist noch denkbar, spieltheoretische Überlegungen in das Theoriegebäude
einzubeziehen. Diesem Weg verschließt sich Luhmann prinzipiell. Und dies nicht nur für das
betrachtete Spiel, sondern - wenn die obige Aussage ernst genommen wird - für sämtliche
spieltheoretische Analysen. Damit, und weil die Kommunikationslösung hier nicht denkbar
ist, ergeben sich auch aus dem Ansatz von Luhmann keine empirisch gehaltvollen Aussagen
zur Lösung der doppelten Kontingenz des Elfmeterschusses.
Daher beschränkt sich die nachfolgende empirische Analyse auf die Analyse spieltheoretisch begründeter Hypothesen. Zuvor wird der einschlägige Forschungsstand zusammengefasst.
4. Bisherige Evidenz zu gemischten Gleichgewichten
Die empirische Forschung zum Verhalten von Menschen in Nullsummenspielsituationen ist
überschaubar. Große Teile der einschlägigen Untersuchungen fanden dabei im Labor statt,
und nur wenige unter realen Bedingungen.
4.1 Tests aufgemischte Gleichgewichtsentscheidungen in Laboruntersuchungen
Es zeigt sich, dass in verschiedenen strategischen Entscheidungssituationen mit gemischten
Gleichgewichten diese tendenziell erreicht werden. Dies gilt sowohl für Situationen mit der
hier betrachteten »matching pennies«-Struktur (vgl. Mookehrjee / Sopher 1994), als auch fUr
andere Nullsummenspiele (vgl. Brown / Rosenthal1990; O'NeillI987; 1991; Rapoport / Boebe11992; Rosenthai et al. 2003; Shachat 2000; 2002) und allgemeine Spiele mit gemischten
Gleich~ewichten (vgl. Bloomfield 1994; Erev / Roth 1998; McKelvey et al. 2000; Ochs
1995). 1 Allerdings zeigen sich häufig Lerneffekte derart, dass in wiederholten Spielen die
vorhergesagten Gleichgewichte eher erreicht werden als mit unerlahrenen Akteuren bzw. in
einfach gespielten Spielen.
4.2 Tests aufgemischte Gleichgewichte anhand von realen Interaktionen im Sport
Bisher existieren nur wenige Untersuchungen zu gemischten Gleichgewichten in realen
Interaktionen. Diese beziehen sich alle auf Interaktionen im Sport, wahrscheinlich aus den
beschriebenen methodischen Gründen.
Fußball
Zwei Analysen befassen sich mit der hier untersuchten Elfmetersituation. Chiappori et al.
(2002) untersuchen alle 459 Strafstöße der ersten französischen (Spielzeiten 1997-1999) und
italienischen (Spielzeiten 1997-2000) Liga. Die Autoren können alle Hypothesen bestätigen.
Sie verwenden dabei die Modellierung mit den drei Strategien {Links, Mitte, Rechts}.
Palacios-Huerta (2003) verwendet einen umfangreicheren Datensatz, der 1417 Strafstöße
aus den Profiligen Spaniens, Englands und Italiens von 1995 bis 2002 umfasst. Wiederum
können alle Hypothesen vollständig bestätigt werden. Allerdings modelliert der Autor nur
21) Neben dem hier im Fokus stehenden Nullsummenspiel »matching pennies« existieren auch verschiedene andere Spiele. die ebenfalls nur ein Gleichgewicht in gemischten Strategien aufweisen, aber keine Nullsummenspiele sind und / oder mehr als zwei Entscheidungsmöglichkeiten haben (vgl. z.B.
Rasmusen 1998, S. 67ff).
410
den Strategienraum {Links, Rechts}. Dafür untersucht er die Elfmeterentscheidung auch
noch bei Elfmeterschießen in Turnieren, in denen der Torwart mindest fünf aufeinander folgende Entscheidungen treffen muss. Er kommt dabei zu der Folgerung, dass sich die Torhüter auch in dieser Situation rational verhalten.
Moschini (2004) analysiert eine andere Spielsituation im Fußball, nämlich den Schuss
aufs Tor aus dem rechten bzw. linken Halbfeld. Hierbei müssen sich die Schützen entscheiden, ob sie in die nähere Torecke (nach rechts von rechts und umgekehrt) oder in die entferntere (nach links von rechts und umgekehrt) schießen. Die Torhüter müssen sich entscheiden,
ob sie eben diese nahe oder die entfernte Ecke besonders abdecken wollen. Die Situation ist
insofern interessant, als die beiden Entscheidungen offenbar nicht die gleichen Erfolgschancen versprechen. Ein Schuss in die nahe Ecke ist einfacher zu bewerkstelligen als einer in die
entferntere Ecke. Für den Torwart ist umgekehrt ein Schuss in die entfernte Ecke einfacher
abzuwehren. Weil sich die Spieler aber wechselseitig an ihren erwarteten Auszahlungen orientieren, werden mehr Schüsse auf und mehr Tore in der entfernten Ecke erwartet, welche
für den Schützen schwieriger zu treffen und für den Torwart einfacher abzusichern ist. Moschini kann diese Hypothesen anhand von Daten aus der italienischen ersten Liga der Spielzeit 2002-2003 bestätigen.
Die doppelte Kontingenz von E/fmeterschüssen
ben. Jede Situation ist dabei durch die folgenden, in Tabelle 1 zusammengefassten Angaben beschrieben: Beteiligte Schützen und Torhüter, Schussfuß des Schützen, Richtung des
Torschusses (Links, Mitte, Rechts), Sprungrichtung der Torhüter (Links, Mitte, Rechts) und
das resultierende Ergebnis in vier Kategorien (»Tor«, »vorbeigeschossen«, »PfostenlLatte«
und »vom Torhüter abgewehrt«.). Die Richtungen werden einmal originär vom jeweiligen
Spieler aus gesehen eingetragen und einmal in der beschriebenen einheitlichen Notation als
»natürliche« Richtung.
Tabelle 1: Deskription des Datensatzes
Schussfuß
Schützen
5. Datensatz und Ergebnisse
Nach einer Beschreibung des verwendeten Datensatzes werden die Ergebnisse der damit
durchgeführten Hypothesentests dargestellt. Dabei werden vorerst die zu Grunde gelegten
Annahmen überprüft.
5.1 Daten
Der verwendete Datensatz22 enthält Angaben zu allen 1043 Elfmetersituationen, die in den
Spielzeiten 1992 / 1993 bis 2003 / 2004 der ersten deutschen Bundesliga stattgefunden ha22) Die Daten wurden von der Firma IMP AG erhoben. Diese beobachtet Bundesligaspiele, um die Daten
anschließend an Interessenten, z.B. an die beteiligten Mannschaften, zu verkaufen. Dabei werden
nicht nur Elfmetersituationen, sondern sämtliche Aktionen eines Spiels von insgesamt vier professionellen Beobachtern dokumentiert.
Ergebnis
R
L
Mitte
R
Tor
vorbei
prostenl
Latte
377
666
441/433
151
451/459
788
27
24
520/542
17
506/484
Torhüter
Die bisherige Evidenz zeigt damit, dass die spieltheoretischen Vorhersagen zu gemischten
Gleichgewichten als Lösung von doppelten Kontingenzen bestätigt werden können; in realen
Situationen vollständig, im Labor mit einigen Abstrichen. Im Folgenden wird untersucht, ob
die obigen Hypothesen auch auf die Entscheidungen von Bundesligaspielern zutreffen.
Schuss bzw. Sprungrichtung jeweils originärl
»natürlich«
L
Tennis
Die untersuchte Interaktionsstruktur findet sich jedoch nicht nur beim Fußball, sondern z.B.
auch beim Tennis. Walker / Wooders (2001) analysieren dazu die Aufschlag- und
Returnentscheidungen von professionellen Tennisspielern. Diese können jeweils auf die linke oder rechte Seite des Feldes aufschlagen. Der Return-Spieler wählt ebenso eine Seite aus.
Die zentralen Hypothesen ergeben sich auch hier aus denselben theoretischen Überlegungen:
Damit die beiden Spieler füreinander unberechenbar bleiben, muss die Wahrscheinlichkeit
eines Punktgewinns unabhängig von der Seitenwahl sein (für beide Spieler, da es sich auch
hier offensichtlich um ein Nullsummenspiel handelt). Anhand von vierzig Finalspielen bei
Grand Slam- und Masters-Turnieren werden diese Hypothesen überprüft. Die Gleichheit der
Gewinnwahrscheinlichkeiten (unabhängig von der gewählten Seite) kann eindeutig bestätigt
werden.
411
23
abgewehrt
204
Die erste Zahl bei der Schuss- bzw. Sprungrichtung L (»Links«) und R (»Rechts«) bezeichnet die tatsächliche Richtung des Schusses bzw. des Sprungs, jeweils vom ausführenden Spieler aus gesehen. Die zweite Zahl bezieht sich auf die natürliche »rechte« und unnatürliche »linke« Richtung vom Torwart aus gesehen; dabei werden Schüsse und Sprünge auf
die - vom Torwart aus gesehen - rechte Seite bei Rechtsfüßem als natürlich und bei Linksfüßern als unnatürlich gezählt.
5.2 Test der Annahmen
Um das dargestellte Modell der Elfmetersituation mit dem Datensatz empirisch überprüfen
zu können, müssen drei Annahmen erfüllt sein: Die Schützen müssen das gleiche Spiel spielen, unabhängig davon, welchen Schussfuß sie benutzen,24 und die Schützen und Torhüter
müssen das gleiche Spiel spielen, unabhängig davon, welche Entscheidung sie treffen. Um
die empirischen Häufigkeiten als Wahrscheinlichkeiten interpretieren zu können, ist weiterhin wichtig, dass das Spiel auch durch den Erwartungsdruck auf den Schützen nicht verändert wird. Der Erwartungsdruck wird durch den Spielstand, das Heimrecht (jeweils aus der
Sicht des Schützen) und die Halbzeit, in der die Strafstoßsituation stattfindet, approximiert.
Ergibt sich hier keine Heterogenität in den Daten, ist dies ein starker Hinweis auf eine homogene Spielsituation bei allen Strafstößen.
Dies ist auch tatsächlich der Fall. In der logistischen Regression mit den obigen unabhängigen Variablen jeweils auf die Wahrscheinlichkeit, ein Tor zu erzielen, ein Tor abzuwehren,
und die Wahrscheinlichkeit »Links« oder »Rechts« zu wählen findet sich kein signifikanter
25
Einfluss. Der höchste t-Wert einer unabhängigen Variable beträgt t=1,11 und zeigt, dass
23) Es handelt sich nur um Meisterschaftsspiele. Der Datensatz enthält also keine Beobachtungen zu
Elfmeterschießen, wie sie bei unentschiedenem Spiel am Ende von Pokalspielen ausgetragen werden.
24) Die Frage, ob das Spiel sich in Abhängigkeit des Schussfußes unterscheidet, differiert von derjenigen,
ob der Schuss auf die natürliche Seite einfacher ist.
25) Aus Einfachheitsgründen wurde der Schuss in die Mitte der natürlichen Seite zugeschlagen. Ein
entsprechender Test mit einer multinomialen logistischen Regression, die alle drei Kategorien berücksichtigt, ändert den Befund aber nicht.
412
das Spiel durch die unabhängigen Variablen nicht beeinflusst wird. Das maximale PseudoR 2 ist mit 0,0013 extrem gering und zeigt ebenfalls, dass die für die theoretische Analyse getroffenen Annahmen empirisch vollständig bestätigt werden können. 26
413
Tabelle 2b: Empirische Verteilung der Trefferwahrscheinlichkeiten des Schützen
Torhüter
Damit kann die eigentliche Überprüfung der Hypothesen vorgenommen werden. Inhaltlich
zeigt sich hier außerdem schon, dass die Spieler sich insofern rational verhalten, als sie ihre
Entscheidungen nicht durch einen erhöhten Erwartungsdruck verändern.
Links
Schütze
Mitte
Links
52,5%
83,3%
96,0%
75,5%
Mitte
74,2%
33,3%
64,00/0
67,5%
Rechts
91,8%
1000/0
64,5%
78,2%
73,1%
82,4%
77,50/0
75,60/0
5.3 Hypothesentests
Die Hypothesen werden in der Reihenfolge der theoretischen Darstellung überprüft.
H 1: Unabhängigkeit der Strategien von Schütze und Torwart
Tabelle 2a zeigt die gemeinsame Verteilung der Strategiewahlen von Schützen und Torhütern. Der X2-Wert der Verteilung beträgt 2,5 bei 4 Freiheitsgraden und ist mit einem
Signifikanzniveau von 0,65 weit davon entfernt, einen statistischen Zusammenhang anzuzeigen. Wie bei einem gemischten Gleichgewicht erforderlich, erfolgen die Entscheidungen der
beiden Spieler damit tatsächlich unabhängig voneinander.
Damit ist im Übrigen auch gezeigt, dass die oben fußballtechnisch belegte Annahme der
Simultanität der Entscheidungen in der Tat zutrifft. Wenn sich die Torhüter nach den Handlungen der Schützen richten würden, müsste sich dies derart bemerkbar machen, dass die
Hauptdiagonale in Tabelle 2a stärker besetzt wäre. Im umgekehrten Fall, wenn die Schützen
auf die Handlung der Torhüter reagieren würden, müsste die Gegendiagonale (ohne die Mitte) stärker besetzt sein. Die entsprechenden Fallzahlen betragen 436 und 448 und unterscheiden sich nicht signifikant (t-Wert=0,30).
Tabelle 2a: Empirische Verteilung der Strategiewahlen von Torwart und Schütze als absolute Häufigkeiten und als Prozentanteile
Torhüter
Schütze
Links
Mitte
Rechts
Links
202
19,4%
6
0,60/0
225
21,6%
433
41,5%
Mitte
62
5,9%
0,30/0
86
8,2%
151
14,5%
Rechts
220
21,1%
0,80/0
231
22,1%
459
44,0%
484
46,4%
17
1,6%
542
52,0%
1043
100%
3
8
Rechts
Die Strategiewahl »Rechts« bezeichnet jeweils den Schuss bzw. den Sprung auf die
natürliche Seite des Schützen. Die Zahlen in den Zellen bezeichnen jeweils die empirische
Erfolgswahrscheinlichkeit (d.h. den Quotienten aus den Treffern und allen Schüssen) für den
Schützen bei der betreffenden Strategiekombination. Die Abwehrwahrscheinlichkeit für den
Torwart ergibt sich jeweils als Gegenwahrscheinlichkeit (vgl. Abb. 2).
H2: Wahl der Option »Mitte«
Es ist eindeutig erkennbar, dass die Schützen eine weit höhere Wahrscheinlichkeit haben, in
die Mitte zu schießen (151 bzw. 14,5% aller Schüsse gehen dorthin), als der Torwart, dort
stehen zu bleiben (17 bzw. 1,6% aller Entscheidungen). Diese beiden Werte unterscheiden
sich hochsignifikant (t-Wert=17,01).
H3a: Gleichheit der Trefferwahrscheinlichkeit für alle Strategien
Aus Tabelle 2b wird ersichtlich, dass insbesondere die beiden Seitenwahlen für die Schützen
ähnliche Erfolgswahrscheinlichkeiten aufweisen. Für die Wabl der»Mitte« trifft dies nur bedingt zu.
Die eigentliche Trefferwahrscheinlichkeit entspricht allerdings der erwarteten Auszahlung für eine Seitenwahl. Diese korrespondiert dabei mit dem Produkt aus dem erwarteten
Nutzen für eine bestimmte Strategiewahl und der Wahrscheinlichkeit, mit der die Strategie
gewählt wird. Da - wie oben theoretisch begründet - die natürliche Seite des Schützen empirisch tatsächlich mit geringeren Kosten (weil einfacher zu schießen) versehen ist, sollte der
Schuss auf diese Seite etwas häufiger vorkommen. Allerdings sind die genauen Kosten, anders als etwa bei »matching pennies«, apriori unbekannt und können nur empirisch aus den
beobachteten Trefferwahrscheinlichkeiten geschätzt werden. Von diesen kann dann auf die
optimale Mischung der Strategien geschlossen werden. 27 Tabelle 3 berichtet die vorhergesagte und beobachtete Mischung der Seitenwahl für die Schützen und Torhüter. Wegen der
wenigen Fälle, in denen der Torwart in der Mitte stehen geblieben ist, wird der Strategienraum dabei auf {Links, Rechts} beschränkt und die Mitte dabei zur natürlichen Seite gezählt
(vgl. oben).
natürliche Seite des Schützen.
26) Eine ausführliche tabellarische Darstellung der Analyse findet sich in Berger I Hammer (2007).
27) Für eine formale Herleitung der Beziehung siehe Berger / Hammer (2007).
414
Tabelle 3: Vorhergesagte und tatsächliche Wahrscheinlichkeiten der Strategiewahlenfür
Schütze und Torhüter in Prozent
Torhüter
Schütze
Links
Rechts
Links
Rechts
vorhergesagte
Wahrscheinlichkeit
35,2
64,8
47,2
52,8
tatsächliche
Wahrscheinlichkeit
41,6
58,4
47,2
52,8
natürliche Seite des Schützen.
Es zeigt sich, dass die Schützen in der Tendenz zwar richtig liegen, aber dennoch erkennbare Unterschiede zwischen vorhergesagtem und beobachtetem Mischungsverhältnis der
Strategien vorliegen. Die Schützen könnten das Mischungsverhältnis optimaler gestalten,
wenn sie etwas häufiger auf ihre natürliche (rechte) Seite schießen würden.
H3b: Gleichheit der Abwehrwahrscheinlichkeitfür alle Strategien
Tabelle 2b weist auch für die Torhüter ähnliche Abwehrwahrscheinlichkeiten für die beiden
Seitenwahlen aus. Wiederum gilt dies nur bedingt für die Wahl der »Mitte«. Allerdings muss
beachtet werden, dass für die Torhüter hierzu kaum Fälle vorliegen, sodass diese Analyse
wenig aussagekräftig ist.
Die vorhergesagte und tatsächliche Strategienmischung der Torhüter wird gleich berechnet wie die optimale Mischung der Schussrichtungen für die Schützen und mit der beobachteten Häufigkeit verglichen. In Tabelle 3 zeigt sich, dass die Torhüter perfekt zwischen den
beiden Seiten mischen, da die vorhergesagten und beobachteten Wahrscheinlichkeiten identisch sind.
H4a: Wahl der natürlichen Ecke durch Schützen
Tatsächlich wählen die Schützen die natürliche rechte Ecke 459mal (46,4% aller Fälle) und
damit signifikant häufiger (K-S Anpassungstest auf Gleichverteilung z=15,5, asymptotisch
signifikant 0,000) als die linke (433mal, 41,0% aller Fälle, vgl. Tab. 2a). Die Hypothese
kann bestätigt werden. 28
H4b: Wahl der natürlichen Ecke durch den Torwart
Dasselbe gilt für die Torhüter. Diese antizipieren offenbar, dass es für die Schützen günstiger
ist auf ihre natürliche Seite zu schießen und springen entsprechend signifikant häufiger
(542mal, 52,0 % der Fälle) dorthin als in die linke Ecke (484mal, 46,4% der Fälle, K-S Anpassungstest auf Gleichverteilung z=16,9, asymptotisch signifikant 0,000, vgl. Tab. 2a).29
28) Alternativ kann hier auch ein t-Test durchgeführt werden. Dieser zeigt an, dass sich die Verteilung
nicht signifikant von einer 50:50-Verteilung unterscheidet (t-Wert=O,87). Werden die Schüsse in die
Mitte in Anlehnung an Palacios-Huerta (2003) dagegen zur natürlichen Seite gezählt, wird die Differenz größer und damit auch signifikant (t-Wert=5,56).
29) Der durch das in der vorangehenden Fußnote beschriebene analoge Vorgehen geschätzte t-Werte lautet hier t= 1,81 und zeigt nur eine knapp signifikante Differenz an.
4f5
H5: Wahl der natürlichen Ecke durch Torwart und Schütze
Es kann bestätigt werden, dass die Torhüter mit größerer Wahrscheinlichkeit auf die natürliche Seite springen als die Schützen dorthin schießen. 459 Schüsse (46,4 %) gehen in die natürliche Ecke, aber die Torhüter springen 542mal (52,0 %) dorthin (vgl. Tab. 2a). Diese Differenz ist jedoch nicht signifikant, wie ein entsprechender t-Test zeigt (t-Wert=0,24).
Wird die Wahl der »Mitte« durch den Schützen zu dessen natürlicher Seite gezählt (vgl.
oben), so ergibt sich ein signifikanter Unterschied mit einem t-Wert von 2,54. Wird weiterhin davon ausgegangen, dass in den Daten nicht identifizierbare, selektive Verzerrungen vorliegen, und die Hypothese deswegen als Häufigkeitsaussage formuliert, so ist die vorliegende Häufigkeitsdifferenz ebenfalls signifikant (t-Wert=2,63).
H6: Abfolge der Strategiekombinationen
Wie vorhergesagt ist die Kombination [R, R] mit 22,1% (231 Fälle) am häufigsten. Danach
folgen mit [L, R] (21,6 %, 225 Fälle) und [R, L] (21,1 %, 220 Fälle) die beiden gemischten
Fälle. Im Durchschnitt treten diese 223mal, und damit in 21,4 % der Fälle auf. Die seltenste
der vier Kombination ist [L, L] mit 19,4 % (202) aller Strategiekombinationen. Ein Maximum Likelihood-Test zeigt allerdings, dass diese Unterscheide nicht signifikant sind. Die
größte Differenz liegt zwischen den Kombinationen [R, R] und [L, L] vor und weist ein
Signifikanzniveau von 16% auf. Für die anderen Kombinationen ist dieser Wert entsprechend geringer.
Wird wiederum die Wahl der »Mitte« durch den Schützen zu dessen natürlicher Seite gezählt (vgl. oben), so ergeben sich hochsignifikante Unterschiede zwischen allen Kombinationen, mit Ausnahme der Differenzen zwischen den beiden Gruppen [L, L] [L, R] und [R,
R] [R, L].
Insgesamt können die spieltheoretischen Vorhersagen damit weitgehend bestätigt werden.
Dies gilt insbesondere für die Torhüter, die sich optimal verhalten. Die Schützen dagegen
zeigen z.T. suboptimale Entscheidungen. Allerdings sind nicht alle untersuchten statistischen
Beziehungen signifikant, obgleich sie immer in die erwartete Richtung weisen.
Diese Einschränkung kann jedoch fallengelassen werden, wenn die Hypothesen nicht als
Wahrscheinlichkeits-, sondern als Häufigkeitsaussagen formuliert werden und / oder in
Anlehnung an Palacios-Huerta (2003) der Strategienraum auf {Links, Rechts} beschränkt
wird. In diesem etwas weniger harten Test der Theorie können nur die Hypothesen 3a und 6
nicht vollständig bestätigt werden.
6. Diskussion
Die Analyse der Elfmetersituation als idealtypisches Beispiel einer doppelten Kontingenz
zeigt, dass nur die Spieltheorie diese, insbesondere von systemtheoretisch orientierten Soziologen als problematisch betrachtete, Situation theoretisch auflösen kann. Nur die Spieltheorie impliziert entsprechende empirisch testbare Hypothesen über das Explanandum der zu erwartenden Handlungsmuster, nicht aber die Ansätze von Parsons und Luhmann. Die
spieltheoretischen Vorhersagen können zudem anhand eines Datensatzes zu Elfmeterschüssen in der ersten Fußballbundesliga weitgehend bestätigt werden.
