The Condorcet Jury Theorem under Cognitive Hierarchies: Theory and Experiments

Abstract. Cognitive hierarchy models have been developed to explain systematic devi-ations from the equilibrium behavior in certain classes of games. This paper introduces an endogenous cognitive hierarchy model, which better explains the behavioral heterogene-ity of the strategies in games for which the standard cognitive hierarchy model provides an unreasonable prediction. As in the previous models, each player in the endogenous cognitive hierarchy model is assumed to best-reply to the other