Der spieltheoretische Ansatz weist damit den zweifachen Vorteil einer größeren theoretischen Reichweite und der bestätigten empirischen Korrektheit gegenüber den beiden anderen betrachteten Ansätzen auf. Derjenige von Parsons ist zwar theoretisch auf Situationen
anwendbar, die einen Kooperationsgewinn versprechen, nicht jedoch auf die hier untersuchten Nullsummenspiele, für die es keine sinnvollen Normen sozialen HandeIns geben kann
416
Roger Berger und Rupert Hamlner
(es sei denn, diejenigen, die in vollständig rationalen Erwartungen gründen). Luhmann
schließt zusätzlich explizit aus, dass die Spieler den auftretenden infiniten Regress von Erwartungen und daran anschließenden Handlungen auflösen können. Denn weil er jede Handlungstheorie und dadurch auch die »common knowledge«-Annahme aufgibt, zieht er genau
den Nagel, der diesen Zirkel von Erwartungen festhält. Damit lassen sich aus den Ausführungen von Luhmann und Parsons apriori keine Lösungen für die doppelte Kontingenz bei
vollständiger Konkurrenz ableiten. Dies gilt insbesondere dann, wenn es sich wie beim
Strafstoß um ein Spiel mit simultanen Zügen handelt, das zusätzlich die Kommunikationslösung ausschließt. Hinzu kommt, dass in reinen Konfliktspielen die Eigennutzannahme keine
empirisch zu bestätigende Vermutung über eine Eigenschaft der beteiligten Akteure ist.
Vielmehr ergibt sie sich hier aus der Struktur der Interaktion und ist damit eine soziale und
keine individuelle Eigenschaft.
Dabei stellt der Elfmeterschuss keineswegs einen zu vernachlässigenden Spezialfall einer
doppelten Kontingenz dar, sondern steht stellvertretend für Nullsummenspiele und damit für
eine ganze Kategorie sozialer Interaktionen. Diese sind insofern von besonderem Interesse,
als sich hier Akteure mit exakt gegenläufigen Interessen gegenüberstehen, die weder kommunizieren wollen noch können, jedoch interagieren und dabei eine stabile und vorhersagbare Form von sozialer Ordnung entstehen lassen. Und dies, obschon beide Akteure gerade
kein Interesse an der Entstehung oder Aufrechterhaltung einer solchen Ordnung haben. Mit
einigen Beispielen kann die soziale Relevanz dieser Form der doppelten Kontingenz ausgemessen werden: Das klassische Beispiel in der Literatur (vgl. z.B. Morgenstern 1976) ist die
Geschichte»The Final Problem« von A.C. Doyle, in der sich Sherlock Holmes in einer ganzen Kaskade solcher doppelter Kontingenzen mit seinem Gegenspieler Professor Moriarty
befindet. Solche Interaktionssituationen ergeben sich allgemein, wenn Ego Alter verfolgt
und Alter genau dies zu vermeiden versucht, und zwar - wie die Beispiele zeigen - unabhängig davon, ob dies innerhalb eines normierten Rahmens geschieht oder nicht. So wird jeder
Polizist (oder eine andere Sanktionsinstanz) versuchen, den Einbrecher (oder einen anderen
Normbrecher) genau dort zu überraschen, wo dieser es nicht erwartet und jeder Einbrecher
versucht, genau dies zu vermeiden. Dies gilt auch für kollektive Akteure, wie ein anderes
Beispiel aus dem Bereich Fußball zeigt: Die Firma Adidas versuchte die Eigenschaften des
von ihr für die Fußballweltmeisterschaft 2006 gefertigten Balls möglichst lange geheim zu
halten und Nachahmerfinnen zu täuschen, um ihnen keine Zeit zu geben, bis zur Durchführung des Turniers ein gefälschtes Produkt auf den Markt zu bringen. Im Extrem findet sich
diese Interaktionsstruktur auch bei strategischen Entscheidungen im Krieg, wie das Beispiel
zeigt, das als »Battle of the Bismarck Sea« in die Literatur eingegangen ist (vgl. Rasmusen
1998, S. 19f).30
Die weitgehende Bestätigung der spieltheoretisch generierten Hypothesen anhand von Daten zu einer realen Situation doppelter Kontingenz ist deshalb ein starkes Argument für deren Anwendung auf das soziologische Kerngeschäft der Analyse von Interaktionen. Wie die
vorgeführte Analyse klar zeigt, kann die dabei unterstellte Rationalität der Akteure nicht als
irgendwie bewusstes, kognitives Abwägen interpretiert werden. 3 ! Vielmehr sollte Rationali-
417
tät als die bisher fruchtbarste »als ob«-Heuristik betrachtet werden, die auf der Individualebene unterstellt werden kann, um auf der Aggregatebene korrekte Prognosen abzugeben.
Rationalität ist dann nicht eine individuelle, sondern eine »ökologische« Eigenschaft der
Interaktionsstruktur (vgl. Smith 2003, auch Becker 1962). Deshalb müssten die spieltheoretischen Hypothesen nicht nur für die bisher betrachteten, ausschließlich professionellen Spieler zutreffen, sondern auch für ungeübte Amateure, die sich in entsprechenden realen
Interaktionssituationen befinden. Diese empirische Analyse steht allerdings bislang noch
aus.
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nördlichen Weg durch die Bismarck-See, wenn er erwartet, dass die amerikanische Flotte ihm im Süden auflauert, was diese veranlasst, doch nach Norden zu fahren, usw. usf.
31) Dies ist auch der Grund, wieso eine qualitativ-beschreibende Analyse von Elfmeterschüssen, wie sie
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die Elfmetersituation oder deren Handlungsmotive zu rekonstruieren, zum Scheitern verurteilt, wenn
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Zusammenfassung: Wie verhalten sich Funktionssysteme zu Organisationen und wie können Organisationen Funktionssystemen zugeordnet werden? Die Systemtheorie ist diesbezüglich uneindeutig, widersprüchlich und kann wenig über Organisationen aussagen, die nicht einem Funktionssystem zugeordnet sind. Die Praxistheorie dagegen liefert dichte Beschreibungen, die
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lassen sich anhand ihrer Organisationsstruktur, ihrer Publikationspraktiken und ihrer Forschungsbegriffe als vermittelnde und mehrdeutige intersystemische Organisationen beschreiben. Der Aufsatz versteht sich zudem als Beitrag zu einer Ethnographie intersystemischer Organisationen und
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Dr. Roger Berger
Dip!. Soz. Rupert Hammer
Universität Leipzig
Institut filr Soziologie
Beethovenstrasse 15
04107 Leipzig
berger@sozio.uni-Ieipzig.de
Eine Firma schreibt auf ihrer Homepage, dass sie »interdisziplinäre Umweltforschung« betreibe. I Die Firma verwendet Instrumente, Software, Methoden und Theorien, wie sie in unterschiedlichen wissenschaftlichen Disziplinen, von Soziologie bis zur Physik, angewandt
werden. Sie publiziert jedoch kaum in wissenschaftlichen Zeitschriften, sondern schreibt Berichte für Auftraggeber, für die sie zum Beispiel Finanzierungsmodelle für den öffentlichen
Verkehr evaluiert und FItisse zur ökonomischen und ökologischen Aufwertung modelliert.
Die Firma beschäftigt als Projektmitarbeiter ausschließlich Personen mit Universitätsabschluss, einige davon mit Doktorat und Lehraufträgen an Universitäten.
Wie soll man nun soziologisch solche Firmen beschreiben? Betreiben diese Firmen Wissenschaft? Soll man sie dem Wissenschaftssystem zurechnen? Oder handelt es sich dabei um
Wirtschaftsorganisationen, die mit Wissen handeln?
Eine Beschreibung solcher Firmen muss sich vor allem mit dem Problem funktionaler Differenzierung beschäftigen und mit der Frage, auf welcher Ebene funktionale Differenzierung
beobachtbar ist. Bis dahin standen sich in dieser Frage eine empirieverliebte Praxistheorie
und eine kommunikationszentrierte Systemtheorie unversöhnlich gegenüber. Beide Ansätze
können jedoch theoretisch intersystemische Organisationen nicht adäquat beschreiben. Die
Systemtheorie konzipiert Systeme als Kommunikationszusammenhänge und bleibt widersprüchlich, wie sich Organisationen zu Funktionssystemen verhalten, insbesondere, wenn
sich Organisationen nicht einzelnen Funktionssystemen eindeutig zuordnen lassen. Die Praxistheorie sieht zwar diese Probleme, bietet jedoch theoretisch keine Alternative an, sondern
belässt es bei der Feststellung, dass sich Organisationen Funktionssystemen nicht zuordnen
lassen. Gerade intersystemische, d.h. nicht einem einzelnen Funktionssystem zuordenbare
Organisationen bleiben dabei für beide Theorien theoretisch nicht fassbar. Dieser Aufsatz
versucht die Defizite der beiden Theoriestränge mit einem Theoriemodell intersystemischer
1) Ich danke Monika Dommann und Jörg Potthast sowie den anonymen Reviewem für hilfreiche Kritik.
Der Aufsatz beruht auf einem Forschungsprojekt »The Production of Socially Robust Knowledge«,
das vom Schweizerischen Nationalfonds gefördert wurde. Eine ausführlichere Version des hier präsentierten Arguments findet sich in Guggenheim (2005).
Soziale Welt 58 (2007), S. 419 -438
The Hinges of History: State-Making and Revolt in Early Modern France
Author(s): Edgar Kiser and April Linton
Source: American Sociological Review, Vol. 67, No. 6 (Dec., 2002), pp. 889-910
Published by: American Sociological Association
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THE HINGES OF HISTORY:
STATEoMAKING AND REVOLT IN
EARLY MODERN FRANCE
EDGAR KISER
University of Washington
APRIL LINTON
Princeton University
The formation of early modern states-combining increases in taxation, warfare,
and administrative centralization-was often violently opposed by subjects. A game
theoretic model of strategic interactions between rulers and subjects is developed to
more fully specify the relationship between state-making and revolt in France between 1515 and 1789. Quantitative analyses of revolts throughout France are combined with a brief case study of revolts in Guyenne (the most quarrelsome French
province) to test propositions derived from the model. Offensive war (but not war in
general) and administrative centralization increased the likelihood of revolt, while
the presence of the Estates General (the national legislative assembly) decreased it.
The effect of taxation on revolt depended on the historical context-high taxes and
offensive wars tended to incite revolts prior to the Fronde (a cluster of revolts in
1648-1653), but had no effect afterwards. It is argued that the outcomes of significant revolts, like the Fronde, often serve as important turning points in the history of
state-making. Potentially similar events in medieval England and early modern
Spain are also discussed.
HE PROCESS
of early modem state-
Imaking was often quite unpopular; it
was marked by frequent wars, increasing
taxation, and the growth and centralization
of administrative institutions. As several
scholars have shown, these factors often
triggered revolts in early modern states
(Barkey 1991; Berce 1987; Bonney
1978:214; Brustein and Levi 1987; Clark
1978; Goldstone 1991; Hopcroft 1999;
Kiser, Drass, and Brustein 1993; Major
1960:127; Markoff 1996:12, 42; Mousnier
1970, 1979:741-42; Tilly 1975, 1986:7,
1993:17, 156-58; Zagorin 1982).
We use a model of the strategic interactions between rulers and taxpaying subjects
Direct correspondence to Edgar Kiser, Department of Sociology, Box 353340, University of
Washington, Seattle WA 98195 (kiser@u.
washington.edu). We thank Julia Adams, Terry
Boswell, Julie Brines, Cai Yong, Jerry Herting,
Peter Hoff, Hyojoung Kim, James Kitts, Becky
Pettit, Kevin Quinn, Ron Schoenberg, Katherine
Stovel, and several anonymous ASR reviewers
for helpful comments.
AMERICAN
to explore the causal relationship between
various aspects of state-making and tax revolts.' Both state-making and revolt are the
result of choices, and these choices are always made in light of the anticipated reactions of other actors. Rulers consider the
possibility of revolt when they think about
raising taxes or pursuing unpopularpolicies.
In deciding whether to revolt, subjects consider both the likelihood of rulers using repression and their other options for decreasing their tax burden,such as tax evasion. The
determinants of the costs of tax evasion, in
part a function of rulers' decisions about administrative techniques, must thus also be
part of a model of revolt.
To provide a rough heuristic model of the
relationship between state-making and revolt, we use a game theoretic decision tree.
1 Revolts were caused by many factors other
than taxation, including religious conflicts, population growth, price increases, elite conflicts, and
the rise of capitalism (Barkey 1991; Goldstone
1991; Lachmann 1989, 2000). We focus only on
revolts against state taxation.
SOCIOLOGICAL REVIEW, 2002,
VOL. 67 (DECEMBER:889-9
10)
889
890
AMERICAN SOCIOLOGICAL
REVIEW
The extensive form of game theory highlights the sequential nature of interaction,
and thus precisely specifies the relationships
between various aspects of state-making
(war, taxation, and administrativecentralization) and revolt. We use the model in a limited way: We look at the state-making process from the point of view of subjects. Explaining the actions of rulers (such as tax increases and war-making) that initiate the
process is beyond the scope of this paper.2
We test the relationship between aspects
of state-making and revolt mainly via quantitative analyses of revolts in France between 1515 and 1789. Early modern France
is a useful case in which to explore these relationships for several reasons. First, many
of the classic historical studies of state-making and revolt cited above focus on this case,
allowing us to draw on their insights in constructing our models and to compare their
qualitative findings with our more quantitative results. Second, early modern France
contains ample variation in the main aspects
of state-making (levels of taxation, war, administrative centralization) and tax revolts,
facilitating the testing of our arguments.
Because tax rates and rates of revolt
(among other things) varied substantially
across provinces (Brustein and Levi 1987;
Collins 1994:20; Major 1994:xviii; Markoff
1996:37; Mousnier 1979:641),3 it is important to supplement our analysis with an examination of these relationships at the provincial level.4 We focus on Guyenne, the
2An adequate test of the game-theoretic model
as a whole would require both endogenizing the
choices of rulers by explaining both tax rates and
policy choices, and using comparative cases to
show the conditions under which state-making
goes down paths not followed in the French case.
3Although aggregated data on French taxation
have been used as a measure of the tax burden in
several exemplary historical analyses (Braudel
1972:684; Goldstone 1991:196-212; Mann
1993:358-400; Skocpol 1979; Tilly 1986:61-63;
Wallerstein 1989), all of these scholars recognize
that provincial variations across early modern
France make incomplete any test that aggregates
across them.
4 Our intent is not to reproduce Brustein and
Levi's (1987) masterful analysis of the geography of revolt-an analysis of one province would
not allow us to do that. We supplement their
work by focusing on the timing of revolt.
province in which revolt occurred most frequently in early modem France-almost onethird of the revolts in France occurred there.
Guyenne is also a useful case because it allows us to explore in more detail the important fiscal and administrativechanges in the
Pays d'Etat (provinces retaining provincial
legislative assemblies in the sixteenth century) in southern France in the early seventeenth century. Because it is not possible to
get quantitative data at the provincial level
for our entire period (especially for tax rates,
prices, and population), we do not reproduce
our statistical analysis for Guyenne. However, we do have sufficient data to roughly
test whether the same causal dynamics operate at national and provincial levels.
STATE-MAKING AND REVOLT AS
STRATEGIC INTERACTION
We begin with two simple assumptions about
the interests of actors.5The rulers (i.e., chief
executives) of states want to maximize tax
revenue while maintaining security of rule
(Kiser 1994; Levi 1988; North 1981). Taxpayers collectively want public goods like
security and social order that require taxation, but individually they want to minimize
their tax burden.6Using these assumptions,
and information and argumentsfrom the historical literatureto specify the structuralconditions within which these actors were embedded, we first outline propositions about
how taxes, war, and centralization affected
revolt in France, and then we construct a
model showing how these factors are interrelated.
TAXATION AND REVOLT
Several scholars have argued that there is a
relationship between levels of taxation and
5 The following discussion, based on these assumptions, outlines a stylized model of strategic
interaction, and should not be taken as a historical description.
6 It is, of course, a simplification to group all
taxpayers together, but the fact that most early
modern tax revolts, in France and elsewhere,
were class collaboration revolts involving a
broad cross-section of subjects (Barkey 1991;
Brustein 1985; Mousnier 1970:42) makes it a
reasonable simplification.
STATE-MAKING AND REVOLT IN EARLY MODERN FRANCE
revolt frequency in early modern France
(Barkey 1991; Berce 1987; Hopcroft 1999;
Mousnier 1979; Tilly 1986; Zagorin 1982).
Our model suggests that this relationship is
produced by two micro-level causal mechanisms. Rulers will try to get as much tax revenue as they can without inciting revolts (because revolts threaten their security and are
costly to suppress), and they will attempt to
find nontax sources of revenue that will be
less likely to instigate revolts. If rulers had
perfect information about the probability of
revolt at various levels of taxation, and if the
costs of revolt were always greater than the
benefits of tax increases, rulerswould always
set taxes at the highest level that would not
incite revolt and we would find no correlation between levels of taxation and revolt.
First, however, rulers did not have perfect
information, and thus would be expected to
miscalculate in setting tax rates, thus sometimes triggering revolts.7 Second, even when
rulers did have good information, there were
some instances in which the gains from raising taxes or the costs of not doing so outweighed the costs of revolts, and rulers chose
to increase taxes even if they thought revolt
was a likely result. The most common early
modem example is from international relations: Rulers could have an opportunity to
begin or continue an unusually profitable offensive war, or fear a very costly invasion.
Thus, for both of these reasons, we expect a
positive relationship between levels of taxation and the frequency of revolts.
WAR AND REVOLT
Our primary argument about the effects of
war on revolt is analogous to our argument
about tax increases. Rulers want to pursue
unpopularpolicies (those that serve their interests more than their subjects' interests),
7 Rulers would have to know the extent of the
costs imposed on subjects by taxation (which will
vary with population changes and the success of
harvests), their military power relative to subjects, and the collective action capacity of subjects. Of course, as with rulers' decisions about
increasing taxes and risking revolt, subjects' calculations that revolt will decrease taxes are made
with incomplete information, and they are thus
expected to miscalculate some proportion of the
time.
891
but they realize that doing so can sometimes
increase the likelihood of revolt. The lower
the benefits to subjects provided by the current policy pursued by rulers (such as an unpopular war), the greater the potential benefit of a successful revolt that would alter or
terminate that policy.
This allows us to specify the relationship
between war and revolt more precisely-it
should depend on the type of war.8 Levi
(1988, 1997) argues that citizens often view
defensive wars as public goods from which
they would benefit and thus for which they
are willing to pay taxes, while they do not
generally support offensive wars. Hopcroft
(1999:82) suggests that this was true in early
modem Europe. Although it is notoriously
difficult to find reliable data on the perceptions of historical actors (Tilly 1975:9; Weber 1968:5-6), there is a great deal of evidence that subjects thought that offensive
wars were less beneficial and legitimate than
defensive wars. Offensive wars were often
seen as enriching monarchs, but not their
subjects, and were thus more difficult to justify (Klaits 1976:87-88; LeRoy Ladurie
1980:200; Rowen 1980; Seyssel [1519]
1981:130-31). The influential sixteenth century political philosopher, Claude de Seyssel
([1519]1981:130-31), argued that defensive
wars were generally more legitimate than
offensive wars and that the latter should only
be initiated under certain limited circumstances. Klaits (1976:87-88) noted that of8There are two main bodies of work on the relationship between war and revolt-one is mainly
quantitative and focuses on the nineteenth and
twentieth centuries, and the second includes
mainly qualitative historical analyses of the early
modern era. In the quantitative literatureon modern states (see Stohl [1980] for a good summary),
findings range from positive to negative relationships, with the majority of studies showing no
strong relationship between the two. In contrast,
almost all qualitative historical studies of early
modern states suggest that war was a primary
cause of revolts (Barkey 1991:703; Brustein
1985; Brustein and Levi 1987; Le Roy Ladurie
1980:292; Lublinskaya 1968:331; Pillorget 1975:
425-36; Tilly 1975, 1985, 1990, 1993). This
raises an obvious question: Are the different findings in the two literatures due to differences in
the time periods studied or differences in the
methods used? A quantitative analysis of an early
modern state should help us find the answer.
892
REVIEW
fensive wars had "ratherdubious legal foundations" and were thus frequently criticized
in political pamphlets. Monarchs also seem
to have been aware of this difference. In a
discussion of offensive wars in his memoirs,
Louis XIV ([1661-1668]1970) notes that he
fears "being accused of recklessness when he
rushes voluntarily into complications" (p.
123), although this fear was clearly not sufficient to stop him. We thus expect the relationship between war and revolt to be stronger for offensive wars than for defensive
wars.9
ADMINISTRATIVE CENTRALIZATION
AND REVOLT
Subjects will choose to pay their full tax bill
only when the options available to them to
reduce or eliminate tax payments are more
costly. Revolt is certainly the most risky and
potentially the most costly strategy for subjects who want to decrease their tax burden.
Therefore, subjects are expected to revolt
only when the costs of their other options are
prohibitively high. The most importantalternative available to subjects is tax evasion.
Subjects can attemptto evade taxes, either
by concealing taxable assets or by colluding
with tax collectors (e.g., offering bribes for
lower tax assessments).10 Tax evasion will
9 We also test an alternative argument about
the relationship between war and revolt. States
are often weak during wars, and thus more likely
to be targets of revolt (Beik 1985:186, 196-97;
Kiser et al. 1993; Tilly 1990:186, 1993:12). Subjects will only revolt when they think the probability of the ruler capitulating or unsuccessfully
using repression is greater than the probability of
rulers successfully repressing the revolt. This argument stresses the opportunities that war provides to potential rebels by temporarily shifting
the balance of power in their favor, thus increasing the probability of a successful revolt. Like
social movements (Tarrow 1998), revolts are thus
expected to respond to shifts in political opportunity structures.The best indication of weakness
is when a ruler's military resources are occupied
elsewhere (e.g., in wartime). If this argument is
correct, revolts will be more frequent during periods of warfare.
l0 Another option is to exit the area being
taxed, but this is prohibitively costly for subjects
not living close to the border of another state
(North and Thomas 1973). In fact, in the early
almost always be preferable to revolt because it entails less cost and risk, does not
require collective action, and provides clear
tangible benefits in the form of lower tax
payments. Therefore, subjects are expected
to revolt more often when the costs of tax
evasion increase. The costs of tax evasion
depend primarilyon the effectiveness of rulers' tax administration apparatus. This is
why both historians and sociologists argue
that administrative centralization generated
revolts (Barkey 1991:700, 708-09; Bonney
1978:214; Collins 1995:52; Mousnier 1970:
34, 38; Parker 1983:95; Westrich 1972:134;
Zagorin 1982:215, 219). Because administrative centralization increases the effectiveness of assessment and collection, and thus
also increases the costs of evasion
(Matthews 1958:47; Mousnier 1979:611;
Pillorget 1975:507-25), the greater the centralization of tax administration, the greater
the expectedfrequency of revolt.
THE HINGES OF HISTORY: TURNING
POINTS IN STATE-MAKING AND REVOLT
Neither rulers nor subjects can be expected
to have perfect information about the relationship between tax levels and revolt, so
many revolts will occur as a result of rulers'
or subjects' miscalculations (see Gartzke
1999 for a similar argumentabout the causes
of war). It is difficult to predict when such
miscalculations will occur in historical
analyses because it would require detailed
knowledge of the information available to
rulers at the time. However, we can predict
that rulers will learn from past miscalculations, especially large miscalculations that
had clear outcomes (Lublinskaya 1968:256).
These events usually come in the form of
major historical turning points (the "hinges"
of history) in which the outcomes of revolts
demonstrate to rulers (and subjects) either
that future tax increases will not be beneficial for rulers (clearly successful revolts) or
that revolting against taxes is likely to be an
unsuccessful strategy in the future (clearly
unsuccessful revolts).
modern period it was very costly for most subjects, as 90 percent or more derived most of their
wealth from land. Exit, thus, was not a viable alternative to revolt.
893
Recent developments in historical methods suggest that these turning points, critical junctures, or transformative events are
important determinants of historical outcomes and are too often ignored in mainstream quantitative sociology (Abbott 1997;
Collier and Collier 1991; Goldstone 1998;
Issac and Griffin 1989; Mahoney 2000;
Peirson 2000; Sewell 1996). Although researchers may use many different terms, all
of their arguments suggest that key events
can dramatically shift the trajectory of historical development. They also agree that
these events can rarely, if ever, be predicted,
but can be recognized by their consequences
after the fact. Our argument focuses on the
microfoundations of historical turning
points. Historical turning points are important because they are likely to alter the structural factors affecting the cost-benefit calculations of actors, and thus (in this case) also
affect the relationship between state-making
and revolt.
Focusing on potential turningpoints is one
way to make quantitativesociology more historical (Issac and Griffin 1989). To begin we
must first turn to the historical literature to
identify them. Historians agree that there was
such a turning point in early modern
France-the relationshipbetween state-making and revolts changed following the collection of related revolts called the Fronde
(1648-1653) (Collins 1995:77-78; Major
1994:xxi; Parker 1983:119; Westrich 1972:
140). As a result of both the information the
Fronde provided about the relative power of
rulers and subjects and the actions rulerstook
in its aftermath(elaborated below), subjects
viewed revolts as much more costly than before. Therefore, after the Fronde, we expect
the relationship between taxation and unpopular policies (such as offensive war) and
revolt to be much weaker than before.
fensive war). Note that the "increase taxes"
move also includes offensive war. We view
these two moves as analytically similar-the
tax rate specifies the costs to subjects, and
the type of policy pursued determines the
benefits. Throughout the game, subjects
have three choices: pay, evade, or revolt
(they are not entirely mutually exclusive, as
subjects will generally choose some mix of
pay and evade).
If the ruler does not increase taxes, subjects will continue to choose some mix of
pay and evade (depending on the costs of
evasion), just as they did in prior years.
(This assumes the conditions affecting the
tax collection process do not change.) We
call this situation a "customary taxation
equilibrium."
The more interesting developments follow
from rulers' choices to increase taxes and
pursue offensive wars, and these choices
were the most common in early modern
France. Subjects have the same three alternatives, but the payoffs for each are now
quite different. The main effect of rulers
choosing this strategy is to increase the costs
of paying taxes or to decrease the benefits
of the policies they fund. Therefore, both
evasion and revolt become relatively more
attractive.1 Subjects are expected to choose
evasion more often (because it is less costly
and less risky than revolt), but the frequency
of revolt is expected to increase somewhat.
The game then proceeds along two separate lines, depending on whether subjects
choose to evade taxes or revolt. If subjects
choose revolt, rulers then have to choose between using repression or giving in to subjects' demands and lowering the tax rate. If
they lower the tax rate, the game ends with
payoffs similar to the customary tax equilibrium. If they use repression, there is some
uncertainty about the outcome-will they
defeat the rebels or not? The role of chance
A MODEL OF STA TE-MAKING
AND REVOLT
IISubjects may still choose to pay the tax, if
the costs of evasion and revolt are too high. This
leads to an upward spiral, as rulers again increase
taxes. This is not a stable equilibrium. Eventually, the costs of paying will be higher than either evading or revolting. Subjects will then
choose one of these two options, pushing them
down to the lower branches of the game tree, as
discussed below (indicated by dotted lines in Figure 1).
Figure 1 outlines the state-making and revolt
game, combining the factors we have discussed in a model of sequential, strategic
decisions. Rulers move first and decide
whether to keep the tax rate the same or increase it, and what policies to pursue (specifically, whether to initiate an unpopularof-
894
REVIEW
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is capturedin game theory as a move by "nature"-either the repression is effective or it
is not. If it is not, we return to something
similar to the customary tax equilibrium. If
it is successful, rulers are able to enforce the
higher tax rate and their preferred policy
choices.
If subjects respond to tax increases or unpopular policies by increasing evasion, as
we expect, rulers will attemptto increase the
costs of evasion by centralizing administration. As with repression, there is an element
of uncertainty regarding the outcome: Centralization may or may not be effective. This
is again modeled as a move by "nature."If
centralization is ineffective, the result is an
outcome characterizedby high tax rates and
high evasion, with a net effect similar to the
customary tax equilibrium. If centralization
is effective, subjects face high costs for both
paying and evading. This is the situation in
which their last-resort option, revolt, becomes most likely.
Rulers respond to revolt either with repression or by conceding and lowering the
tax rate. If they choose repression, it may or
may not be effective (a move by "nature"as
above). If it is not effective, the result is an
unstable outcome characterized by high tax
rates and frequent revolts. If it is effective,
subjects will be forced to pay the higher tax
rates and endure the unpopularpolicies chosen by rulers.
We argue that this last outcome, a high
tax equilibrium, is what eventually happened in early modem France. Rulers often
chose to increase taxes and fight unpopular
offensive wars, especially in the seventeenth century. Subjects sometimes revolted, but most often increased their tax
evasion. Rulers responded by centralizing,
primarily with the use of intendants. This
centralization was in part successful, and
when it increased the costs of evasion, revolts became much more common, culminating in the largest revolt of all, the
Fronde. Rulers successfully used repression
against this revolt (and co-optation after it),
thus convincing subjects that future revolts
would be unlikely to succeed. The result
was a high tax equilibrium after the Fronde,
as French rulers were able to raise taxes and
fight offensive wars with little resistance
from their subjects. Our quantitative analy-
895
Table 1. Description of Variables Used in the
Analyses: Tax Revolt Initiations in
France, 1515 to 1789
Variable
Mean S.D.
Tax revolt initiation
(1 = yes)
.11
Total tax per capita
(in 100,000 it.)
5.06
Range
0-1
4.46
.87-37.12
Before and during
the Fronde(1 = yes)
.51
Administrativecentralization (1 = 1642 on)
.53
-
0-1
Estates General
(1 = yes)
.37
-
0-1
Warin progress
(1 = yes)
.65
0-1
Defensive war in
.34
0-1
.50
0-1
0-1
progress (1 = yes)
Offensive war in
progress (1 = yes)
ses and provincial case study provide tests
of many of the links in this causal chain.'2
DATA AND MEASURES
Table 1 describes the variables corresponding to the empirical expectations discussed
above, and Appendices A and B list the dates
of all revolts and wars. Measures of the independent variables are lagged to assure the
proper temporal order in our findings.
The descriptive statistics in Table 1 document several interesting features of early
modem Frenchhistory. The French state was
forged by force, both internally and externally. Revolts were relatively frequent
events, taking place in about 20 percent of
the years between 1515 and 1789. They were
initiated in about 11 percent of these years
(see Appendix A). Wars were in progress
during about 65 percent of the years during
this period. Offensive wars were somewhat
more common than defensive wars-France
was involved in offensive wars in about 50
percent of the years, and in defensive wars
in about 34 percent.
12Unfortunately,we cannot test all of the links,
due to lack of data. There are no systematic data
on tax evasion, for example.
896
REVIEW
REVOLTS
Our dependent variable is "tax revolt initiation." Coded dichotomously, it marks the
beginning of one or more tax revolts in a
particularyear.'3The data are compiled from
Heller (1991), Kiser et al. (1993), and Tilly
(1986, 1993). We include what Tilly (1993)
calls "revolutionarysituations,"in which the
rebels held considerable instrumentsof state
power, as well as regional events that he designates as "serious tax rebellions." These insurrections "stemmed from essentially the
same processes" (Tilly 1993:156).14 Both
shared the same objective-to lessen the tax
burden-and entailed similar risks. They often cost thousands of lives.
TAXATION
Due in part to fires in the treasury archives,
and in part to poor record-keeping by the
monarchy, data on taxation in early modem
Franceare incomplete and sometimes unreliable. Historians give very different estimates
of the tax revenues in a particular year-a
"reason for considerable caution" (Rasler
and Thompson 1989:133). Thus, it is essential to know the literaturewell so as to make
wise choices among conflicting figures. Our
estimates of gross total taxation drawheavily
on research by Guery (1978), Hoffman
(1986, 1996), and Rasler and Thompson
(1989).15 To arrive at a total tax amount for
each year, it was sometimes necessary to ex13 In some cases, more than one revolt started
in the same year (see Appendix A). An analysis
in which revolt initiation is coded as the number
of revolts beginning in a given year yields results
that are substantively similar to the ones we report.
141
In earlier analyses, we found that coding revolt initiation according to revolt severity did not
meaningfully alter our findings.
15 Direct taxation in early modern France took
two main forms: the taille, levied on property,
and capitation, levied on individuals. Collins
(1988), Clamageran (1980), Lewis (1968), and
Morineau (1968) offer considerable data on both
of these. Indirect taxes primarily include a variety of tariffs such as the gabelle, a salt tax; aides,
a tax levied on the consumption of a variety of
products; and traites, duties paid when merchandise was imported and/or sold.
trapolatebased on the data at hand. We have
done this by (1) subtracting nontax revenue
(revenue from crown lands and the sale of
offices) from the total revenue figure for a
given year, (2) aggregating data on all revenues contributing to total tax, or (3) carrying established figures from year to year.
Because we are interested in measuring
the real tax burden that French citizens bore,
we express taxation in terms of livres
tournois (1.t.) per capita.'6 Ideally, we would
include in our models a control for both real
wages and taxpayers' other main expenses
(such as rents and tithes), but we lack reliable and comprehensive data on these factors during the early modem period.'7
HISTORICAL TURNING POINT:
THE FRONDE
The Fronde was a large-scale set of revolts
with a very clear outcome. The crown
emerged victorious and the state subse16 The population of France increased by over
10 million during the time span considered here.
Dupaquier (1979) is our principal source of
population data. We also use estimates by Bean
(1973), Bonney (1979), and Wilson and Parker
(1977). When yearly estimates were unavailable
or contradictory, we smoothed the data between
benchmark figures, allocating an average rate of
population increase/decrease per year (cf. Goldstone 1991).
17 To explore the possibility that tax revolts really reflected a more general resentment toward
rising costs or shortages, we tested models including (1) the price of wheat, and (2) a standardized tax variable that reflects the amount of
wheat, in setiers (a common measure of grain
that ranged in volume from 150 to 300 liters),
that could be purchased with the per capita tax
revenue for a given year (Baulant 1968). The
wheat price variable was never significant, even
with per capita tax absent from the model. The
results of models with standardized tax are very
similar to those we report in Tables 1 and 2, although overall model fit was poorer. We also investigated the possibility that subjects responded
to nominal tax increases more than to the level
of taxation (Goldstone 1991; Le Roy Ladurie
1980:263). The annual percent change in nominal or standardized taxes was never significant.
This finding, however, does not conclusively discredit the proposition that tax increases prompted
revolts-to do so would require additional case
studies, preferably with better data.
quently became stronger and more centralized (Hoffman 1994:247; Mousnier 1979:
571, 624). Tilly (1986) argues that the "midseventeenth century served as a hinge in the
history of contention" (p. 40).
In the aftermath of the state's "military
victory" in the Fronde (Mousnier 1979:624;
also see Lachmann and Adams 1988:154),
several changes increased the power of the
state relative to potential rebels. After the
Fronde, a new law was passed confiscating
half of town revenues for the central state,
and intendants took more direct control of
town spending (Berce 1987:16-17; Doyle
1996:19; Mousnier 1979:572). Town walls
also atrophied after the Fronde. Towns expanded; tree-lined streets replaced old
moats; rings of boundary stones replaced
town walls (Berce 1987:54-55). Subjects
lost power in judicial institutions that had
been used to spreadinformationabout crown
policies contrary to their interests. Moote
(1971) argues that the limitation of the right
of remonstrance in law courts (parlements)
until after laws had been registered was "by
far the most successful aspect of the continuing royalist revival after the Fronde" (pp.
356-57). Localities and provinces lost an
important political tactic, substantial revenue, and the ability to defend against royal
attacks. The development of a standing army
also increased the costs of revolt by making
quick repression more likely (Ranum
1993:346). In these ways, the Fronde "extinguished local resistance to the fiscal offensive of the crown" (Berce 1987:17; also see
Parker 1983:119; Pillorget 1975:900-10).
The aftermath of the Fronde was marked
not just by repression but by concessions and
co-optation as well (Lachmann and Adams
1988; Tilly 1986:40), and this too made revolt less likely. Opposition to the state was
"subdued but not eradicated" after the
Fronde (Moote 1971:355). Therefore, Louis
XIV and subsequent rulers had to learn how
to compromise (Mettam 1988:3-4, 11-12).
They were more careful not to disrupt traditional privileges, and they provided additional lucrative state jobs to those elites
whose supportthey required (Lachmann and
Adams 1988:155-58).
As our argument suggests, the one important result of this clear state victory, coupled
with co-optation, is that potential rebels
897
learned that revolt was likely to be unsuccessful, so they shifted to more cautious and
covert forms of disobedience (Mettam
1988:3-4, 11-12; Parker 1983:102-03).18
Because the crown emerged victorious and
the state subsequently became stronger and
more centralized, it is probable that the
Fronde altered the relationship between
state-making and revolt. We therefore include a variable coded 1 for the years before
and during the Fronde (1515-1653), and 0
for the years thereafter.
ADMINISTRATIVE CENTRALIZATION
Direct tax collection in early modern states
was generally decentralized. In almost all
states, taxes were assessed and collected by
officials elected or appointed and controlled
locally, not by the central state. France was
no exception. Rulers generally negotiated
lump sum payments from regions and towns,
and left it to the locals to collect these taxes
as they saw fit (Markoff 1996:237). Although direct tax collection was never fully
centralized in early modern France (even the
revolution did not totally change this), there
was a major turning point in the seventeenth
century: the use of intendants (Kettering
1986:6). Parker(1983) notes that intendants
were the "principalagent through which the
concentration of authority was effected" (p.
81; also see Collins 1995:53). The intendants were part of a long list of royal attempts to use ad hoc commissioned officials,
centrally appointed and controlled, to supervise local tax collection (dating back to the
medieval bailiffs). Although Richelieu used
intendants, their numbers and their powers
were significantly increased in 1642, when
they were given full authority to supervise
tax collection (Bonney 1988:82). This was
the most important administrative transformation in direct tax administration prior to
the revolution, so we include a dummy variable for "administrative centralization" to
capture this shift.
18 Tilly (1993) remarks that post-Fronde revolts were different in substance from earlier uprisings. Although nominally still tax revolts, they
were more importantly protests against "the expense, arbitrariness, and corruption of the government"(p. 163).
898
REVIEW
WARS
Our war data come from Kiser et al. (1993,
1995), with additions for the eighteenth century from Dupuy and Dupuy (1977) (see Appendix B). The war variables are dichotomous. A value of 1 indicates that the state
was involved in a conflict during a given
year; a value of 0 for war or for both offensive and defensive war means that no war
took place. This allows us to assess the general relationship between war and revolt initiation, as well as to contrast the impact of
defensive and offensive wars.
NATIONAL AND PROVINCIAL
REPRESENTATIVE INSTITUTIONS
AS CONTROL VARIABLES
Subjects can attemptto negotiate with rulers
collectively to lower their tax obligations or
to modify policies, usually throughrepresentative political institutions. There are two
contrasting arguments about how the presence of representative institutions might affect revolt. First, they were important sites
for the exchange of informationbetween rulers and subjects (Mousnier 1979:215). By
increasing the flow of information between
parties, they could decrease the level of uncertainty and thus decrease the frequency of
revolt. Second, however, representative political institutions could enhance the collective action capacity of subjects and thus increase the frequency of revolt (Bonney
1978:347-48; Brustein and Levi 1987).19
19Collective action capacity is important, but
the main question involves the level at which
these institutions are most effective. Is it the
country as a whole (Estates General), provinces
(provincial estates), parishes (ad hoc meetings of
groups of communities), or local communes? Until its demise in 1614, the Estates General intermittently brought together representatives from
all over France. It served as a viable forum for
negotiation about taxes (Mousnier 1979:215;
Parker 1983:81), but was probably too large and
heterogeneous to facilitate collective action,
which was almost never organized at the level of
the country as a whole. Provincial estates, which
existed (decreasingly over time) in some regions
but not others, were forums for negotiation
(Collins 1994:23; Hoffman 1994:230; Mousnier
1979:610), but may also have been too large to
facilitate collective action. We suspect that lo-
Both of these possibilities, pushing in opposite directions, are consistent with the microfoundations of our model. We thus have no
clear prediction about the effects of representative institutions; it will depend on
which effect is stronger.We include both national and provincial representative institutions as control factors.
The broadest of these institutions was the
Estates General, a national legislative assembly comprised of representatives of the
clergy, nobility, and the primarily bourgeois
"third estate." It met intermittently until
1614, consulting kings on importantmatters
such as war and taxes, and presenting lists
of grievances. We therefore include a
dummy variable for the existence of the Estates General, coded 1 prior to 1615, and 0
after that. We also explore the role of the
provincial estates, even though we cannot
include them in our regression analyses. In
Table 4, we note, by region, whether a provincial estate existed when revolts were initiated. We discuss the effects of provincial
estates along with our regression results.
DATA ANALYSIS AND RESULTS
REVOLTS IN FRANCE:
REGRESSION ANALYSES
Some degree of autocorrelation is common
in time-series analysis. The logit regression
model does not provide for unmeasuredfactors affecting the occurrence of revolts, nor
does it allow for possible serial correlation
due to the dependence of the observations.
While this means that the estimates of the
coefficients are not efficient, they are consistent (Robinson 1982). For statistical inference we use QML (quasi-maximum likelihood) standarderrors, which are consistent
under misspecification of the model
cally based institutions were more important determinants of collective action capacity. Berce
(1987:75-76) stresses the importance of collective action at the parish level, with several communes (usually led by local notables) assembling
to discuss shared interests, including possible revolts. Unfortunately, systematic data on the
power and activities of these assemblies at the
parish and commune level are not available for
this period, so we cannot add this as a variable in
our quantitative analyses.
899
Table 2. Logit Coefficients from the Regression of Tax Revolt Initiation on Selected Independent
Variables: France, 1515 to 1789
IndependentVariable
Total tax per capita (in 100,000 i.t.)
(lagged one year)
Model 1
Model 2
-.114*
(.049)
Before and duringthe Fronde
1.296**
(.450)
Model 3
Model 4
-.249
(.275)
-.062
(.134)
-1.407
(.310)
.710*
Before and during the Fronde
x total tax per capita
(.310)
1.852*
Administrative centralization
(lagged one year)
Constant
AIC
2.532**
(.864)
(.845)
-1.161***
(.266)
180.35
-2.914***
(.388)
175.89
-1.107
(1.724)
157.75
-4.060***
(.984)
165.89
Note: N = 275 for each model. QML standarderrorsare shown in parentheses.
*** < .001 (two-tailedtests)
** <.01
*p<.05
(Arminger 1995; Gourieroux, Monfort, and
Trognon 1984; White 1982).20 The AIC
(Akaike information criterion) fit statistic
provides an accounting of use of degrees of
freedom, and is especially useful when comparing nonnested models such as these.
Comparatively small values indicate an improvement in fit.
The models in Table 2 test the degree to
which the level of taxation, the Fronde, and
administrative centralization influence the
likelihood of revolt initiation. By itself, the
level of taxation is negatively related to revolt initiation (Model 1). Taxes were highest
in the eighteenth century; revolts were least
frequent then. Models 2 and 3 incorporate a
dummy variable for the period before and
during the Fronde-alone and in interaction
with taxation. Model 3 specifically examines
the effect of the Fronde on the relationship
between taxation and revolt initiation. The
impact of taxation on the probability of revolt is positive before and during the Fronde,
whereas after the Fronde it is not significant.
This finding demonstrates quantitatively
what many historians have argued-that the
Fronde was indeed a key turning point in
20
We also rana modelof revoltinitiationthat
includeda laggeddependentvariable(revoltinitiationin thepreviousyear),andfoundverysimilar results. The lag did not contributesignificantlyto any of ourmodels.
French history which changed the relationship between state-making and revolt
(Collins 1995:77-78; Major 1994:xxi;
Mousnier 1979:571, 624). This is easy to see
graphically as well; although the Fronde divides the period covered in our study almost
exactly in half, there were more than three
times as many revolts prior to its conclusion
than after it. As we argued above, the decisive defeat of the rebels signaled to all subjects that revolts were unlikely to be successful strategies for opposing taxation
(Berce 1987:17; Mettam 1988:3-4, 11-12;
Pillorget 1975:900-910). After the Fronde,
rulers in France were able to raise taxes
without fear of revolt.
Model 4 incorporates administrative centralization after 1642. Here it appears that
both the period before and during the Fronde
and the years of direct tax centralization
were times in which revolts were likely to
begin. Ten revolt initiations-a third of the
total-occurred in the years for which positive values for these variables overlap: 1643
through 1653. In substantive terms, this effect is explained by opposition to the use of
intendants, central semibureaucratic royal
agents that increasingly intervened in direct
tax administration, eliminating some forms
of local corruption that had benefited subjects at the expense of the monarch
(Mousnier 1979:611; Pillorget 1975:50725). There is thus some supportfor the argu-
900
REVIEW
Table 3. Logit Coefficients from the Regression of Tax Revolt Initiation on Selected Independent
Variables: France, 1515 to 1789
Model 1
Model 2
Model 3
Model 4
Model 5
-.185
Total tax per capita
(in 100,000 It.) (lagged one year) (.168)
.022
(.115)
-.013
(.107)
-.081
(.107)
-.23
(.221)
Before and duringthe Fronde
.168
(.963)
1.487
(.814)
-.853
(1.071)
1.531*
(.730)
IndependentVariable
1.732*
(.768)
-2.497***
Estates General
-2.233***
(.639)
War in progress (lagged one year)
(.693)
1.984**
(.661)
Defensive war in progress
.647
.659
.198
(.409)
(.431)
(.435)
Offensive war in progress
1.378**
-.541
1.131*
(lagged one year)
(.507)
(.758)
(.581)
(lagged one year)
Before/during the Fronde
2.910**
x offensive war in progress
(1.006)
Constant
-1.516
(1.201)
-4.787***
(1.113)
-4.085***
(.999)
-2.268**
(.962)
-2.109
(1.253)
AIC
151.08
156.89
156.22
145.90
140.82
Note: N = 275 for each model. QML standarderrorsare shown in parentheses.
*p <.05
** < .01
*** < .001 (two-tailed tests)
ment that administrative centralization was
an additional aspect of state-making that
stimulated revolts, but its effect is temporally limited.
The models in Table 3 explore the effects
of representativeinstitutions and wars on the
probability of revolt. The odds of a revolt
initiation were almost 50 percent lower in
years when the Estates General convened. In
Model 1, both a restraining effect of the Estates General and a positive before/duringthe-Fronde effect are prominent. Half of the
revolt initiations that we consider occurred
between 1616 and 1653-years before or
during the Fronde, but after the Estates General ceased to meet. Including both "before
and during the Fronde" and "Estates General" markers in the same model (Model 1)
effectively shows that, although revolts were
much more likely to take place before or during the Fronde, this was not the case when a
central legislative body existed and met. This
finding suggests that the Estates General
worked not as a collective action mechanism
facilitating revolt, but as a forum for negotiation and information exchange that provided a less costly alternative to revolt.
Although we could not include provincial
estates in our regression analyses, we did
gather data to assess their effects on revolt
(see Table 4). Our data neither support our
argument that their presence decreased revolts, nor Brustein and Levi's (1987) contention that they facilitated revolt. Rather, we
find no significant difference in revolt initiation across provinces with and without
provincial estates, or across time in areas
where provincial estates met during only
some of the years from 1514 to 1789. Table
4 shows that 17 tax revolts occurred in provinces where and at times when provincial
estates met, whereas 18 took place where or
when they did not. When we compare blocks
of total province-years in which provincial
estates met (3,544 years) and did not meet
(7,681 years), we see that revolt initiations
happened .46 percent of the time in the first
block of years and .23 percent of the time in
the second. Revolts thus seem to be slightly
more likely when provincial estates were
present, thus providing a bit more support
for Brustein and Levi's view than for ours,
but the difference is too small to be substantively significant.
901
Table 4. Provincial Estates and Revolts by Province: France, 1514 to 1789
Revolt Initiations
Province
Anjou
Auvergne
Bearne
Berry
Bigorre
Boulonnais
Bourbonnaise
Bresse
Brittany
Burgundy
Champagne
Dauphind
Foix
Gavardan
Guyenne
he de France
Ile de R6
Ile d'Oleron
Labourd
Languodoc
Limosin
Maine
Marche
Marsan
Metz
Navarre
Nebouzan
Nivernais
Normandy
Orleanais
Picardy
Poitou
Provence
Quatre-Vallees
Saintonge
Saumurois
Soissonnais
Soule
Toul
Touraine
Verdun
Total
Provincial
Estates
No
No
Yes
No
Yes until 1622
Yes
No
Yes
Yes
Yes
No
Yes until 1628
Yes
Yes until 1622
Yes until 1622
No
No
No
Yes until 1622
Yes
No
No
No
Yes until 1622
No
Yes
Yes until 1622
No
Yes until 1655
No
No
No
Yes
Yes until 1622
No
No
No
Yes until 1622
No
No
No
Numberof Years Numberof Years
Provincial
ProvincialEstates
EstatesMet
Did Not Meet
When
When
EstatesDid
EstatesMet Not Meet
0
0
275
0
108
275
0
275
275
275
0
114
225
108
108
0
0
0
108
275
0
0
0
108
0
275
108
0
141
0
0
0
275
108
0
0
0
108
0
0
0
275
275
0
275
167
0
275
0
0
0
275
161
0
167
167
275
275
275
167
0
275
275
275
167
275
0
167
275
134
275
275
275
0
167
275
275
275
167
275
275
275
0
0
3
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
3,544
7,681
17
18
902
REVIEW
Getting back to Table 3, Models 2 and 3
contrast two ways of measuring war.21
Model 2 considers all wars together; Model
3 separates offensive and defensive wars.
Although the general war variable has the
expected effect, comparison reveals that the
type of war is of crucial importance: Offensive wars were responsible for the positive
effect of war on revolt initiation. This test
allows us to adjudicate between the three
possible causal mechanisms linking war to
revolt.
It seems clear now that the relationship
between war and revolt was not entirely due
to the costs of war. Although we unfortunately have no data on the costs of each
war, there is no reason to expect offensive
wars to be significantly more expensive,
and this would be accounted for by the tax
variable in any case. Nor is the relationship
due only to the weakening of the state due
to war, because if anything, defensive wars
might be expected to weaken the state more
(Tilly 1990:186; 1993:12). The strong effect of offensive war in Model 3 suggests
that subjects cared about how their tax
money was spent. They were willing to pay
for defensive wars that protected them from
external threats, but not for offensive wars
from which they expected few if any benefits and could pay very high costs
(Hopcroft 1999; Klaits 1976:87-88; Rowen
1980; Seyssel 1981:130-35). They seem to
have thought that defensive wars were public goods, but that offensive wars served
narrower interests (Levi 1988, 1997). Of
course, it would take a detailed cultural
analysis of subjects' reactions to different
types of wars to fully demonstrate this, and
that is beyond the scope of this paper.22
21
TheFrondevariableapproachessignificance
in thesemodels(p = .080 in Model2 and.068 in
Model5).
22 Buena de Mesquita, Silverson, and Woller
(1992) report that the outcome of wars, in conjunction with who initiated them, has a strong effect on revolt. We tried a fourfold differentiation
like theirs: successful offensive wars, lost offensive wars, successful defensive wars, lost defensive wars. We found, however, that whether an
offensive (or defensive) war was won or lost did
not change the relationships we report. Variables
that reflect outcome were nonsignificant in our
models.
Model 4 tests the proposition that the relationship between offensive wars-an unpopular policy-and revolt was weaker after the Fronde. Indeed, we find that offensive wars affect the likelihood of revolt
only in the period before and during the
Fronde.
Model 5 best fits the observed pattern of
revolt initiations.23It accounts for the combined effects of taxation, the Fronde, the Estates General, and wars. Here we see clear
evidence of the multiple causal mechanisms
linking state-making and revolts. Tax revolts
were not simply a response to high taxes;
they were facilitated or hindered by other
factors that are key to the state-making process-notably offensive wars and the presence or absence of representative institutions.
A PROVINCIALCASE STUDY:
REVOLTS IN GUYENNE
Figure 2 shows the geographic distribution
of tax revolts in France in three periods: the
reign of Francis I (1515-1548), the period
between the death of Francis I and the beginning of the Fronde (1549-1648), and the
years during and after the Fronde (16491789). In the first period, all of the revolts
occur in the south and southwest. The two
later periods show more geographical variation, although most revolts are still found in
the south and southwest. This pattern has
been documented and explained by Brustein
and Levi (1987) and Hopcroft (1999). Although our focus is on temporal variation,
the geographic concentration of revolts in
southern and southwestern France suggests
that it would be wise to look more closely
at these areas to provide an additional and
more precise test of our arguments.
We selected the province with the highest
rate of revolt in France, Guyenne -12 of the
36 tax revolts in early modern France occurred in this southwestern province.
Guyenne was part of the dramatic change in
the status of the Pays d'Etat in the seventeenth century, involving increases in taxation and centralization, and diminishing or
23 The fit is significantlybetter than that of
modelsin whichtax centralizationis substituted
for the EstatesGeneralvariable.
903
*
~~~~~~~~~*
f~~~
*
f
* 1514-1548
*
Figue 2
*+*i
*
R*
Figure 2. Tax Revolt Initiations in France, 1515 to 1789
eliminating the provincial estates.24Prior to
the seventeenth century, Pays d'Etat generally had more autonomy from the crown,
both legislatively (through provincial estates) and administratively,which usually allowed them to minimize their tax burden
relative to the more centrally controlled Pays
d'IElection.25This began to change between
24 Le Roy Ladurie (1980:201) argues that the
general factors causing revolts were similar
throughout southern France, and historians discussing the southern provinces mention the same
factors we have discussed for France as a
whole-taxes, war, centralization, the role of
provincial estates, and changes brought about by
the Fronde (Beik 1985; Collins 1994; Le Roy
Ladurie 1980:198, 201-202, 286; Major 1966;
Mousnier 1979:622-23; Westrich 1972; Wolff
1969:210, 230).
25 The assault on the Pays d'Etat did not affect
all provinces equally. Guyenne was a relatively
rich province (as indicated by high levels of meat
consumption [Ranum 1993:217-18]), known
then and now primarily for the export of great
wine (Bordeaux). In part because its wealth made
1549-1648
* 1649-1789
**
D
A
about 1620 and 1670 (Collins 1988:105), in
what Major (1994) calls a shift from a "renaissance monarchy" to an "absolute monarchy."
Tax increases were thus a key component
of this transformation. As Collins (1994)
puts it, "[K]ings saw the Pays d'Etat as an
untapped (or poorly tapped) financial resource. After 1628, [Louis XIII] dramatically raised taxes in all of them" (p. 152).
Although precise data are not available, the
significant tax increases that hit all of the
Pays d'Etat began in Guyenne in the 1620s
(Ranum 1993: 220).
To increase taxes, the administrative and
legislative autonomy of the Pays d'Etat were
decreased, and in some cases terminatedentirely (Barkey 1991:702). The process of administrative centralization (imposition of intendants) was complicated in Guyenne. Init an appealing place for monarchs to look for
more revenue, Guyenne was hit especially hard,
losing its Pays d'Etat status (Languedoc, for example, retained that status).
904
REVIEW
tendants were imposed, abolished, and then
re-imposed several times between 1616 and
1653 (after which they remained in place).26
The elimination of representative institutions mattered less is Guyenne than elsewhere. Even when it was a Pays d'Etat, the
provincial estates were always weak in
Guyenne and were virtually eliminated after
1621 (Collins 1994:154; Major 1966:369;
Parker 1983:81).27
With these rough measures of our independent variables at the provincial level, we
can now explore their effects on revolts in
Guyenne. Taxes alone had little effect-revolts were instigated in 4.7 percent of the
years prior to the major increases in 1623
and in 4.2 percent of the years after those
tax increases. However, just as for France as
a whole, adding the turning point of the
Fronde clarifies the relationship between
taxation and revolt. Revolts were three times
as likely in Guyenne before the Fronde, and
tax increases before the Fronde were over
five times as likely to cause revolts as were
tax increases after the Fronde (13 percent of
years with tax increases resulted in revolts
before the Fronde, compared with only 2.2
percent after the Fronde).
The effects of administrative centralization on revolts are similar-they too are
highly conditioned by the Fronde. In the preFronde period, the imposition of indendants
more than doubled the likelihood of revolt
initiation (revolts startedin about 13 percent
of years with intendants but in less than 5
percent of years without intendants prior to
the Fronde in Guyenne). Just as it did with
tax increases, the Fronde virtually eliminates
the relationship between administrativecentralization and revolt-the use of intendants
is more than five times more likely to produce revolt before the Fronde as after it.
War had a very strong effect on revolt in
Guyenne-11 of the 12 revolts in Guyenne
were initiated during a French war. Revolts
26 Intendants were present in Guyenne in 1616,
1619, 1622-1625, 1627-1628, 1630-1648,
1650-1651, and 1653-1788.
27 The estates in Languedoc, for example, were
always more powerful and met more frequently.
But although they survived the onslaught on the
Pays d'Etat, they were weakened substantially after 1663 (Hoffman 1994:230, 241; Major 1994:
346-47; Mousnier 1979:610-23).
were initiated in roughly 8 percent of years
experiencing warfare, but in less than 1 percent of the peaceful years. Revolts were
slightly more likely to occur during offensive wars, but that effect is not strong. Revolts were initiated in about 5 percent of
years with offensive wars, and in 3.6 percent
of years in which France was fighting a defensive war.
The presence of representativeinstitutions
had no effect on revolt in Guyenne. Neither
the Estates General nor the provincial estates
affected revolt initiation. (Because the provincial estates were always weak in
Guyenne [Major 1966], we would not expect
them to affect revolts.)
Overall, our results at the provincial level
are similar to those for France as a wholetaxation, administrative centralization, and
war (especially offensive war) are important
causes of revolts, and the effects of the first
two factors interact strongly with the
Fronde. Because these results are based on
only a few cases (12 revolts) and very rough
measures of some of our causal factors (i.e.,
taxation), we cannot make any strong conclusions based on this analysis of Guyenne.
However, its consistency with our nationallevel findings provides good evidence for
the robustness of our conclusions.
CONCLUSION
We model the relationship between statemaking and tax revolt as the product of strategic interactions between rulers and subjects. Both groups are making cost-benefit
calculations in which an important part of
the decision-making process is their anticipation of the actions of others. Neither rulers nor subjects have perfect information, so
both are expected to miscalculate sometimes. However, both are also expected to
learn over time, especially when outcomes
are clear and decisive, so experience should
lead to fewer miscalculations.28
28 We do not want to overstate the extent of
learning in this case. Although rulers did have
some information about the policies of prior rulers (and reactions to those policies), Peirson
(2000) is correct to note that learning is more difficult in the context of political institutions than
in the context of markets.
We find that the three main aspects of
early modern state-making-war, tax increases, and administrative centralizationall incited tax revolts in early modern
France. However, in each case, our findings
show that these relationships are complex
and often contingent on other factors.
Our initial analyses show an effect of war
on revolt, but this effect operates only
through offensive wars. When we decompose wars into offensive and defensive
types, our quantitativeresults show that only
offensive wars consistently generated revolts. Our provincial analysis of Guyenne
also shows a slightly stronger effect of offensive wars. This is consistent with our hypothesis, but the effect is stronger than we
anticipated. The opportunity for revolt
(based on the weakness of the state) was
clearly not all that mattered-subjects primarily reacted to how their tax money was
being spent. When wars were fought to defend them, subjects were more willing to
pay; when rulers pursuedoffensive wars that
seemed to provide few benefits, subjects frequently revolted. As Levi (1988, 1997) argues, subjects' compliance is in part a function of whether they think the state is providing them with public goods or not.
These findings help us explain the difference between the strong effects of war on
revolt found in most qualitative studies of
early modern states and the weak effects
found in quantitative studies of the nineteenth and twentieth centuries. Our quantitative analysis reinforces the qualitative
findings for early modern states, and suggests that the early modern period is indeed
different-that it is thus necessary to specify
a scope condition for the relationship between war and revolt. Perhaps the relationship between warfare and revolt changes
with the advent of nationalism in the nineteenth century (Hechter 2000). When "subjects" are transformed into "citizens" with
some stake in the wars of "their"country, a
"rally 'round the flag" reaction may become
more common than revolt. However, because our data do not extend to the nineteenth century, we cannot test this hypothesis.
Our control variable measuring the existence of representative institutions produced
mixed results. The Estates General tended to
905
suppress revolt in France as a whole, suggesting that it worked as a forum for negotiation and information exchange in early
modem France, but it had no effect on revolts in Guyenne. Moreover, we found no
effect for provincial estates-they did not
affect revolts in Guyenne, and had virtually
no effect in our rough analysis of France as
a whole.
The effects of taxation and offensive war
on revolt are complicated, due primarily to
the existence of a significant historical turning point in our period. As we anticipated,
the relationship between taxation and revolt
was very different before the Fronde than
after it. Prior to the Fronde, tax increases
tended to generate revolts; after the Fronde
they rarely did. The effects of offensive war
on revolt are similar, in that they too were
strongly affected by the Fronde. Offensive
wars generated revolts prior to the Fronde.
As with tax increases, the Fronde proved to
be a decisive turningpoint-indicated in this
case by the fact that offensive wars following the Fronde had no effect on revolt.
These findings clearly demonstrate that
history matters. Particularhistorical turning
points change the causal relationships between variables (Goldstone 1998; Issac and
Griffin 1989; Mahoney 2000; Peirson 2000).
In this case, the Fronde was a clear and decisive victory for the state over rebellious
subjects. The combination of repression and
co-optation that followed it significantly
changed the costs and benefits of revolt for
more than a century. After the Fronde, subjects less often thought of revolt as a potentially successful strategy for decreasing
taxes or opposing offensive wars, and statemaking proceeded relatively unimpeded.
Although our empirical analysis is limited
to France, we believe many of our arguments
could apply to other early modern states in
the process of state formation. For example,
other states could also have experienced turning points that transformed the relationship
between state-making and revolt. Although
further research would be necessary to test
this, it is possible that the "GreatRevolt" of
1381 in England and the Comuneros revolt
in Spain (1520-1521) may have played roles
similar to the Fronde. Both were responses
to state-making, increased taxation, and administrativecentralization(Elliott 1963:141-
906
REVIEW
49; Fryde 1981:9-11; Hopcroft 1999:74-75;
Thompson 1994:182-85). Fryde (1981) and
Hopcroft (1999) argue that the English tax
revolt remained in popular memory and
shaped the fiscal evolution of the English
state for centuries by defining the limits of
taxation (specifically, an invasive tax like the
poll tax would not be tolerated). The
Comuneros revolt in Spain, like the Fronde,
resulted in a decisive victory for the state
(Elliott 1963: 149; Thompson 1994:184).
After thatpoint, the Cortes was marginalized,
administrative centralization and taxes increased, yet "there were no more revolts in
Castile against the power of the crown"
(Elliott 1963:149). These and other turning
points may well be keys to increasing our understandingof early modern state formation
and reactions against it.
APPENDIX
Edgar Kiser is Professor of Sociology at the University of Washington. He has published articles
in sociology, political science, and economics
journals on topics including the determinants of
war and revolt, the development and decline of
voting institutions, the centralization and bureaucratization of state administration, and the
methodology of historical sociology.
April Linton is currently a visiting research fellow at the Office of Population Research,
Princeton University, and will be, effective July
2004, Assistant Professor of Sociology at the
University of California, San Diego. Her dissertation, completed in July 2002 at the Department
of Sociology, University of Washington, is titled
"Spanish for Americans? The Politics of Bilingualism in the United States." Currently she is
pursuing research about bilingualism and language policy, thefair trade movement, and revolutions that incite large-scale social transformations.
A
Tax Revolts in France, 1514 to 1789
Year
Location
Description
1514
Agen, Guyenne
Taxation and political exclusion
1528
Bordeaux, Guyenne
Excise tax on wine
1539
Marseille, Provence
Gabelle
1542
La Rochelle and Les Iles, Saintonge
Gabelle
1544
St. Maixent, Poitou
Taxation, religion
1545
Perigeux, St Foy, and Duras, NW Guyenne
Gabelle
1545
Sarlat, Niort, and Saintes, Poitou
Taxation
1545
St. Maixent, Poitou
Taxation
1548-1551
Guyenne
Pitaud insurrection
1594-1595
Guyenne
Croquantrebellions
1621-1622
Bearn
First Bearnese Revolt
1625-1626
B6arn
Second Bearnese Revolt
1627-1629
Bearn
Third Bearnese Revolt
1629-1630
Guyenne
Croquantuprising
1635-1636
Guyenne
Croquantuprising
1635-1636
Languodoc
Croquantuprising
1637-1641
Perigord and Quercy, Guyenne
Croquantuprising
1639
Normandy
Nu-pieds
1640
Moulins, Bourbonnais
Taxation
1640
Rennes, Brittany
Taxation
1641
Poitou
Taxation
1641
Saintonge
Taxation
1643-1644
Languodoc
Rouerge revolt in the South and West
1645
Montpellier, Languodoc
Taxation
1648-1653
Angers, Anjou
The Fronde
(Continued on next page)
(AppendixA continued)
Year
Location
1650-1651
Bordeaux, Guyenne
The Fronde
1650
Tulle, Limosin
The Fronde
1652
Guyenne, Ormee of Bordeaux
1655-1657
Guyenne
1658
Orldanais
Sabotiers rebellion
1661-1662
Guyenne
Benauge rebellion
1662
Boulonnais (Artois)
Lustucru rebellion
1663
Roussillon, Languodoc
Angelets guerilla warfare
1663-1670
Gascony, Guyenne
Audijos rebellion
1675
Brittany
Papier Timbre, Bonnets Rouges
(Torreben) rebellions
1789
French Revolution
Description
Tardanizatrebellion
Sources: Heller (1991); Kiser et al. (1993); Tilly (1986, 1993).
APPENDIX
B
Wars Involving the French, 1515 to 1788
Year
War
Type of Wara
1521-1526
First Italian War
Defensive
1526-1530
Second Italian War
Defensive
1535-1538
Third Italian War
Offensive
1542-1544
Fourth Italian War
Offensive
1544-1546
Anglo-French War
Defensive
1547-1559
Hapsburg-Valois War
Offensive
1549-1550
1557-1561
Anglo-French War
Anglo-French War
War of the Three Henries
Defensive
1609-1614
1624-1648
War of the Julich Succession
Offensive
French Thirty Years War
Offensive
1627-1628
Defensive
1628-1631
Anglo-French War
War of the Mantuan Succession
1642-1696
Iroquois-French War
1648-1659
1667-1668
Offensive
1672-1689
Franco-Spanish War
War of Devolution
Third Dutch War
1676-1679
Messian Rebellion
Offensive
1688-1697
1701-1714
War of the Grand Alliance
Offensive
Spanish Succession
Offensive
1718-1720
1733-1738
1744-1748
Quadruple Alliance
Polish Succession
King George's War
French and Italian War
Seven Years War
Corsican War
American Revolution
Defensive
Offensive
Defensive
Offensive
Defensive
Offensive
Offensive
1589-1598
1754-1763
1756-1763
1764-1769
1775-1783
a
We define wars initiated by powers other than France as defensive wars.
Sources: Dupuy and Dupuy (1977); Kiser et al. (1993, 1995).
Defensive
Offensive
Defensive
Defensive
Offensive
Offensive
907
908
APPENDIX
REVIEW
C
Pearson Correlation Coefficients for Variables Used in the Regression Analyses of Tax Revolt
Initiation in France, 1515 to 1789
Variable
Variable
(1)
(1) Revolt Initiation
1.000
(2) Total tax per capita
-.129*
(3) Before/during the Fronde
.183**
(4) Administrative centralization
-.094
(5) Estates General
-.073
(3)
(2)
(4)
(5)
(6)
(7)
(8)
1.000
-.776*** 1.000
.776*** -.923*** 1.000
.754*** -.816*** 1.000
-.705***
(6) War
.185**
.039
-.152**
.211*** -.227*** 1.000
(7) Defensive war
.068
.012
-.223***
.334*** -.279***
.516*** 1.000
(8) Offensive war
.185**
.077
-.055
.135*
.741***
-.206***
.120*
1.000
Note: All independent variables are lagged one year.
*** < .001 (two-tailed tests)
** <.01
*p <.05
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Hardnose the Dictator
By TODD L . CHERRY, PETER FRYKBLOM, AND JASON F . SHOGREN*
Lab experiments have gone to extremes to
isolate and repress other-regarding behavior in
extensive-form bargaining games, with limited
success. Consider, for example, Elizabedi Hoffman et al.'s (19%; hereafter HMS) Anonymous
Dictator game. This game controls self-interested
strategic behavior by giving a person complete
control over the distribudon of wealth, and complete anonymity from all others including the
experimenter. While theory predicts people wilh
complete control and complete anonymity will
offer up nodiing to others, in fact diey sdll share
die wealdi in about 40 percent of die observed
bargains. Such other-regarding choice is another example in which individual behavior differs from that predicted by subgame perfection,
and supports the call for a new "behavioral
game dieory" (Colin F. Camerer, 1997).
Herein we extend the work of HMS to reveal
a setting in which 95 percent of dictators follow
game-theoredc predictions. In contrast to previous studies, our design has people bargain over
eamed wealth rather than uneamed wealth
granted by the experimenter. We aigue that just
as rewaids must be salient (Kyung Hwan Baik
et al., 1999), the assets in a baigain must be
legidmate to produce radonal behavior.' Our
results support this conjecture. Dictators bargaining over eamed wealth were more selfinterested than observed in previous studies;
* Cheny: Depaitment of Economics, Appalachian State
Univeisity, Boone. NC 28608; Ftykblom: Department of
Economics. Swedish Univenity of Agricultural Sciences.
Uppsala, Sweden: Shogren: Department of Economics and
Fmance. University of Wyoming. Laramie. WY 82071.
This research benefited grndy fiom Cheny's visit to the
Economic Science Laboiatoiy at dw Univeisity of Arizona.
Financial suppoit was partially provided by STINT, the
Univeisity of Central Florida, and dw Bugas Fund at dw
University of Wyoming. Charles Holt, Stephan Kroll, John
List, Nicholas Rupp, and an anonymous referee provided
helpful comments.
' While diis proposidon has not been explicidy examined in bargaining behavior, diere is closely related work
widiin dw economics and psychology literature: for example, found-money effiect and mental accoundng (e.g.. Milton
Friedman, 1957; James P. Keeler et al.. 1985; Richard
Thaler, 1990: Hal Arices et al.. 1994; James Konow. 2000).
and when they had complete anonymity, selfless
behavior is essendally eliminated.
L Ex
PreUminaries.—Subjects wererecruitedfrom
die undeigraduale student body at die University of Central Florida. All subjects were unfamiliar with bargaining games. We conducted
three sessions, each having 52 or 61 bargaining
pairs. Participants were randomly assigned to
two groups, split into rooms A and B. The two
groups did not have any contact before, during,
or after the session. Subjects were only allowed
to talk to administrators.
Stages.—The experiment had two stuges
(eamings and bargaining), each with a written
protocol to ensure consistency. The eamings
stage had subjects in Room A participate in a
money-eaming session without knowledge of
die second bargaining stage. Subjects eamed
money by taking a quiz containing 17 questions
taken from the sample secdon of the Graduate
Management Admission Test (GMAT).- The
amount eamed was determined by the following
mle: if the subject answered at least ten quesdons correcdy, he or she would eam $40; otherwise, he or she received $10. Subjects knew
they had 45 minutes to complete the quiz. After
the dme elapsed, the monitors collected and
graded the quizzes, and distributed cash eamings to each subject in confidence according to
the specified eamings mle. After receiving their
money, the subjects who eamed $40 were put in
a separate room (Room Al) from those who
eamed $10 (Room A2).
The bargaining stage randomly matched subjects in Room Al and A2 with diose in Room B
to form baigaining pairs. The person in Room A
was thefirstmover (i.e.. dictator) and bargained
over his or her eamed wealth. Instmctions for
-The instrucdons are available upon request and the
earnings quiz is provided in John A. List and Cheny (2000).
Pilot sessions indicate die effect of dw earnings session is
robust acioss tasks other than a quiz.
1218
VOL 92 NO. 4
CHERRY ETAL: HARDNOSE THE DICTATOR
the dictator game were read aloud to both
groups.^ All bargaining games were one-shot,
and players had complete information. For each
pair, the player in Room Al or A2 dictated a
split of his or her wealth with the person in
Room B. Administrators carried the offers from
Room Al and A2 to Room B. Final eamings
were paid according to the dictated split, and
subjects departed one at a time with their cash
payment. This concluded the bargaining stage,
and ended the session.
1219
The only adjustments we make to incorporate
the eaming session with HMS's isolation design
is to separate those that eamed $40 versus $10,
and adjust the number of blank slips of paper in
the envelopes; 40 slips and bills, or 10 slips and
bills.
n. Resuits and Condnsion
Figures 1 and 2 provide the cumulative distributions from our low- and high-stakes experiments. Results indicate that other-regarding
Treatments.—^Based on the two-stage design, behavior is greatly diminished when bargaining
involves eamed wealth, and this behavior is
we created three treatments: baseline, eamings,
nearly eliminated when eamed stakes are comand double blind with eamings. Given the dichotbined with anonymity.
omous outcome of earnings, each of the three
In the baseline treatments, the theoretically
treatments had a high- and low-stakes session. In
predicted "zero offer" occurred in 19 percent of
the baseline treatment (B), subjects did not particthe low-stakes bargains and 15 percent of the
ipate in an eamings stage prior to the baigaining
high-stakes bargains. In contrast, legitimizing
stage. As in previous studies, dictates in Room A
wealth with an eamings session prior to barwere provided their wealth by the experimenter.
gaining dramatically reduced off-equilibrium
Specifically, subjects were tokl that "$X has been
provisionally allocated to each pair and the person behavior, with zero offers arising in 79 and 70
percent of the bargains in the low- and highin Room A can propose how much of this each
stakes eamings treatments. As the diagrams
person is to receive." Dictators were allocated
illustrate. Fisher's exact and Wilcoxon tests reeither $40 or $10 to provide a clean comparison to
veal that the proportions of nonzero offers and
the two potential eamings outcomes.
the distribution of offers in the eamings treatIn the eamings treatment (E), subjects in
ments are significantly lower than those found
Room A participated in the eamings stage prior
in the baseline treatments (p < 0.0000 in all
to the bargaining stage. Instructions informed
cases).^
all subjects that "the person in Room A has
eamed an amount of money by participating in
Now consider the double-blind eamings treata previous session" and "the person in Room B
ment. When isolated dictators acted over eamed
has not had the opportunity to eam any money."
wealth, self-interested game-theoretic behavior
Further, they were informed "the person in
was the norm. Bargainers made zero offers 95
Room A decides how much of his or her eamings they are to receive and how much of his or
her eamings the person in Room B is to rethe administrator reads the instructions aloud; (c) each perceive." For time management, subjects in Room
son in Room A individually and randomly selects one of
N + 2 opaque envelopes, in which N envelopes contain 10
B arrived one hour after those in Room A.
(or 40) one-dollar bills and 10 (or 40) slips of paper, and the
The double blind with earnings (DBE) treattwo additional envelopes contain 20 (or 80) slips of blank
ment was identical to the eamings treatment,
paper: (d) subjects open the envelope behind a large cardexcept that the bargaining stage was identical to
board box and decide how many bills to leave for tbe person
in Room B, where slips of paper replace bills to ensure
the Double Blind 1 (DBl) protocol in
'*
^ As in HMS, we used the experimental instructions from
Robert Forsythe et al. (1994) as the baseline with the adjustment to incorporate whether die wealth was eamed or
allocated. We note that it was common knowledge whether
the stakes were eamed or allocated but only dictators knew
of the two stake levels ($10 vs. $40).
* In the DB 1 experiment, (a) the administrator chooses a
subject from Room A to oversee the bargaining stage: (b)
consistency in envelope thickness; (e) subjects seal the
envelope and drop it in a box as they exit; (f) the process is
repeated for all people in Rooms Al and A2; (g) the
administrator takes the box of envelopes outside of the door
of Room B; (h) people in Room B individually exit, in
which they randomly select an envelope and the contents
arerecordedby the administrator; (i) this process is repeated
for eveiyone in Room B; and (j) the experiment concludes
with the payment of the overseer selected in step (a).
' The Wilcoxon test statistic was W = 4.S7 for high
stakes and W = 4.32 for low stakes.
1220
THE AMERICAN ECONOMIC REVIEW
4
SEPTEMBER 20O2
5
6
Offer (USS)
RGURE I. CUMULATIVE DISTRIBUTIONS OF OFFERS IN THE $10 DICTATOR GAME.S
FIGURE 2. CIAIULATIVE DISTRIBUTIONS OF OFFERS IN TOE $40 DICTATOR GAME.S
percent of the time in the double-blind eamings
treatments and 97 percent of the time in the
high-stakes treatment. Such hardnose behavior
by dictators stands in stark ccmtrast to previous
work that reports only 20-60 percent of observed behavior adhere to subgame perfection.
The frequency of nonzero offers and the distribution of offers observed in the double-blind
eamings sessions is significantly lower than
those in the baseline (p < 0.0000). Comparing
the double-blind eamings and the straight eamings treatments, tests indicate that the increased
anonymity from the double-blind pmtacol significantly lowered the frequency and distribution of off-equilibrium behavior in the highstakes sessions (Fisher's exact, p < 0.007;
IV = 3.14, p = 0.002). Tests were less con-
vincing for the low-stakes sessions (Fisher's
exact, p = 0.256 and W = 1.40, p = 0.16).*
We conclude with two observations that have
broader implications. First, legidmizing wealth
with effort is no less important than controlling
reciprocity in explaining other-regarding behavior in simple bargaining games. It follows that
asset origin could affect the degree of anomalistic behavior witnessed in other experimental
settings. WindfaU wealth, for instance, might
explain the lack of free-riding in the provision
of public goods in the lab(»atory. Second, asset
" Note tiiat behavior was statistically equivalent across
^ and low stakes. Uw result of no wealtii efftcts witii
eamed money conesponds to previous findings witii allocated wealtii (e.g., Foisytiw et al.. 1994).
VOL 92 NO. 4
CHERRY ETAL: HARDNOSE THE DICTATOR
origin combined with isolation closed a longstanding gap between standard game theoiy and
observation. When assets are legitimized with
effort and strategic concems are controlled with
isolation, altmism was the exception and selfinterest was the mle. Strategic concems—not
faimess—appear to be the motivation for otherregarding behavior when people baigain over
eamed wealth. This raises the question of when
the efforts to explain the gq> generated by windfall assets are necessaiy.
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and Sefton, Martin. "Faimess in Simple Bar-
1221
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Konow, James. "Fair Shares: Accountability and
Cognitive Dissonance in Allocation Decisions." American Economic Review, September 2000, 90(4), pp. 1072-91.
List, John A. and Cherry, Todd L. "Leaming to
Accept in the Ultimatum Game: Evidence
fiom an Experimental Design that Generates
Low Offers." Experimental Economics, June
2000, J(l), pp. 11-29.
Thaler, Richard. "Savings, Fungibility, and
Mental Accounts." Joumal of Economic
Perspectives, Winter 1990, 4(1), pp. 193205.
In Search of Homo Economicus: Behavioral Experiments
in 15 Small-Scale Societies
By JOSEPH HENRICH, ROBERT BOYD, SAMUEL BOWLES, COLIN CAMERER, ERNST FEHR,
HERBERT GINTIS, AND RICHARD MCELREATH*
Recent investigations have uncovered large,
consistent deviations from the predictions of the
textbook representation of Homo economicus
(Alvin E. Roth et al,, 1991; Ernst Fehr and
Simon Gachter, 2000; Colin Camerer, 2001),
One problem appears to lie in economists' canonical assumption that individuals are entirely
self-interested: in addition to their own material
payoffs, many experimental subjects appear to
care about fairness and reciprocity, are willing
to change the distribution of material outcomes
at personal cost, and are willing to reward those
who act in a cooperative manner while punishing those who do not even when these actions
are costly to the individual. These deviations
from what we will term the canonical model
have important consequences for a wide range
of economic phenomena, including the optimal
design of institutions and contracts, the allocation of property rights, the conditions for successful collective action, the analysis of
incomplete contracts, and the persistence of
noncompetitive wage premia.
Fundamental questions remain unanswered.
Are the deviations from the canonical model
evidence of universal patterns of behavior, or do
the individual's economic and social environ* Henrich: School of Business Administration, University of Michigan, Ann Arbor, Ml 48109; Boyd and McElreath: Department of Anthropology, University of
California at Los Angeles, Los Angeles, CA 90095;
Bowles: Department of Economics, University of Massachusetts, Amherst, MA 01003, and Santa Fe Institute; Camerer: Department of Economics, California Institute of
Technology, Pasadena, CA 91125; Fehr: Institute for Empirical Research in Economics, University of Zurich, Blumlisalpstrasse 10, CH-8006, Zurich, Switzerland; Gintis;
University of Massachusetts, Amherst, MA 01003, The
research described in this paper was funded by the
MacArthur Foundation's Research Group on the Nature and
Origin of Norms and Preferences, directed by Robert Boyd
and Herbert Gintis. The field experiments were carried out
by Henrich, MeElreath, Michael Alvard, Abigail Barr, Jean
Ensminger, Francisco Gil-White, Michael Gurven, Kim Hill,
Frank Marlowe, John Patton, Natalie Stnith, and David Tracer.
ments shape behavior? If the latter, which economic and social conditions are involved? Is
reciprocal behavior better explained statistically
by individuals' attributes such as their sex, age,
or relative wealth, or by the attributes of the
group to which the individuals belong? Are
there cultures that approximate the canonical
account of self-regarding behavior?
Existing research cannot answer such questions because virtually all subjects have been
university students, and while there are cultural
differences among student populations throughout the world, these differences are small compared to the range of all social and cultural
environments. To address the above questions,
we and our collaborators undertook a large
cross-cultural study of behavior in ultimatum,
public good, and dictator games. Twelve experienced field researchers, working in 12 countries on five continents, recruited subjects from
15 small-scale societies exhibiting a wide variety of economic and cultural conditions. Our
sample consists of three foraging societies, six
that practice slash-and-bum horticulture, four
nomadic herding groups, and three sedentary,
small-scale agriculturalist societies. Our results
are described in detail, with extensive ethnographic accounts of the cultures we studied and
citations to the relevant literature, in Henrich et
al. (2001); an extended overview paper is available online.'
We can summarize our results as follows.
First, the canonical model is not supported in
any society studied. Second, there is considerably more behavioral variability across groups
than had been found in previous cross-cultural
research, and the canonical model fails in a
wider variety of ways than in previous experiments. Third, group-level differences in economic organization and the degree of market
' URL: {www.santafe.edu)
73
AEA PAPERS AND PROCEEDINGS
74
integration explain a substantial portion of the
behavioral variation across societies: the higher
the degree of market integration and the higher
the payoffs to cooperation, the greater the level
of cooperation in experimental games. Fourth,
individual-level economic and demographic
variables do not explain behavior either within
or across groups. Fifth, behavior in the experiments is generally consistent with economic
patterns of everyday life in these societies.
I. The Evidence
Because the ultimatum game (UG) has been
conducted throughout the world with student
populations and has generated robust violations
of the canonical model, we conducted this game
in all of our 17 societies. The "proposer" in this
game is provisionally assigned an amount
equivalent to a day or two's wages in the society
and asked to propose an offer to a second person, the "respondent." The respondent may then
either accept the offer, in which case the two
players receive the proposed amounts, or reject
it, in which case the two receive nothing. If both
players conform to the canonical model and if
this is common knowledge, it is easy to see that
the proposer will know that the respondent will
accept any positive offer and so will offer the
smallest possible amount, which will be
accepted.
In most of our field experiments subjects
played anonymously, not knowing the identity
of the person or persons with whom they were
paired. The stakes of most games were denominated in money (though in some cases tobacco
or other goods were used). In all cases, we
tested prospective participants for their comprehension of the experiment and eliminated any
who appeared not to grasp the game.
The systematic deviations from the canonical
model in our sample of simple societies can be
inferred from Table 1, which lists all groups
where UG's were conducted. Contrary to the
prediction of the standard model, even the
groups with the smallest offers have mean offers greater than 25 percent of stake size. Illustrating our second result (the large variation in
mean offers across societies), others, including
the Torguud and the Mapuche, offered between
30 percent and 40 percent, while still others,
including the Achuar and the Sangu, offered
MAY 2001
TABLE 1—THE ULTIMATUM GAME IN SMALL-SCALE
SOCIETIES
Group
Macbiguenga
Country
Peru
Mean
offer"
0.26
Tanzania
Hadza
(big camp)
Tanzania
Hadza
(small
camp)
Tsiman6
Bolivia
0.40
Quichua
Ecuador
0.27
Torguud
Mongolia
0.35
Khazax
Mapuche
Mongolia
Chile
0.36
0.34
Au
PNG
0.43
Gnau
PNG
0.38
0.27
(38)
0.37
Sangu
farmers
Sangu
herders
Unresettled
villagers
Resettled
villagers
Achuar
Tanzania
0.41
Tanzania
0.42
Zimbabwe
0.41
Zimbabwe
0.45
Ecuador
0.42
Orma
Kenya
0.44
Achi
Paraguay
0.51
Lamelara^
Indonesia
0.58
Lowoffer
rejection
rate''
Modes'"
Rejection
rate'
0.15/0.25
(72)
0.50
(28)
0.20
(8/29)
0.048
(1/21)
0.19
(5/26)
0.28
(5/16)
0.10
(I/IO)
0.80
(4/5)
0.31
0.5/0.3/0.25
(65)
0.25
(47)
0.25
(30)
0.25
0.50/0.33
(46)
0.3
(33)
0.00
(0)70)
0.15
(2/13)
0.05
(1/20)
0.00
(0/5)
0.50
(i/2)
0.00
(0/1)
0.067
(2/30)
0.27
(8/30)
0.2
(2/10)
1.00
(1/1)
0.50
(3/6)
1.00
(1/1)
1.00
(1/1)
0.33
(2/5)
0.57
(4/7)
0.00
(0/1)
0.00
(0/0)
0.00
(0/8)
0.00
(4/20)
0.4
(32)
0.50
(35)
0.50
(40)
0.50
(56)
0.50
(70)
0.50
(36)
0.50
(54)
0.50/0.40
(75)
0.50
(63)
0.4
(10/25)
0.25
(5/20)
0.05
(1/20)
0.1
(3/31)
0.07
(12/86)
0.00
(0/16)
0.04
(2/56)
0.00
(0/51)
0.00
(3/8)
Note: PNG = Papua New Guinea.
° This column sbows the mean offer (as a proportion) in the ultimatum
game for each society.
"•Tbis column shows the modal offer(s), with the percentage of
subjects who make modal offers (in parentheses).
" The rejection rate (as a proportion), with the actual numbers given in
parentheses.
'' Tbe rejection rate for offers of 20 percent or less, with the actual
numbers given in parentheses.
' Includes experimenter-generated low offers.
between 40 percent and 50 percent. Finally, the
Ache and the Lamelara had mean offers greater
than 50 percent.
These group differences are strikingly large
compared to previous cross-cultural work comparing ultimatum-game behavior among university students (Roth et al., 1991). While mean
offers in industrial societies are typically close
to 44 percent, the mean offers in our sample
range from 26 percent to 58 percent. Similarly,
while modal offers are consistently 50 percent
VOL 91 NO. 2
ECONOMICS AND SOCIAL BEHAVIOR
in industrialized societies, our sample modes
vary from 15 percent to 50 percent.
As shown in the last two columns of Table
1, rejections are also much more variable than
previously observed. While in industrial societies offers below 20 percent are rejected with
probability 0.40 to 0.60, rejections of low offers
are extremely rare among some groups. In other
groups, however, we observe substantial rejections rates, including frequent rejections of offers above 50 percent. Among the Achuar, Ach6
and Tsimane, we observe zero rejections after
16, 51, and 70 proposer offers, respectively.
Moreover, while the Ach6 and Achuar made
fairly equitable offers, nearly 50 percent of Tsiman6 offers were at or below 30 percent, yet all
were accepted. Similarly, Machiguenga responders rejected only one offer, despite the
fact that over 75 percent of their offers were
below 30 percent. At the other end of the rejection scale, Hadza responders rejected 24 percent
of all proposer offers and 43 percent of offers at
20 percent and below. Unlike the Hadza, who
preferentially rejected low offers, the Au and
Gnau of Papua New Guinea rejected both unfair
and hyper-fair (greater than 50 percent) offers
with nearly equal frequency.
In experiments with university subjects,
offers are generally consistent with incomemaximization, given the distribution of rejections. In our sample, however, in the majority
of groups the modal behavior of the proposers is not consistent with expected incomemaximization. In the Tsimane and Ach6 cases,
for instance, there are no rejections of offers
below 20 percent, although there were several
low offers. The rejection rate for all other
offers is also zero. Yet the modal offer in both
groups is 50 percent, and the average offers
are 37 percent and 51 percent, respectively.
Where possible, we used the relationship
between the size of the offer and the fraction of rejections to estimate income-maximizing offers for the group in question. In one
group, the Hadza proposers approximated the
income-maximizing offer quite closely, thus
confirming the canonical model; but Hadza
responders frequently rejected substantial
positive offers, thus violating the canonical
model. In all other groups, average offers
exceeded the income-maximizing offer, in
most cases by a substantial amount.
75
Data from public-goods games played in
seven of these societies also show much greater
variation than previously found, and again they
exhibit novel deviations from the predictions of
the canonical model. Public-goods games ask
subjects to contribute to a common pool that
will be expanded by the experimenter and then
redistributed to all subjects. The canonical
prediction is that everyone will free-ride, contributing nothing. Typical distributions of publicgoods game contributions with students have a
U-shape, with the mode at contributing nothing,
a secondary mode at full cooperation, and mean
contribution between 40 percent and 60 percent.
By contrast, for instance, the Machiguenga have
a mode at contributing nothing, with not a single subject cooperating fully, yielding a mean
contribution of 22 percent. Also, the Achd and
Tsiman6 both exhibit inverted distributions,
with few or no contributions at full free-riding
or full cooperation.
In three dictator games played in three of
these societies, groups also deviate both from
typical behavior in industrialized societies and
the canonical predictions. The dictator game
allows the proposer simply to assign some fraction of the stake to a passive second party who
receives that amount. Among university students, the distribution of "offers" in the dictator
game typically has a mode at zero and a secondary mode at 50/50, while the canonical
model predicts that people will give zero. Contrasting with both, the Orma have a mode at 50
percent and a secondary mode at 20 percent.
Hadza dictators show a mode at 10 percent.
Offers of 0 percent and 50 percent are also
popular. Among the Tsiman6, there were no
zero offers; the mean was 32 percent, and the
mode was 25 percent,
II. What Explains Group-Level Differences?
The large variations across the different
cultural groups suggest that preferences or expectations are affected by group-specific conditions, such as social institutions or cultural
fairness norms. The large variance in institutions and norms in our sample allowed us to
address this question systematically. Because of
space limits we here concentrate on the behavior of proposers in the UG, We rank-ordered the
societies along two dimensions:
76
MAY 2001
(i) Payoffs to cooperation (PCj.—How important and how large is a group's payoff from
cooperation in economic production?
(ii) Market integration (MI).—How much do
people rely on market exchange in their
daily lives?
On the first dimension, payoffs to cooperation, the Machiguenga and Tsimane rank the
lowest; they are almost entirely economically
independent at the family level and engage
rarely in productive activities involving more
than members of a family. By contrast, the
Lamelara whale-hunters go to sea in large canoes manned by a dozen or more individuals.
The rationale for PC as a predictor of UG offers
is that with little cooperative production there
will be little necessity to share returns, while
those whose livelihood depends on large-scale
cooperation like the Lamelara must develop
ways of sharing the joint surplus. Thus we
might expect that a higher level of PC will
increase sharing behavior in the UG. The rationale for market integration as an explanatory
variable is that the more frequently people experience market transactions, the more they will
also experience abstract sharing principles concerning behaviors toward strangers of which the
UG is an example.
We sought to explain group mean UG offers
on the basis of these two dimensions of economic structure. In a regression, both PC and
MI were highly significant, their (positive) normalized regression coefficients were large in
magnitude (about 0.3), and the two measures
jointly explained 68 percent of the variance.
The impact of PC and MI remains large and
robust in an equation predicting individual offers, including individual measures such as sex,
age, relative wealth, village population size,
stake size, and experimenter experience with the
group. Surprisingly, none of these individual level
measures was significantly related to offers.
A plausible interpretation of our subjects'
behaviors is that, when faced with a novel situation (the experiment), they looked for analogues in their daily experience, asking "What
familiar situation is this game like?" and then
acted in a way appropriate for the analogous
situation. For instance, the hyper-fair UG offers
(greater than 50 percent) and the frequent rejections of these offers among the Au and Gnau
reflect the culture of gift-giving found in these
societies. Among these groups, like many in
New Guinea, accepting gifts, even unsolicited
ones, commits one to reciprocate at some future
time to be determined by the giver. Receipt of
large gifts also establishes one in a subordinate
position. Consequently, excessively large gifts,
especially unsolicited ones, will frequently be
refused because of the anxiety about the unspecific strings attached. Similarly the low offers
and high rejection rates of the Hadza appear to
reflect their reluctant process of sharing (termed
"tolerated theft" by a leading ethnographer of
the Hadza). While the Hadza extensively share
meat, many hunters look for opportunities to
avoid sharing and share only because they fear
the social consequences of not sharing, in the
form of informal social sanctions, gossip, and
ostracism. This behavior is apparently transferred to the experimental setting.
Unlike the Hadza, the Ache did not reject low
offers, and despite this the vast majority of the
Ache (94 percent) made offers above 40 percent
of the stake size. This coincides neatly with
ethnographic descriptions indicating widespread
meat-sharing and cooperation in community
projects despite the absence of a fear of punishment in Ache society. Ache hunters, returning
home, quietly leave their kill at the edge of
camp, often claiming that the hunt was fruitless;
their catch is later discovered and collected by
others and then meticulously shared among all
in the camp. We think it likely that the stake in
the game seemed to some of the Ach^ subjects
as analogous to their catch.
The Machiguenga show the lowest cooperation rates in public-good games, reflecting ethnographic descriptions of Machiguenga life,
which report little cooperation, exchange, or
sharing beyond the family unit. By contrast,
Orma experimental subjects quickly dubbed the
public-goods experiment a haramhee game, referring to the widespread institution of villagelevel voluntary contributions for public-goods
projects such as schools or roads. Not surprisingly, they contributed generously (58 percent
of the stake), somewhat higher than most U.S.
subjects contribute in similar experiments.
III. Discussion
Our data indicate that the degree of cooperation, sharing, and punishment exhibited by
VOL 91 NO. 2
77
ECONOMICS AND SOCIAL BEHAVIOR
experimental subjects closely corresponds to
templates for these behaviors in the subjects'
daily lives, and that the substantial variability in
experimental behaviors across groups is an expression of the large between-group differences
in the structures of social interaction and modes
of livelihood. How do we interpret these results?
Some of the variability among groups may be
due to variations in implementation. We doubt
that this explains the markedly differing behaviors across groups, however, since the experiments were run from identical protocols across
groups and were thus as similar in procedures
and stake size as we could achieve. Where we
could test for experimenter effects we found
none. It is possible also that our subjects presumed that their actions would somehow become public. In a good many of our cases,
however, subsequent conversations with participants convinced us that this was not the case.
Finally, it could be that participants thought
they were in a repeated interaction, even though
the games we used were clearly one-shot. We
do not find this interpretation compelling, however, since there is extensive evidence from
experiments in advanced economies that subjects understand the game very well, and those
who reject a positive offer in the ultimatum
game, when interviewed by the experimenter,
typically do not say that they made an error, but
rather affirm having goals besides maximizing a
monetary payoff.
Why are many subjects willing to share
resources and undertake costly reciprocal actions in anonymous one-shot interactions?
Bowles et al, (2001) will provide a more
extensive response than can be offered here.
We suspect that a proximate reason for these
behaviors is that situations cue emotional responses which induce the behaviors we have
measured. For example, many ultimatumgame responders from advanced societies,
when facing a low offer, experience an emotional impulse to hurt the proposer for being
unfair, just as the subject might in a real-life
bargaining situation. Similarly, the New Guinea
responders who rejected hyper-fair offers in the
UG may have experienced the same anxiety that
emerges when somebody gives them an unsolicited gift in everyday life.
What are the ultimate determinants of our
emotions and situation-specific cues? Here
long-run evolutionary processes governing the
distribution of genes and cultural practices
could well have resulted in a substantial fraction
of each population being predisposed in certain
situations to forgo material payoffs in order to
share with others, or to punish unfair actions, as
our experimental subjects did, A number of
recent contributions have shown that, under
conditions that appear to approximate the social
and physical environments of early human populations, prosocial behavior can proliferate in a
population in which it is initially rare (Bowles et
al,, 2001),
IV. Conclusion
While our results do not imply that economists should abandon the rational-actor framework, they do suggest two major revisions.
First, the canonical model of the self-interested
material payoff-maximizing actor is systematically violated. In all societies studied, UG offers
are strictly positive and often substantially in
excess of the expected income-maximizing offer, as are contributions in the public-goods
game, while rejections of positive offers in
some societies occur at a considerable rate. Second, preferences over economic choices are not
exogenous as the canonical model would have
it, but rather are shaped by the economic and
social interactions of everyday life. This result
implies that judgments in welfare economics
that assume exogenous preferences are questionable, as are predictions of the effects of
changing economic policies and institutions that
fail to take account of behavioral change. Finally, the connection between experimental behavior and the structure of everyday economic
life should provide an important clue in revising
the canonical model of individual choice
behavior,
REFERENCES
Bowles, Samuel; Boyd, Richard; Fehr, Ernst and
Gintis, Herbert, eds. The foundations of social
reciprocity. Unpublished manuscript. University of Massachusetts, 2001.
Camerer, Colin F. Behavioral economics. Princeton, NJ: Princeton University Press, 2001
(forthcoming).
78
Fehr, Ernst and Gachter, Simon. "Fairness and
Retaliation: The Economics of Reciprocity."
Journal of Economic Perspectives., Summer
2000, 74(3), pp. 159-81.
Henrich, Joseph; Boyd, Robert; Bowles, Samuel;
Camerer, Colin; Fehr, Ernst; Gintis, Herhert
and McElreath, Richard. "Cooperation, Reciprocity and Punishment in Fifteen Small-
MAY 2001
Scale Societies." Working paper, Santa Fe
Institute, 2001.
Roth, Alvin E.; Prasnikar, Vesna; Okuno-
Fujiwara, Masahiro and Zamir, Shmuel. "Bargaining and Market Behavior in Jerusalem,
Ljubljana, Pittsburgh, and Tokyo: An Experimental Study." American Economic Review,
December 1991, 57(5), pp. 1068-95.
Chimpanzees Are Rational Maximizers in an
Ultimatum Game
Keith Jensen, et al.
Science 318, 107 (2007);
DOI: 10.1126/science.1145850
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REPORTS
Keith Jensen,* Josep Call, Michael Tomasello
Traditional models of economic decision-making assume that people are self-interested rational
maximizers. Empirical research has demonstrated, however, that people will take into account
the interests of others and are sensitive to norms of cooperation and fairness. In one of the most
robust tests of this finding, the ultimatum game, individuals will reject a proposed division of a
monetary windfall, at a cost to themselves, if they perceive it as unfair. Here we show that in an
ultimatum game, humans’ closest living relatives, chimpanzees (Pan troglodytes), are rational
maximizers and are not sensitive to fairness. These results support the hypothesis that otherregarding preferences and aversion to inequitable outcomes, which play key roles in human social
organization, distinguish us from our closest living relatives.
umans are able to live in very large
groups and to cooperate with unrelated
individuals whom they expect never to
encounter again, conditions that make the standard mechanisms for cooperation unlikely (1),
namely kin selection (2) and reciprocal altruism
(3). Nevertheless, people help others, sometimes
at great personal cost. But people are not obligate altruists; they do not tolerate abuse of their
generosity. Not only will they punish or shun
individuals who free-ride or exploit them, they
will do so even if they themselves do not benefit from correcting the behavior of norm violators (4). The willingness both to cooperate and
to punish noncooperators has been termed strong
reciprocity (5) and has been claimed to be
uniquely human (6). To cooperate in these ways,
humans must be more than self-regarding rational decision-makers; they must also, at least to
H
Max Planck Institute for Evolutionary Anthropology, Deutscher
Platz 6, D-04103, Leipzig, Germany.
*To whom correspondence should be addressed. E-mail:
jensen@eva.mpg.de
A
some degree, have concern for outcomes and
behaviors affecting others (other-regarding preferences) (4) as well as a general concern for
norms of fairness (7, 8).
The benchmark test for examining sensitivity
to fairness and other-regarding preferences is the
ultimatum game (9). In the standard version of
the game, two anonymous individuals are assigned the roles of proposer and responder. The
proposer is offered a sum of money and can
decide whether to divide this windfall with the
responder. The crucial feature of the ultimatum
game is that the responder can accept or reject
the proposer’s offer. If the responder accepts it,
both players receive the proposed division; if the
responder rejects it, both get nothing. The canonical economic model of pure self-interest
predicts that the proposer will offer the smallest
share possible and that the responder will accept
any nonzero offer. This is not what happens.
Although the specifics vary across culture and
setting, the basic finding is that proposers
typically make offers of 40 to 50% and
responders routinely reject offers under 20%
(10). These findings suggest that responders are
B
food dish
sensitive to unfairness and punish proposers who
make inequitable offers by rejecting those offers
at a cost to themselves, and knowing this, proposers make strategic offers that are less likely
to be refused.
The ultimatum game has been used in
dozens, possibly hundreds of studies, including
various human cultures (11) and children (12).
Testing the ultimatum game on other species
would be an important contribution to the debate on the evolution and possible uniqueness of
human cooperation (6). Chimpanzees are our
closest extant relatives and engage in cooperative
behavior such as group hunting, coalitionary
aggression, and territorial patrols (13). Furthermore, in experiments they have been shown to
coordinate their behavior (14) and to provide
help (15, 16). However, there is ongoing debate
about whether chimpanzees are sensitive to, and
tolerant of, unfairness (17) or whether they
simply attend to their own expectations with no
regard for what others receive (18). Additionally,
experiments have failed to reveal other-regarding
preferences when food was involved (19, 20)
other than to punish direct theft (21). Having
chimpanzees play the ultimatum game would
address these conflicting findings on fairness and
negative reciprocity and allow direct comparisons to humans.
In the current study, we tested chimpanzees
in a mini-ultimatum game. The mini-ultimatum
game is a reduced form of the ultimatum game
in which proposers are given a choice between
making one of two pre-set offers which the
responder can then accept or reject (22). In one
such study (23), there were four different games.
In all games, the proposer had as one option an
amount that would typically be rejected by a
human responder as unfair, namely 80% for the
proposer and 20% for the responder (8/2 offer;
the proposer received the amount to the left of
the slash and the responder received the amount
to the right). In the 5/5 (fair) game, the proposer
Chimpanzees Are Rational Maximizers
in an Ultimatum Game
C
divider
tray
rope ends
Proposer
rods
Responder
Fig. 1. Illustration of the testing environment. The proposer, who makes the
first choice, sits to the responder’s left. The apparatus, which has two sliding
trays connected by a single rope, is outside of the cages. (A) By first sliding a
Plexiglas panel (not shown) to access one rope end and by then pulling it,
www.sciencemag.org
SCIENCE
the proposer draws one of the baited trays halfway toward the two subjects.
(B) The responder can then pull the attached rod, now within reach, to bring
the proposed food tray to the cage mesh so that (C) both subjects can eat
from their respective food dishes (clearly separated by a translucent divider).
VOL 318
5 OCTOBER 2007
107
was faced with the choice of 8/2 versus 5/5. The
other games were 8/2 versus 2/8 (unfair versus
hyperfair), 8/2 versus 8/2 (no choice), and 8/2
versus 10/0 (unfair versus hyperunfair). Human
responders rejected the 8/2 offer most when the
alternative was fair (5/5 game), less when the
alternative was hyperfair (2/8 game), even less
when there was no alternative (8/2 game), and
hardly at all when the alternative was for the
proposer to be even more selfish (10/0 game)
(23). The differential rejection of unfair outcomes across the games suggests that people are
not sensitive solely to unfair distributions (7) nor
solely to unfair intent (24) but to a combination
of both (8). If chimpanzees are sensitive to unfairness and are negatively reciprocal, they would
behave like Homo reciprocans (25), whereas if
they accept any nonzero offer regardless of
alternatives for the proposer, they will be more
like the hypothetical Homo economicus (26).
Subjects were 11 chimpanzees from a grouphoused colony at the Wolfgang Köhler Primate
Research Center (27). The proposer sat to the
left of the responder, who was in an adjacent
cage in an L-shaped arrangement. The test apparatus, which was outside of the cages, had
two sliding trays. On each tray were two dishes
with raisins, separated by translucent dividers:
one for the proposer and the other for the
responder (Fig. 1). Proposers would first choose
one of the two trays by pulling it halfway to the
cages (as far as it would go); responders could
accept the offer by pulling the proposed tray the
remaining distance (via the rod which came into
reach only as a result of the proposer’s pull) or
could reject it by not pulling at all within 1 min.
The responder’s acceptance led to both subjects
being able to reach the food in their respective
dishes. Rejection led to both getting nothing,
because the experimenter would remove all
food dishes after the trial ended. There were
four games (as in the study described above), all
played within a single session: 2/8, 5/5, 8/2, and
10/0—each versus 8/2. The order of games was
counterbalanced across subjects.
The most important finding is that responders tended to accept any offer. As can be seen in
Fig. 2, responders rejected 8/2 offers at overall
Proposer
Payoffs
Responder
Fig. 2. Offers made by
Offers
Proposer Responder Rejections
proposers and rejections Game
by responders in the four
8
2
games. In each game, the
39 (75%)
2 (5%)
proposer could choose
5/5
between two payoff op5
5
13 (25%)
0 (0%)
tions: 8/2 (8 raisins for
the proposer and 2 for
the responder) and an
alternate [2/8 (2 for the
8
2
45 (87%)
3 (7%)
proposer and 8 for the
2/8
responder), 5/5 (5 for
2
8
7 (13%)
0 (0%)
the proposer and 5 for
the responder), 8/2 (8
for the proposer and 2
8
2
for the responder), and
10/0 (10 for the proposer
53 (100%)
6 (11%)
8/2
8
2
and 0 for the responder)]. Results on the left
show the total number
and corresponding per8
2
centage of offers for each
29 (54%)
4 (14%)
option made by propos10/0
10
0
ers in each game. (Trials
25 (46%)
11 (44%)
in which the proposer did
not participate are not included, therefore the total number of offers varies across the games; percentages
are therefore based on the total number of offers for each option out of the total number of trials played for
each game.) Results on the right indicate the total number of each offer rejected and the corresponding
percentage of rejections out of the total number of offers for each game.
50
Rejection Rate (%)
Fig. 3. Rejection rates (% of
trials) of 8/2 offers in the four
games for chimpanzees in this
study (black bars) and for human
participants (white bars) [data are
from (23)].
40
30
20
10
0
5/5
2/8
8/2
Game
108
5 OCTOBER 2007
VOL 318
SCIENCE
10/0
low rates (from 5 to 14% of the time). There
was a trend toward different rejection rates of
8/2 offers across the four games (Friedman’s c23
test = 6.643, P = 0.069). However, all paired
comparisons were nonsignificant, indicating that,
crucially, chimpanzees rejected 8/2 offers equally
often regardless of the alternatives available to
the proposers (27). Moreover, this trend toward
rejections was in the opposite direction of the
finding for humans (23). When proposers offered
non-8/2 alternatives (available in all but the 8/2
game), responders accepted them differentially
across the games (Friedman’s c22 test = 10.00,
P = 0.012). In line with the principle of selfinterest to accept any nonzero offer, responders
rejected 10/0 offers (in which the responder
receives nothing) more often than 5/5 offers
[Wilcoxon T+ test = 28.00, n = 8 (1 tie), P =
0.016] and marginally more often than 2/8 offers
[Wilcoxon T+ test = 15.00, n = 7 (2 ties), P =
0.063]. Indeed, the only offers rejected by responders more than 0% of the time were 10/0
offers (one-sample t test t9 = 4.735, P = 0.001). In
short, responders did not reject unfair offers when
the proposer had the option of making a fair offer;
they accepted almost all nonzero offers; and they
reliably rejected only offers of zero. As can be
seen in Fig. 3, these results contrast strongly with
those of adult humans, who reject 8/2 offers most
often when a fair (5/5) option is available for the
proposer and least often when the alternative for
the responder is even more selfish than the 8/2
option (10/0) (23). Furthermore, unlike human
responders, who report being angry when
confronted with unfair offers (28), chimpanzee
responders showed signs of arousal [displays and
tantrums (13, 29)] in less than 2% of the test trials
(all occurrences were by one individual in all
trials of a single session), whereas in a previous
study in which the subjects had food taken away
from them, these same individuals exhibited
tantrums or displays 40% of the time (21).
Consistent with previous studies on chimpanzees (19, 20), proposers did not appear to
take outcomes affecting the responder into
account. When given the opportunity, proposers
did not make fair offers (Fig. 2) [see also (27),
and fig. S1]. Given the propensity of responders
to accept any nonzero offer, it is not surprising
that chimpanzee proposers acted according to
traditional economic models of self-interest.
However, it is perhaps surprising that proposers
made zero offers to the responders, given that
these offers were rejected at the highest rate
(Fig. 2); chimpanzees are certainly capable of
distinguishing two pieces of food from zero
when choosing for themselves (30).
To rule out more trivial interpretations of our
results, it was necessary to demonstrate that responders and proposers understood the critical
features of the task. To this end, we conducted
familiarization and probe trials as well as a
follow-up study. First, sensitivity to fairness in
the ultimatum game requires that responders and
proposers each know what the other gains. We
www.sciencemag.org
REPORTS
REPORTS
We gave chimpanzees the most widely recognized test for a sensitivity to fairness, the ultimatum
game, and found that they did not systematically
make fair offers to conspecifics, nor did they systematically refuse to accept unfair offers from
conspecifics even though they could discriminate
between the quantities available to themselves
and their partners. It thus would seem that in
this context, one of humans’ closest living relatives behaves according to traditional economic
models of self-interest, unlike humans, and that
this species does not share the human sensitivity
to fairness.
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Widespread Role for the Flowering-Time
Regulators FCA and FPA in
RNA-Mediated Chromatin Silencing
Isabel Bäurle,1* Lisa Smith,2† David C. Baulcombe,2‡ Caroline Dean1*
The RRM-domain proteins FCA and FPA have previously been characterized as flowering-time
regulators in Arabidopsis. We show that they are required for RNA-mediated chromatin silencing of
a range of loci in the genome. At some target loci, FCA and FPA promote asymmetric DNA
methylation, whereas at others they function in parallel to DNA methylation. Female gametophytic
development and early embryonic development are particularly susceptible to malfunctions in FCA
and FPA. We propose that FCA and FPA regulate chromatin silencing of single and low-copy genes
and interact in a locus-dependent manner with the canonical small interfering RNA–directed DNA
methylation pathway to regulate common targets.
eterochromatin in many organisms is
characterized by extensive DNA methylation and histone modifications (1).
Plants display cytosine methylation in CG,
CNG (N = any nucleotide), and CHH (H = A,
H
C, or T) sequence contexts. In Arabidopsis, small
interfering RNAs (siRNAs) are involved in
localizing and maintaining these chromatin
modifications in processes requiring RNADEPENDENT RNA POLYMERASE2 (RDR2),
www.sciencemag.org
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31. However, the same subjects could discriminate 10 from
8 in a previous study (35), and chimpanzees can reliably
discriminate 0 from 2 (30), which they would have done
had they attended to responder outcomes.
32. M. Shinada, T. Yamagishi, Y. Ohmura, Evol. Hum. Behav.
25, 379 (2004).
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36. We thank the keepers of the Leipzig zoo, notably
S. Leideritz, D. Geissler, N. Schenk, and “Mozart”
Herrmann for their help; G. Sandler for reliability coding;
R. Mundry for statistical advice; and two anonymous
reviewers for helpful comments.
therefore ran follow-up probe trials to determine
whether the chimpanzees were capable of attending to the amount of food available to the
partner. Subjects were tested alone, and they had
to look into the distal food dishes to correctly
choose the tray that would yield the largest
payoff from the partner’s position before going
through the open door to the adjacent cage to
get it. They chose correctly at greater than chance
levels, demonstrating that they would have been
capable of seeing payoffs to the partner (27).
Second, in inhibition probe trials, we found that
subjects could inhibit pulling the rod when it led
to no food gain about 64% of the time, about the
same rate of pulling as in the 10/0 condition,
suggesting that some of the failure to reject zero
offers was due, at least some of the time, to an
inability to inhibit a natural tendency to pull.
Third, in discrimination probe trials, responders
could distinguish between all offers available to
them (fig. S2), and proposers could do so for all
but 10/0 versus 8/2 (fig. S1) (31), demonstrating
that subjects were able to make maximizing
choices.
Our subjects were from a single social group,
they did not interact anonymously, and they
played both roles in the game. However, anonymous one-shot games are used in experiments
with humans to decrease the likelihood of making fair offers or accepting unfair offers (32, 33),
and so if anything, our experimental design
should have been skewed in favor of finding
fairness sensitivity. The fact that chimpanzees in
this study did not punish other individuals for
making unfair offers may be in part a reflection of
the fact that active food sharing is rare in this
species (34) and may also be because they were
unwilling to pay a cost to punish.
Supporting Online Material
www.sciencemag.org/cgi/content/full/318/5847/107/DC1
Materials and Methods
SOM Text
Figs. S1 and S2
References
Movies S1 and S2
30 May 2007; accepted 16 August 2007
10.1126/science.1145850
DICER-LIKE3 (DCL3), ARGONAUTE4 (AGO4),
and the two RNA polymerase IV isoforms, Pol
IVa and b (2–9).
To identify further components required for
siRNA-mediated chromatin silencing, we used
a reporter system in which the Arabidopsis
phytoene desaturase (PDS) gene is silenced in
response to a homologous inverted repeat (SUCPDS) (10). Two mutants that partially suppressed
the silencing of PDS (Fig. 1, A, B, C, and E)
showed late flowering that was reversible by
vernalization. The silencing and flowering phenotypes cosegregated, and the mutations mapped
to chromosomes 2 and 4. The flowering phenotype suggested involvement of FPA and FCA,
two members of the autonomous pathway (11),
mapping to those genomic regions. Sequencing
revealed a premature termination codon in FPA
(Trp98*, G to A, fpa-8) and FCA (Gln537*, C to
T, fca-11). The flowering defect was confirmed
by complementation analysis with previously
known flowering mutants (fca-9, fpa-7, and
fve-3; Fig. 1F), which also showed PDS silencing (fig. S1). Thus, FCA and FPA are required
5 OCTOBER 2007
109
Institute for Empirical Research in Economics
University of Zurich
Working Paper Series
ISSN 1424-0459
Working Paper No. 318
Discrimination and In-group Favoritism in a
Citywide Trust Experiment
Armin Falk and Christian Zehnder
April 2007
Discrimination and In-group Favoritism
in a Citywide Trust Experiment∗
Armin Falk and Christian Zehnder†
April 2007
Abstract
This paper provides field experimental evidence on the prevalence and determinants of
discrimination and in-group favoritism in trust decisions. We observe choices of about
1,000 inhabitants of the city of Zurich who take part in a sequential trust game, in which
first movers can condition their investments on the residential districts of second movers.
Our main results can be summarized as follows: First movers discriminate significantly
in their investment choices, i.e., strangers receive different investments depending on the
district they live in. The systematics of the discrimination pattern is underlined by data
from an additional newspaper study, where participants correctly guessed the outcome of
the study. In terms of district characteristics two factors seem to be key for a district’s
reputation: while expected trustworthiness of a district increases in the socio-economic
status it decreases in the degree of ethnic heterogeneity. Observed discrimination is not
just based on mistaken stereotypes but can at least partly be classified as statistical
discrimination. This can be inferred from the fact that, on a district level, both expected
return on investment and actual investments are positively correlated with actual back
transfers. First movers correctly anticipate different levels of trustworthiness and discriminate accordingly. Furthermore, we provide evidence of in-group favoritism, i.e., people
trust strangers from their own district significantly more than strangers from other districts. Finally, we discuss individual determinants of discrimination and in-group favoritism.
JEL-Classifications: C90, D63
Keywords: Discrimination, In-group Favoritism, Trust, Trustworthiness, Reciprocity, Social
Capital, City Development
∗
Financial support by the Research Committee and the Young Academics Support Committee of the
University of Zurich is gratefully acknowledged. We thank the Statistical Office of Zurich for very valuable
support. We also like to thank seminar participants at Caltech, ENABLE Workshop (Fraueninsel), Mac
Arthur Research Network Workshop (Philadelphia), University of Southern California, University of
Chicago and University of Munich.
†
Armin Falk: IZA and University of Bonn, Schaumburg-Lippe-Strasse 7/9, D-53113 Bonn,
falk@iza.org; Christian Zehnder: Institute for Empirical Research in Economics, University of Zurich,
Bluemlisalpstrasse 10, CH-8006 Zurich, zehnder@iew.unizh.ch.
1
Introduction
Trust is an elementary component of social and economic life. It is therefore not surprising that economists have accumulated a large body of evidence on the existence and
economic consequences of trust using field data, experiments and surveys. Surprisingly
little is known, however, about whether people discriminate in their trust and if so, what
determines whether they trust strangers from a particular group more than members from
another group. We also know little about whether trust discrimination is based on stereotypes or actual differences in trustworthiness and what determines trust discrimination
at the individual level.
We address these questions with the help of a field experiment conducted among
roughly 1,000 inhabitants of the city of Zurich. The experimental game is a variant of
the so-called trust or investment game.1 In this sequential two-player game first movers
send money to second movers, which is tripled by the experimenters. Second movers
then decide how much to return. The amounts sent and returned inform us about the
levels of trust and trustworthiness, respectively. Studying trust discrimination requires a
social environment that defines distinct groups. In our study these groups are defined by
the 12 districts of the city of Zurich. We think that districts of a city are a well-suited
environment to study trust discrimination: districts are natural geographic entities, have a
social meaning and are sufficiently heterogenous to potentially justify different reputations
with respect to trust and trustworthiness. Moreover, district affiliation is relevant in
every day transactions, which means that investments observed in the experiment can
be interpreted as a proxy for efficiency enhancing and trust-related decisions taken every
day, such as car repair or hiring and moving decisions.
First movers in the experiment made a contingent decision: before knowing the residential district of their second mover they had to decide on an investment decision for
each of the 12 districts, including their own district. This design feature allows us to
study discrimination in a straightforward way, simply by comparing the amounts sent
into the different districts. First movers were also asked about expected back transfers
for each investment. Second mover decisions were elicited with the help of the contingent
respond method, which enables us to measure actual trustworthiness of the inhabitants
of different districts.
Our data on the choices of first and second movers are complemented by socioeconomic
and individual background information about all participants. The data come from two
sources, the statistical office of Zurich and a questionnaire that each participant in the
1
This game was introduced by Berg et al. (1995).
1
experiment had to complete. We also use statistical information about the districts and
data from an additional newspaper experiment we conducted in collaboration with a large
daily newspaper in the Zurich area. In this experiment we asked newspaper readers from
Zurich, who were informed about the rules of the experiment, to predict the outcome of the
study. In particular they had to indicate the two districts that they thought would receive
the lowest investments and the two districts that would receive the highest investments.
To guarantee incentive compatibility we paid three randomly chosen readers among those
whose answers were correct a prize of CHF 200. The results of our newspaper study
provide a robustness check for our main experiment. If the newspaper readers predict
the participants’ choices correctly, we have additional evidence that the discrimination
pattern in our experiment is systematic.
Our main findings can be summarized as follows. First, we investigate the prevalence
of trust discrimination. We find that investment levels differ systematically across the
residential districts of second movers, i.e., many first movers discriminate. Across districts
first movers expect very different returns on investment and invest accordingly. The
systematics of the discrimination pattern is supported by the results of our newspaper
study. The readers predict which districts receive the highest and lowest investments
extremely well. This underlines that beliefs about the districts’ different reputations
are commonly shared. In terms of district characteristics that determine a trustworthy
reputation, two factors are key: socioeconomic status and ethnic heterogeneity. The
higher the economic status and the lower the ethnic heterogeneity, the higher is the
reputation of a particular district, i.e., the higher is the expectation that a stranger from
this district is actually trustworthy.
Second, we explore the nature of the discrimination process. It turns out that observed
discrimination is at least in part statistical in nature. This can be inferred from the fact
that – on a district level – both expected return on investment as well as investments
are positively and significantly correlated with actual trustworthiness. In other words,
first movers correctly anticipate different levels of trustworthiness and discriminate on
the basis of this belief.
In a third step, we explore in-group favoritism, which is a particular form of discrimination, where people tend to favor members of their own group. We show that first
movers invest significantly higher amounts to strangers who belong to their own district,
compared to strangers from other districts. This in-group bias is not just taste driven
as our data on expected back transfers reveals: first movers not only send more money,
they also believe that fellow citizens from their own district are more trustworthy than
strangers from other districts.
2
In a final step of the analysis we turn to the individual determinants of discrimination.
We classify people who invest different amounts into different districts as discriminators
and show that better educated people as well as people who have children discriminate
less, while older people as well as people who favor right wing parties discriminate more.
Turning to individual determinants of in-group favoritism we find that in-group favoritism
is not significantly correlated with individual characteristics, such as gender or age. The
only variable that significantly explains different levels of in-group favoritism is the degree
to which people feel closely associated with their own district.
Our paper offers several contributions to the literature. First, to the best of our
knowledge, it is the first to document trust discrimination based on residential districts,
i.e., on a community level.2 This type of discrimination is particular important in light of
the fact that trust and trustworthiness constitute central components of a community’s
social capital (see, e.g., the definitions in Loury, 1977; Coleman, 1990; Putnam, 2000),
which influences a wide range of important economic phenomena, such as governmental
and judicial efficiency (Putnam et al., 1993; La Porta et al., 1997), financial development
and volume of trade (Guiso et al., 2004) or the rate of overall economic growth (Knack
and Keefer, 1997; Knack and Zak, 2001). In this sense trust can be seen as a sort of
lubricant for economic transactions, especially if markets are imperfect and contracts
remain incomplete.3
Second, our results show that trust discrimination can be the result of statistical discrimination: first movers have relatively accurate expectations about districts’ trustworthiness and invest more in districts that are actually more trustworthy. This is different
to previous studies where discrimination has not been statistical in nature. Fershtman
and Gneezy (2001), e.g., investigated gender and race effects in a trust game played
between Ashkenazic and Eastern Jews from two Universities in Israel. While there is
no evidence for ethnic discrimination to and by women, male subjects exhibit a significant discrimination pattern, transferring less money to Eastern males than to Ashkenazic
males. Different to our findings, however, this discrimination is not statistical but turns
out to be the consequence of largely mistaken stereotypes.
Third, our findings shed new light on the controversial issue of in-group favoritism.
Starting with the famous “Robber’s Cave Experiment” by Sherif et al. (1961) many experiments in psychology have demonstrated the presence of in-group favoritism even if
2
Previous studies on discrimination have predominantly focused on ethnic or gender discrimination,
starting with the seminal paper by Fershtman and Gneezy (2001), who investigated gender and race
effects in a trust game played between Ashkenazic and Eastern Jews from two Universities in Israel.
3
In a famous quote Kenneth Arrow notes: “Virtually every commercial transaction has within itself
an element of trust...”, see Arrow (1972), p. 357.
3
group affiliations are created artificially (see Yamagishi et al., 1999, for a survey of this
literature). In recent years many economists have become interested in the phenomenon
of in-group favoritism in trust decisions. Interestingly, the present state of the literature
is fairly mixed. In experiments conducted on the basis of the minimal group paradigm
the evidence in favor of an in-group bias is very weak (see e.g., Buchan et al., forthcoming; Güth et al., 2005). But also studies based on naturally defined groups provide
ambiguous evidence. While a number of studies find no or only weak evidence for ingroup favoritism (see, e.g., Fershtman and Gneezy, 2001; Glaeser et al., 2000; Bouckaert
and Dhaene, 2004; Haile et al., 2006), there are two studies which report a significant
in-group bias in trust decisions (see, Bernhard et al., 2006; Götte et al., 2006).
We contribute to the emerging literature on in-group favoritism in several ways. First,
we show that in the context of city districts in-group favoritism is relevant in naturally
occurring groups. Subjects in our study use their experience from every day life to determine how much they trust inhabitants from different parts of the city they live in.
Second, we do not only document the existence of in-group favoritism but we are also
able to explain at least part of it with subjects’ beliefs. Investments to the own district
are not only higher because of taste but also reflect the fact that people expect higher
returns on investments in their own district.
Finally, we contribute to the existing literature by studying individual determinants
that are driving trust discrimination and in-group favoritism. Our large and heterogenous
non-student subject pool allows us to do this in a meaningful way.
The remainder of the paper is organized as follows: in the next section we describe the
design and the used background information. In section 3 we present our results. Section
4 summarizes and concludes the paper.
2
Design and Background Information
In this section we first describe the details of the trust experiment and the questionnaire
subjects had to complete. We then discuss the design of the complementary newspaper
study. Finally, we describe data provided by the statistical office of Zurich.
2.1
A Field Experiment on Trust and Discrimination
Our experimental tool to measure trust and trustworthiness is a variant of the so-called
trust or investment game introduced by Berg et al. (1995). Two randomly chosen subjects
constitute an interaction group. At the beginning of the experiment both subjects receive
an endowment of 20 Swiss Francs (CHF 1 ∼ US-$ 0.8). One person is assigned the role
4
of the first mover, the other the one of the second mover, respectively. The first mover
decides how much of his endowment to transfer to the second mover. The transfer can be
any amount in steps of 2 Swiss Francs, i.e., 0, 2, 4, ..., or 20 Francs. The chosen transfer
is tripled by the experimenter and passed to the second mover. Contingent upon the first
mover’s transfer the second mover decides on a back transfer to the first mover. This
back transfer can be any integer amount between 0 and 80 Swiss Francs. Given the back
transfer of the second mover incomes are determined: the first mover earns his endowment
minus his own transfer plus the back transfer of the second mover. The second mover
gets his endowment plus 3 times the first mover’s transfer minus the back transfer.
Our design differs in important ways from previous trust experiments. Since we are
mainly interested in discrimination based on group affiliation we add concrete context
to the decision environment. In particular, first movers could condition their investment
decision on the residential district of the second mover. When they took their decision,
they did not yet know the residential district of their second mover. Therefore they had
to make twelve investment decisions, one for each of the 12 districts of Zurich. First
movers made their decisions with the help of a table with twelve rows (see Table 1). The
first column of this table stated the following question: “Suppose the other person lives
in district ... . How much of your CHF 20 do you invest? ”. In the second column
first movers indicated how much they invest if the second mover lives in district 1, in
district 2 etc. up to district 12. In Column (3), first movers were also asked to state their
beliefs about the second movers’ repayment decision for each of the twelve districts. Thus
first movers made 12 investment decisions and indicated 12 beliefs, one for each district.
Knowing first movers’ beliefs is important as it allows us to calculate expected returns on
investments and to distinguish between different motivations behind investments. We can
identify, e.g., whether high investments are made in the expectation of high back transfers
or simply reflect a desire to be altruistic.
The instructions also contained a map of Zurich, which displayed the district borders
as well as the names of the neighborhoods in each district (see Figure 1). Notice, however,
that we did not provide subjects with any statistical information concerning the districts’
characteristics. Thus, any observed differentiation across districts is based on the subjects’
everyday knowledge about Zurich.
The fact that first movers made multiple decisions may raise concerns about a potential
experimenter demand effect. One could argue that by presenting twelve options, subjects
were induced to differentiate their investment decisions biasing our results in favor of
discrimination. While this is a potentially important concern we are quite confident
that it does not compromise our findings. First, previous discrimination studies have
5
argued against a contingent elicitation procedure because it would underestimate the
amount of discrimination, simply because subjects may not like to reveal that they are
discriminating. Second, independent of the level of discrimination our method does not
induce a particular pattern of discrimination. In other words, if subjects were simply
induced to choose different investments in different rows, the resulting pattern would
not be systematic but random. Even more important, multiple observations for each
individual provide us with valuable information, which is why we chose to implement
this procedure. It enables us to classify individuals as discriminators (if investments vary
across districts) or non-discriminators (if investments are all the same). This classification
is necessary to identify individual determinants of discrimination. The same argument can
be made with respect to our interest in studying in-group favoritism: since first movers
invest in all districts, including their own, we can easily identify whether first movers
perceive strangers from their own district as more or less trustworthy than strangers from
other districts. Moreover, we are able to study individual determinants of such an in-group
favoritism.
In order to elicit second movers’ willingness to reciprocate, we used the contingent
response method. This means that each second mover, before knowing the actual first
mover’s investment, made a back transfer decision for each of the 11 possible investments
(0, 2, ..., 20). Whether this method overestimates or underestimates people’s willingness
to reciprocate is an open question.4 For our purpose, however, the contingent response
method provides reliable information about second movers’ willingness to reciprocate,
which is key for calculating the level of reciprocation on a district level as well as understanding individual determinants of reciprocation. Moreover, we are not predominantly
interested in the level of reciprocity but in the differences across districts, which should
not be confounded by the usage of this elicitation method. Finally, since the strategy
method allows for the simultaneous elicitation of first and second mover decisions it also
facilitated the procedures of our experiment considerably.
Our mailing also included a questionnaire to elicit detailed information about socioeconomic and individual background of participants. In the cover letter it was emphasized that the questionnaire was part of the experiment and had to be completed. The
questionnaire asked about personal attributes like gender, age, marital status, profession,
nationality and number of siblings. In addition we elicited information about the personal
and residential background of participants: political orientation, duration of residency in
4
For example, Güth et al. (2001) report behavioral differences between a game where subjects played
a game sequentially vs. playing the strategy method. On the other hand, Brandts and Charness (2000)
and Cason and Mui (1998) report evidence indicating that the strategy method does not induce different
behavior.
6
district and city, how closely associated subjects feel with their district and city, number
of phone calls during last week, whether subjects are afraid of crime in their district and
number of club memberships.
In addition to the information collected with the help of the questionnaire, we also
received individual background information from the Statistical Office of Zurich. Together
with the random sample of address files which we needed to run the study, we received a
set of individual characteristics of the participants such as taxable income, gender, age,
type of profession, religious affiliation, number of children and foreigner status. This data
is of great value as it allows us to complement our questionnaire data and to verify its
accuracy. The Statistical Office of Zurich also provides very detailed information about
district characteristics. In the results section we use several of these characteristics, such
as median per capita income, fraction of foreigners or religious background (see Table 4).
2.2
Experimental Procedures
Our subjects are a random sample of the city of Zurich, implying that our subject pool exhibits much greater variance with respect to socioeconomic and personal background than
the typically used student samples. This feature of our data is a prerequisite to investigate
the impact of person specific characteristics on trust, discrimination and trustworthiness
in a meaningful way. For logistical reasons the experiment was conducted via mail correspondence. The Statistical Office of Zurich provided us with address files for each of
the twelve city districts of Zurich. The address files constituted a random sample of the
population of each district. In total 986 persons took part in the experiment (509 first
movers and 477 second movers).
All potential participants received a mailing including a cover letter, detailed instructions, a decision sheet and a questionnaire. The cover letter informed subjects about the
possibility to take part in a paid experiment, conducted by the University of Zurich. In
order to enhance the credibility that we would actually pay subjects we added the remark
that the Legal Service of the University (Rechtsdienst) guarantees that the study is run
exactly according to the rules stated in the instructions. We also made clear to subjects
that the study was run in accordance with the data protection legislation of the city of
Zurich. In particular, we stated that all data will be used only for scientific purposes
and not given to any third parties. Moreover, we guaranteed that data will be stored in
anonymous form and that any information specific to persons will be destroyed after the
data collection will be completed. We offered participants to send us an email (using a
neutral University email address) or to call us, in order to answer potential questions.
Only very few people made use of these options. The instructions explained the idea and
7
the rules of the experiment in detail. First and second movers were told that they were
matched with another anonymous person who was randomly selected and lives in Zurich.
Participants had to complete the questionnaire and the decision sheet, i.e., first movers
filled out the table concerning investments and beliefs and second movers filled out the
table concerning back transfers. Subjects then returned the completed decision sheet to
us, using a pre-stamped envelope. It was made clear in the cover letter that the decision
sheets had to be returned before the end of a deadline, which was about one week after
subjects had received their letter. Among all participants we randomly formed pairs.
Given the district of the second mover we determined the respective investment of the
first mover. Using the investment we then checked the corresponding back transfer.5 In
a second mailing all participants were informed about the outcome of the experiment,
including the district of the second mover, the investment and back transfer decisions and
the resulting payoffs for both players. The second mailing also contained the payments
in a sealed envelope.6
2.3
The Newspaper Study
In order to get additional and independent information about the systematics and robustness of our discrimination results from the field experiment we ran an additional
newspaper experiment. Several months after we had collected the data from our field
experiment we contacted a large daily newspaper in the Zurich area, the Tages-Anzeiger.
We decided to publish two articles in the newspaper. The first one reported in detail
aims and design of the study. In particular, we explained the rules of the experiment
and the fact that randomly drawn people from all districts of Zurich had taken part in
the study. The first article did not mention any result, however. Instead readers were
invited to take part in a quiz. They were asked to answer the following two questions: (1)
What do you think, which are the two districts that received the lowest investments? (2)
What do you think, which are the two districts that received the highest investments? To
guarantee incentive compatibility, we promised to randomly select three readers among
all those readers whose answers are correct, and to pay them 200 Swiss Francs. Readers
could either email their answers or send them by postcard, within three days after the
article had been published. A total of 281 readers took part. The second article appeared
one week after the first one and contained the results of our field experiment and the
newspaper study. Since there was much public interest in the study, the second article
5
As there were a few more first movers than second movers, some second movers were matched twice.
The payoff of these players was determined by the decisions associated with the first match.
6
We deleted all names and address files after having sent the second mailing.
8
also contained an interview with the authors of the study as well as with the mayor of
Zurich.
3
Results
In this section we present our results. We first investigate prevalence and determinants
of trust discrimination. We then explore the nature of this discrimination process by
relating the trust reputation of districts to their average level of trustworthiness. In a
third step we investigate a particular form of discrimination, in-group favoritism. Finally,
we identify determinants of trust discrimination and in-group favoritism on an individual
level.
3.1
Discrimination
Our first result concerns the level of trust and district specific discrimination.
Result 1 (Trust and discrimination) On average first movers reveal a relatively high
willingness to trust and invest about 66 percent of their endowment. However, trust levels
differ systematically across the residential districts of second movers, i.e., first movers
discriminate.
Support for Result 1 comes from Figure 2 and Tables 2 and 3. Figure 2 shows a histogram of all investment decisions of first movers.7 The amounts invested are comparable
to what has been observed in laboratory studies and reveal that the citizens of Zurich display a relatively high level of trust towards their fellow citizens. On average, first movers
invest 13.16 Swiss Francs, which corresponds to 66 percent of their endowment, with a
standard deviation of 7.07.
In the presence of trust discrimination we should observe that first movers send different amounts of money into different districts. Table 2 shows the average investment levels
into each of the 12 districts of second movers. These investments indeed vary: the district
with the lowest average investment, e.g., is district 4 while the district that received the
highest investment is district 8.8 In terms of magnitude the variation between lowest and
highest investments is 11 percent. Thus, the mere fact that someone lives in a district with
7
Since we used the strategy method to collect the decisions, each first mover made 12 investment
decisions, one for each of the possible residential districts of the second mover. All these decisions are
included in Figure 2.
8
These differences at the aggregate level are the result of the investment behavior of the 55 percent
of first movers who discriminate. 45 percent of first movers send the same amount into each district. In
Section 3.3 we investigate discrimination at the individual level in more detail.
9
a low vs. a high reputation, reduces received investments by a remarkable amount. In
¢
¡
back transfer
the second row we calculate the expected return on investment = expected
−1
investment
for each district.9 The resulting levels vary substantially, from 0.15 in districts 4 and 5
to 0.30 in district 1. Moreover, at the district level investments and expected returns
on investment are strongly positively correlated, which suggests that different levels of
investments are in fact driven by different expectations concerning the districts’ levels of
trustworthiness (Spearman’s rho = 0.863, p < 0.001).10
Table 3 reveals that the investment differences displayed in Table 2 are significant for
most district comparisons. This table reports the p-values of Wilcoxon-signed-rank tests
conducted for pairs of districts. In the table districts are sorted by the level of received
average investment. For example, investments into districts 4 and 12, the two districts
with the lowest reputation, are not significantly different. Neither are districts 4 and
5 significantly different. However, from district 9 up to district 8, all districts received
significantly higher investments than district 4. In total we find that out of the 66 possible
comparisons, 51 are significant at least at the 5 percent level.11
How robust and systematic is the ranking of the districts’ trust reputation shown in
Table 2? Does it reflect a stable and commonly held perception of district reputation
or is this ranking rather arbitrary? A good test for the systematics of the ranking is to
ask inhabitants of Zurich and check whether they are able to predict it. This is what
we did in our newspaper study. As outlined in more detail in section 2.3, we asked the
readers of a large daily newspaper from Zurich to assess which are the two districts that
received the lowest and highest investments, respectively. 281 readers took part in this
incentive compatible study. Their answers are shown in Figure 3. The grey bars indicate
the fraction of readers who think that a specific district is among the two districts that
received the lowest investments, the black ones represent the respective fraction of readers
9
We calculate the expected return on investment for each single positive investment decision of first
movers. In cases where investments are zero, no meaningful values can be calculated. These observations
are therefore neglected (7 percent of our observations contain investments equal to zero; in 91 percent of
these cases expected back transfers are zero as well).
10
Since first movers not only state their investment decision for each district but also their belief about
the second mover’s back transfer, we can also check whether first movers who do not discriminate, i.e.,
who send the same amount to all districts expect different back transfers from each district. We find that
among those first movers who do not discriminate, 37 percent indicate varying beliefs, i.e., they expect
district specific levels of trustworthiness. When we compare this belief based ranking with the one that
results from the differences in investments (see Table 2) we find a positive and significant correlation
(Spearman’s Rho = 0.59; p = 0.041). This finding reinforces the systematics of discrimination across
different districts.
11
An alternative way to show the significance of the investment differences across districts is to simply
regress the first mover investments on district dummies (robust standard errors, clustering on individuals).
An F-Test shows that district differences are significantly different from zero (p < 0.0001).
10
concerning the two districts with the highest reputation. Districts are displayed on the
horizontal axis, ordered according to the actual level of received investments. Figure 3
shows that the newspaper readers predicted the outcome of the experiment extremely well.
For example, almost 70 percent think that district 4 is among the two districts receiving
the lowest investments and about 50 percent think that this holds for districts 12 and
5, respectively. Almost nobody believes that districts 3 or higher (in terms of actually
received investments) are among the two lowest districts. Likewise almost nobody believes
that districts 3 or lower (in terms of investments) belong to the group of districts that are
among the two districts that received the highest investments. The correlation between
the rank order resulting from the answers of the newspaper readers and actual investment
ranks is strong and highly significant. For answers concerning the two high investment
districts the respective Spearman’s rho is 0.89 (p < 0.0001) while for the two low districts
it is -0.88 (p < 0.001). Thus the results from the newspaper study provide strong and
independent evidence that districts in Zurich differ significantly and systematically in
their perceived trustworthiness. In the next section we analyze potential reasons for these
differences.
Result 2 (Determinants of trust discrimination) Districts characterized by higher
economic status and lower ethnic heterogeneity receive higher investments.
In the social capital literature several factors that are associated with trust have been
discussed. In this literature subjects from different regions within or across countries
are asked about how willing they are to trust strangers. An important difference of this
approach with respect to ours concerns the specification of the group that is supposed
to be trusted. In the previous literature this group typically remains unspecified and it
is not not entirely clear what group concept subjects have in mind when answering the
trust question. In contrast, we explicitly fix the group and ask about trustworthiness of a
stranger from a specific district of the city of Zurich. Moreover, we are interested in trust
discrimination and elicit different levels of trust for different groups. In the following we
check whether the factors that have been shown to be relevant for understanding trust in
the previous literature also explain group specific trust, i.e., trust discrimination.
Some authors have pointed out a positive relation between economic and social status and trust or social capital (Alesina and La Ferrara, 2002; Knack and Keefer, 1997).
Another important factor identified in the literature is ethnic and religious heterogeneity
(Costa and Kahn, 2002; Alesina and La Ferrara, 2002). The negative correlation between
heterogeneity and trust may reflect the fact that each ethnic and religious group is characterized by specific cultural and social norms. The more different norms and cultures are in
11
a district, the more difficult it is to build up social networks and trust. In a similar vein a
high degree of mobility and low rates of home ownership have been shown to be negatively
correlated with social capital (Glaeser et al., 2002; DiPasquale and Glaeser, 1999; Alesina
and La Ferrara, 2002). Finally, it has been argued that members of rather ‘hierarchical’
religions (roman Catholics and Muslims) show relatively low levels of trust. In contrast to
the rather liberal tradition of protestant churches, catholic and islamic churches are characterized by strong hierarchies and authorities making it more difficult to establish trust
and social capital (La Porta et al., 1997; Knack and Keefer, 1997; Gabriel et al., 2002).
Table 4 shows how these variables are distributed across the 12 districts of Zurich.
The data is provided by the statistical office of Zurich. Social and economic status is
measured by the variables income and high education. Income is the taxable median
income per district in 1000 Swiss Francs. High education measures the fraction of people
who hold at least a “Matura” degree, an exam that comes at the end of university-track
high school in Switzerland and is a prerequisite for attending university. Our measure of
ethnic heterogeneity is the fraction of foreigners in a given district. As Column (4) in
Table 4 shows, the variation in the fraction of foreigners is quite substantial ranging from
19 percent in district 7 to 44 percent in district 4. Religious heterogeneity is measured
with a fragmentation index, i.e., 1 minus the sum of squared fractions of the following
religious groups: protestant, catholic, muslim, jewish and other. We measure mobility
with the variable years of residency, which shows how long people have lived in their
respective district, on average. For example, while the average time lived in district 5 is
6.7 years, people in district 9 live 11.3 years in their district, on average. The variable
home ownership shows the fraction of apartments owned by inhabitants. Finally, the
variable hierarchical religion measures the fraction of people who are roman catholics.
The two rows at the bottom of Table 4 show how the district characteristics are
correlated with the mean investments into the districts together with respective p-values
of Spearman rank tests in brackets. All coefficients have the expected sign. The correlation
for years of residency is insignificant, all others are significant at least at the 5-percent
level. For example, the richer a district or the higher educated its inhabitants, the higher
its reputation measured in terms of received investments. Likewise, the higher the degree
of heterogeneity the lower the trust reputation.
Table 5 explores the determinants of trust discrimination in more detail. It shows
OLS-regressions where the first mover investments are regressed on district specific characteristics. The dependent variable contains 12 investment decisions per first mover;
robust standard errors (in brackets) allow for clustering at the individual level. Note that
it makes little sense to run multivariate regressions, regressing investments on all district
12
characteristics simultaneously. The reason is that most of the characteristics are highly
correlated and there are only 12 districts to identify the effects. For example, the correlation between income and fraction of foreigners is strong and highly significant (Spearman’s
rho=-0.84, p < 0.001). We therefore chose the following estimation strategy. We selected
the two variables that are most strongly correlated with investments, income and fraction
of foreigners, and show that they are highly significantly correlated with investments, even
jointly (see Columns (1) to (3) of Table 5). In Columns (4) to (8) of Table 5 we include all
other variables but only one at a time. It turns out that income and ethnic heterogeneity
remain highly significant while all other variables are insignificant. The results therefore
suggest that economic status and ethnic heterogeneity are important determinants of a
district’s trust reputation. Living in a district with a high economic status and a low
level of ethnic heterogeneity implies receiving higher investments. Controlling for these
two factors all other district characteristics are of less importance.
We now turn to the behavior of second movers. We first study whether second movers
reciprocate the trust of first movers. In a second step we explore the nature of district
specific discrimination and correlate trust and reciprocation at the district level.
Result 3 (Back transfers) On average, second movers are reciprocal: the higher the
first mover investments, the higher are the back transfers. Moreover, the level of the back
transfers exceeds first movers’ expectations.
Support for Result 3 comes from Figure 4. It shows averages of expected and actual
second mover back transfers for each possible first mover investment. The dark bars
show the reciprocal repayment pattern of second movers. It is obvious from Figure 4
that higher investments are reciprocated with higher back transfers. Moreover, the extent
of reciprocation is quite high. Compared to student populations where the returns on
investment are often close to zero (see, e.g., Camerer (2003), p. 86, and the references
therein), second movers from our non-student subjects pool reveal a relatively strong
reciprocal inclination. For example, second movers are willing to send back about 35
Swiss Francs if they received 20 Francs. This means that they almost equalize final
payments. Over the whole range of investments the slope between investment and pay
backs estimated from a simple OLS-regression is about 1.6.
Figure 4 also shows that first movers expect reciprocation on the side of the second
movers (grey bars). The more they invest, the more they expect to get back. They also
expect to get back more than they invest. For example, those who send 20 Swiss Francs
expect a back transfer of 27 Francs, on average.12 Comparing expectations and actual
12
This also suggests that high investments are made in the expectation of high back transfers and are
not predominantly driven by the desire to be simply altruistic.
13
back transfers reveals that the average level of reciprocation is systematically higher than
expected by first movers. In other words first movers generally underestimate the amount
of reciprocation that is prevalent in the population of Zurich.
Turning to second mover behavior on a district level, we now check whether reciprocation varies across districts and, in particular, whether there is a correlation between
investments and the level of reciprocation:
Result 4 (Statistical discrimination) Different levels of investment into districts as
well as expected returns on investment are both significantly correlated with respective
back transfers. This indicates that first movers’ investment decisions are at least in part
motivated by statistical discrimination and not just by mistaken stereotypes.
We know already that investments into districts correspond to different levels of expected returns on investment (see Table 2). In this sense we can already say that investments are not purely taste driven but actually reflect different levels of expected trustworthiness. In this section we go one step further, however, and ask whether investments
and expected returns are actually correlated with back transfers. In other words we investigate whether the observed different expectations merely represent mistaken stereotypes
or whether they are actually justified in terms of different levels of trustworthiness.
In order to assess a district’s trustworthiness we aggregate people’s back transfers in a
given district. In order to so, we cannot only use those back transfers that were actually
executed and paid, because even if reciprocal inclinations across districts would be identical, we would find that districts that receive high investments return more than districts
that receive low investments. Instead we use data from the contingent response method,
which informs us about willingness to reciprocate independent of actual investments. In
a first step, we calculate for each subject the relation between investment and back transfer: running simple OLS regressions of back transfer on investment and forcing the slope
through the origin we get an estimate of a subject’s reciprocal inclination.13 The higher
the estimated coefficient the more sensitive is a second mover’s reaction to varying levels
of investments. In a next step, we calculate the averages of these slope for every district.
The resulting variation is quite substantial and ranges from about 1.4 to about 2.
Figure 5 displays how these district averages are associated with average investments
into the respective districts. The numbered dots represent the 12 districts, the dashed
line is a weighted linear trend. Figure 5 shows that investments and back transfers
are positively and significantly correlated on a district level (Spearman’s rho = 0.67, p
13
We also estimated reciprocal inclinations using individuals’ average back transfers for all possible
investments. Qualitatively this yields the same result.
14
< 0.02). Moreover, mean trustworthiness of districts is also correlated with expected
return on ivestment (see third row of Table 2). The respective Spearman rank correlation
between expected return on investment and average level of reciprocation on a district
level is 0.7113 (p < 0.01). This brings us full circle: first movers hold particular beliefs
about the trustworthiness of different districts, which determine their trusting decisions.
These beliefs correspond on average with actual trustworthiness.
3.2
In-group Favoritism
A particular form of discrimination is in-group favoritism, i.e., the tendency to favor
strangers who belong to one’s own group. While the relevance of in-group favoritism is
well established for simple allocation tasks (see Yamagishi et al., 1999), the literature
is yet quite inconclusive about the existence, importance and determinants of in-group
favoritism in the context of trust decisions. In trust experiments conducted on the basis
of the minimal group paradigm the evidence in favor of an in-group bias is weak. Buchan
et al. (forthcoming) and Güth et al. (2005) conducted trust games within and across
minimal groups. While Buchan et al. (forthcoming) find some in-group favoritism in
trust for American students but not for Chinese students, Güth et al. (2005) don’t find
any indication of an in-group bias at all. Similarly, studies based on naturally defined
groups provide rather mixed evidence. The discrimination pattern identified in Fershtman
and Gneezy (2001) is not a consequence of an ingroup bias. Both, Ashkenazic and Eastern
males invest less money if their opponent is an Ashkenazic male. In their trust game study
among Harvard undergraduates Glaeser et al. (2000) find that in pairs with participants
from different countries or races trust and trustworthiness are lower, but the effect is only
of statistical significance for the latter. Bouckaert and Dhaene (2004) report results from
trust games with small businessmen of Turkish or Belgian origin in the city of Ghent.
Their data does not contain any evidence for the existence of ethnic discrimination or
in-group favoritism. Haile et al. (2006) conducted trust experiments with students from
two South African Universities. While they do not find evidence for in-group favoritism
in total, they observe that low income subjects of both races trust high income subjects
from the other race significantly less. Two exceptions that provide evidence in favor of
ingroup-favoritism are Bernhard et al. (2006) and Götte et al. (2006). The former is an
experiment with two non-hostile clans in Papua New Guinea. First movers in a trust
game transfer significantly more to members of their own clan. The latter reports results
from experiments with officer candidates in the Swiss Army. Subjects show higher levels
of cooperation in a simultaneous prisoner’s dilemma when they interact with a member
of their own platoon.
15
Our field experiment offers an ideal set-up to study in-group favoritism in a natural
environment. Since first movers make investments for each possible residential district
of the second mover, including their own district, we can assess the extent of in-group
favoritism by comparing investments into own district relative to other districts.
Result 5 (In-group favoritism) We observe a pronounced in-group bias in trust. First
movers invest significantly higher amounts into their own districts compared to other
districts.
Result 5 is supported by the fact that 11 out of the 12 districts invest more to their
own district than they invest on average to the other districts. Finding this outcome in
the absence of in-group favoritism is very unlikely (Binomial test, p < 0.01). In Table
6 we explore the nature of in-group favoritism in more detail. In the first column we
regress first movers’ investments on a dummy for own district, which takes value 1 if the
particular investment is meant for the own district and 0 otherwise. The coefficient is
positive and highly significant, revealing that first movers systematically favor their own
district over other districts. On average they invest 1.40 Swiss Francs more into their
own district, which is about 10 percent more than they send on average into the other
districts.
It turns out that the observed in-group favoritism in trust is in part driven by different
expectations about trustworthiness. In Column (2) we regress expected back transfers on
the own district dummy. In addition we control for investments. The dummy coefficient
is positive and highly significant, suggesting that in-group favoritism is partly explained
by different expected levels of trustworthiness: for a given investment, subjects believe
that back transfers are 1.08 Francs higher if they interact with strangers from their own
district compared to interactions with strangers from other districts. Put differently,
people believe that fellow citizens from their own district are more trustworthy than the
average citizen, which means that in-group favoritism does not just reflect a particular
taste to favor members of one’s own group.
3.3
Individual Determinants of Discrimination and In-group Favoritism
Little is known about individual determinants of discrimination and in-group favoritism.
Due to a lack of appropriate behavioral data and insufficient variation in personal characteristics of student subject pools, previous work has mainly focused on establishing average
effects. In this last results section we combine behavioral data from the contingent re-
16
sponse method with individual background data, and explore individual determinants of
discrimination and in-group favoritism.
We first examine personal characteristics of people who discriminate in our trust experiment. Overall, 55 percent of the first movers differentiate their investments, while 45
percent send the same amount into each district. Those who discriminate are significantly
less trusting than those who don’t. Discriminators send on average CHF 9.47, which is
significantly less than the amount sent by those who don’t discriminate (CHF 17.65). In
columns (1) to (3) of Table 8 we estimate Probit models, where the dependent variable
is an indicator variable, which takes value one if the respective first mover has discriminated and zero otherwise. All estimation results are based on robust standard errors. In
the first column we regress the indicator variable on a non-linear specification for age,
gender and whether the first mover is an only child. We find no gender and only child
effects but a strong age effect. Older people are more likely to discriminate than younger
people. In Columns (2) and (3) we add individual characteristics that are influenced by a
person’s choices in life. These variables are potentially endogenous and therefore not easy
to interpret in a causal way. Column (2) includes variables on income, education, marital
status, the number of children, and whether the first mover is a foreigner. In Column (3)
we add ideological, religious and attitudinal variables. We find that education and having
children reduces the amount of discrimination, while those who classify themselves politically as right-wingers tend to discriminate more. Interestingly, discrimination is neither
associated with the time a first mover has lived in Zurich or in his district nor with how
associated he feels to Zurich or his district, respectively.
In Columns (4), (5) and (6) of Table 8 we study individual characteristics that potentially explain in-group favoritism. We report OLS-estimates where the dependent variable
is the individual in-group bias, i.e., the difference between a first mover’s investment into
his own district and his average investment into the other districts. In Column (4) the
explanatory variables are age dummies and two dummies for gender and only child. None
of the coefficients is significant. We add further explanatory variables in Columns (5)
and (6), analogously to Columns (2) and (3). Again, none of the variables is significant,
with one exception: first movers who feel closely associated to their own district display
significantly stronger in-group favoritism.14
These results suggest that in-group favoritism in terms of trust is not a particular
gender or age specific phenomenon. Moreover, family, religious or political background
14
The exact wording of the question, which we asked in the questionnaire reads as “How strongly
associated do you feel with your city district?” Answers could be given on a five point scale, ranging
from ‘not at all’ to ‘very strongly’. We constructed a dummy, which takes value one if a subject answers
the question with ‘very strongly’ and zero otherwise.
17
don’t seem to matter. What does matter – quite intuitively – is the nature of the relationship with the particular in-group. People who identify with their group and state
that they feel associated favor in-group members over members from other groups, even
in anonymous interactions.
4
Concluding remarks
In this paper we study prevalence and determinants of discrimination, in-group favoritism
and trust and reciprocity across different districts of Zurich. Many people discriminate
and trust strangers from different districts differently. Given that Zurich is a relatively
homogenous city, in comparison with many other cities, it is quite striking to find discrimination even here. We speculate that discrimination is even more pronounced in more
heterogenous cities or regions. Our data reveal that first movers hold particular beliefs
about the trustworthiness of different districts, which are associated with their trusting
decisions. These beliefs correspond on average with actual trustworthiness. This is a
strong result. It implies that first movers know quite a lot about their city and use this
information to determine their decisions. As a consequence, first movers invest more into
districts that are actually characterized by higher levels of trustworthiness. In this sense,
we can interpret the observed discrimination pattern, at least in part, in terms of statistical discrimination. Rather than being only driven by taste or prejudice, many people
in the city of Zurich discriminate on the basis of their relatively accurate beliefs. We also
find strong support for the existence of in-group favoritism in trust. Citizens of Zurich
tend to favor strangers from their own district, in part because they expect them to be
more trustworthy than strangers from other districts.
The fact that people discriminate between strangers from different districts can have
important economic and social consequences, not only for an individual living in a particular district but also for districts as a whole. On an individual level it is relevant insofar
as many economically relevant transactions involve some element of trust. In the hiring
process, e.g., two otherwise equal applicants may be treated differently simply because
they come from different parts of the city. On the level of districts, trust discrimination may foster the process of segregation. The Zurich case shows that districts with a
relatively high socio-economic status are also those, which enjoy the highest reputation
of being trustworthy. Since this reputation favors investments there is an endogenous
tendency to reinforce inner city inequalities. Relatively richer districts are trusted more
and therefore become even richer. This process is reinforced by housing rents and moving
decisions. Those who can afford it will move to high reputation districts, again increasing
18
district inequalities.
Our results are also relevant from a city development point of view. The study demonstrates that policy makers can use field experiments to identify the reputation of different
neighborhoods in a way that is relevant for the citizens of the respective city or region.
Running similar experiments could help identify problem areas in a cheap and reliable
way. It also helps providing potential indicators for future district development, which
allows targeting appropriate policies to specific districts.
19
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22
Figure 1: Map of Zurich as distributed to participants
23
0
.1
Relative frequency
.2
.3
.4
Figure 2: Histogram of first mover investments
0
2
4
6
8
10
12
Investments
24
14
16
18
20
Fraction of participants in the newspaper study
.1
.2
.3
.4
.5
.6
.7
.8
Figure 3: Answers of newspaper readers
0
High
Low
4
12
5
9
11
3
2
1
Receiving districts
25
10
6
7
8
Average back transfer
10
15
20
25
30
35
Figure 4: Actual and expected second mover back transfers
0
5
Exp. back transfer
Back transfer
0
2
4
6
8
10
12
Investment
26
14
16
18
20
2.2
Figure 5: Correlation of investments and reciprocal inclination
Mean reciprocal inclination
1.6
1.8
2
1
6
7
2
8
9
5
10
3
4
11
1.4
12
12.5
13
13.5
Mean received investment
14
Notes: Each numbered dot in the figure corresponds to one of Zurich’s districts. The line
represents the predicted values for the mean reciprocal inclination based on a linear regression
of mean reciprocal inclination on mean received investments.
27
Table 1: Decision table for first movers
Suppose the other
person lives in
district
1
2
...
12
How much of your
CHF 20 do you
invest?
28
How much do you
expect to get
back?
Table 2: Average investment into districts and expected back transfers
Into district
Investment
Expected back transfer
Expected return on investment1
1
2
3
4
5
6
13.41 13.30 13.04 12.44 12.50 13.72
18.22 17.43 16.73 15.12 15.26 18.15
0.30 0.23 0.24 0.15 0.15 0.24
Into district
Investment
Expected back transfer
Expected return on investment1
7
8
9
10
11
12
13.74 13.83 12.90 13.68 12.91 12.45
17.87 18.17 16.07 17.63 15.96 15.07
0.25 0.25 0.19 0.23 0.17 0.16
´
³
back transfer
We calculate the expected return on investment = expected
−
1
for each single
investment
positive investment decision of first movers. Note that in cases where investments are zero,
no meaningful values can be calculated. These observations are therefore neglected (7 percent
of our observations contain investments equal to zero; in 91 percent of these cases expected
back transfers are zero as well).
1
29
Table 3: Pair-wise comparison of investments into districts
Districts
4
12
5
9
11
3
2
1
10
6
7
12
0.99
5
9
11
3
2
0.20 0.00 0.00 0.00 0.00
0.35 0.00 0.00 0.00 0.00
0.01 0.01 0.00 0.00
0.86 0.20 0.00
0.10 0.00
0.03
1
0.00
0.00
0.00
0.01
0.01
0.10
0.80
10
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.17
6
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.57
7
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.22
0.43
8
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.03
0.65
0.53
0.89
Notes: The table reports p-values of pair-wise Wilcoxon-signed-rank tests. The units of observation are individual first mover investments. Districts are ordered by received investments
such that districts with similar received investment are located close to each other.
30
31
Income
39
40
35
30
36
40
44
42
36
40
36
31
0.92
[0.000]
High
education2
0.48
0.33
0.26
0.25
0.30
0.44
0.47
0.44
0.19
0.33
0.24
0.15
0.83
[0.001]
Foreigners
0.22
0.23
0.33
0.44
0.39
0.23
0.19
0.25
0.33
0.25
0.33
0.35
-0.85
[0.000]
3
Religious
heterogeneity4
0.68
0.72
0.72
0.71
0.71
0.69
0.68
0.69
0.70
0.70
0.71
0.71
-0.65
[0.022]
Years of
residency5
8.1
10.9
9.4
7.7
6.7
9.9
10.8
10.0
11.3
10.3
9.4
11.0
0.18
[0.572]
Home
ownership6
0.09
0.06
0.04
0.04
0.06
0.06
0.13
0.08
0.05
0.09
0.06
0.04
0.74
[0.006]
Notes: Source: Statistical Office of Zurich and Statistical Yearbook of the City of Zurich (2003)
1
median per capita income in 1000 Swiss Francs (data for unmarried persons only)
2
population fraction with at least a ”matura” degree (prerequisite for attending university)
3
population fraction of foreigners
4
fragmentation index = 1 - sum of squared population fractions of all religions
5
average number of years with residency in the same district per person
6
fraction of apartments owned by inhabitants
7
population fraction of Catholics
8
Spearman’s Rho for the correlation of first mover investments and the variable (p-values in brackets)
District
1
2
3
4
5
6
7
8
9
10
11
12
Spearm. Rho8
1
Table 4: District characteristics
Catholics7
0.27
0.31
0.33
0.36
0.32
0.32
0.28
0.31
0.37
0.32
0.35
0.34
-0.75
[0.005]
32
8.928***
[0.616]
YES
6087
0.85
(1)
0.113***
[0.017]
14.981***
[0.280]
YES
6087
0.85
-6.239***
[0.952]
(2)
11.740***
[0.892]
YES
6087
0.85
(3)
0.063***
[0.018]
-3.150***
[1.134]
11.889***
[0.881]
YES
6087
0.85
(4)
0.051***
[0.020]
-2.954**
[1.168]
0.677
[0.747]
10.547***
[1.432]
YES
6087
0.85
4.252
[3.691]
(5)
0.058***
[0.018]
-2.803**
[1.168]
Received investment
11.716***
[1.155]
YES
6087
0.85
0.001
[0.038]
(6)
0.063***
[0.018]
-3.129**
[1.253]
11.263***
[0.926]
YES
6087
0.85
-3.869
[2.485]
(7)
0.082***
[0.021]
-3.197***
[1.135]
2.268
[2.285]
11.085***
[1.081]
YES
6087
0.85
(8)
0.065***
[0.018]
-3.694***
[1.281]
Notes: OLS-estimation with robust standard errors clustered on individuals in brackets. The dependent variable contains 12 investment
decisions per first mover (one for each district). Details on the independent variables are found in Table 4. * significant at 10%; ** significant
at 5%; *** significant at 1%.
Individual fixed effects
Observations
R-squared
Constant
Roman catholics
Home ownership
Years of residency
Religious heterogeneity
High education
Foreigners
Income
Dependent variable
Table 5: Determinants of received investments at the district level
Table 6: First mover’s in-group bias
Dependent variable
Own district
Investment
Exp. back transfer
(1)
1.396***
[0.160]
(2)
1.076***
[0.247]
1.097***
[0.067]
2.294***
[0.872]
YES
6086
0.89
First mover’s investment
Constant
Individual fixed effects
Observations
R-squared
13.032***
[0.013]
YES
6087
0.85
Notes: OLS-estimations with robust standard errors clustered on
individuals in brackets. The dependent variables contain 12 observations (investments resp. expected back transfers) per first mover
(one for each district). * significant at 10%; ** significant at 5%; ***
significant at 1%. We lose one observation in Column (2) due to a
non-response.
33
Table 7: Definitions of variables (personal chararacteristics)
Age X-Y
Female
Only Child
Tax Income
High skilled
Married
Children
Foreigner
Years of residency in city
Associated with city
Years of residency in district
Associated with own district
Rightwinger
Leftwinger
Catholic
Protestant
Other religion
Dummy variable that takes on the value 1 if the person is in the
age range X to Y and 0 otherwise.
Dummy variable that takes on the value 1 if the person is female
and 0 otherwise.
Dummy variable that takes on the value 1 if the person does not
have siblings.
Taxable income as reported to the tax authorities of Zurich (in
10’000 Swiss Francs). As married couples only report their combined
income to the authorities, we divide the reported value by 2
in case of married people.
Dummy variable that takes on the value 1 if the person has a
ISCO skill level of 4 and 0 otherwise. The International Standard
Classification of Occupations (ISCO-88) organizes occupations
in an hierarchical framework and assigns a skill level (1 (elementary
occupations) to 4 (professionals)) to each occupation.
Dummy variable that takes on the value 1 if the person is married
and 0 otherwise.
Number of children of the person
Dummy variable that takes on the value 1 if the person is not a
Swiss citizen and 0 otherwise.
Number of years that the person has lived in the city of Zurich.
Dummy variable that indicates whether the person feels strongly
associated with the city of Zurich; originally measured on a four-point
scale from 1 (not at all) to 4 (very strongly). The dummy takes on
the value 1 if the person has ticked “very strongly” and 0 otherwise.
Number of years that the person has lived in the current district
of residency.
Dummy variable that indicates whether the person feels strongly
associated with her district of residency; originally measured on a
four-point scale from 1 (not at all) to 4 (very strongly). The dummy
takes on the value 1 if the person has ticked “very strongly” and
0 otherwise.
Dummy variable that indicates whether the person conceives
herself as a rightwinger; originally measured on a
five-point scale from 1 (leftwing) to 5 (rightwing). The dummy
takes on the value 1 if the person has ticked “rightwing” and
0 otherwise.
Dummy variable that indicates whether the person conceives
herself as a leftwinger; originally measured on a
five-point scale from 1 (leftwing) to 5 (rightwing). The dummy
takes on the value 1 if the person has ticked “leftwing” and
0 otherwise.
Dummy variable that takes on the value 1 if the person is a roman
Catholic and 0 otherwise.
Dummy variable that takes on the value 1 if the person is a Protestant
and 0 otherwise.
Dummy variable that takes on the value 1 if the person reports a
confession other than Catholic or Protestant (but not no confession) and
0 otherwise.
34
Table 8: Individual determinants of discrimination and in-group favoritism
Dependent variable
Age 31-45
Age 46-60
Age 61-75
Age 76 and older
Female
Only child
Discrimination
(1)
-0.027
[0.168]
0.175
[0.188]
0.691***
[0.219]
0.955***
[0.300]
0.05
[0.125]
0.113
[0.182]
(2)
0.049
[0.181]
0.213
[0.201]
0.568**
[0.246]
0.727**
[0.359]
0.041
[0.133]
0.027
[0.192]
0.001
[0.016]
-0.362***
[0.125]
0.042
[0.150]
-0.148*
[0.083]
0.249
[0.228]
-0.116
[0.154]
491
0.019
[0.178]
470
Tax Income
High skilled
Married
Children
Foreigner
Years of residency in city
Associated with city
Years of residency in district
Associated with own district
Rightwinger
Leftwinger
Catholic
Protestant
Other religion
Constant
Observations
R-squared
In-group Bias
(3)
0.051
[0.190]
0.291
[0.220]
0.551*
[0.289]
0.752*
[0.428]
0.021
[0.138]
-0.02
[0.195]
-0.01
[0.017]
-0.327**
[0.128]
0.035
[0.153]
-0.151*
[0.083]
0.257
[0.234]
0.003
[0.006]
0.124
[0.136]
-0.003
[0.007]
0.086
[0.182]
0.822**
[0.392]
-0.211
[0.162]
0.087
[0.198]
-0.303
[0.190]
-0.161
[0.217]
0.092
[0.251]
467
(4)
-0.774
[0.480]
-0.593
[0.538]
0.298
[0.606]
0.509
[0.767]
0.136
[0.353]
0.344
[0.516]
(5)
-0.722
[0.512]
-0.601
[0.570]
0.327
[0.672]
0.392
[0.938]
0.109
[0.374]
0.614
[0.538]
0.026
[0.047]
-0.35
[0.352]
-0.052
[0.416]
-0.047
[0.224]
0.183
[0.632]
1.713***
[0.441]
491
0.02
1.771***
[0.507]
470
0.02
(6)
-0.647
[0.527]
-0.561
[0.612]
0.285
[0.795]
0.13
[1.123]
0.047
[0.380]
0.573
[0.548]
0.034
[0.050]
-0.391
[0.358]
-0.02
[0.422]
-0.11
[0.228]
0.295
[0.651]
0.008
[0.015]
0.255
[0.381]
-0.007
[0.018]
1.433***
[0.519]
-0.226
[0.973]
0.137
[0.447]
-0.242
[0.545]
-0.597
[0.529]
-0.38
[0.600]
1.712**
[0.690]
467
0.05
Notes: Columns (1) to (3): Probit estimations with robust standard errors in brackets. The dependent
variable is an indicator variable that takes the value 1 if the first mover has discriminated and 0 otherwise.
Columns (4) to (6): OLS-estimations with robust standard errors clustered on individuals in brackets.
The dependent variable is the difference between a first mover’s investment into his own district and his
average investment into other districts. Details on the independent variables in all regressions of this
table are found in Table 7. * significant at 10%; ** significant at 5%; *** significant at 1%. We lose
observations in Columns (2), (3), (5) and (6) due to non-responses.
35

Die doppelte Kontingenz von Elfmeterschüssen.

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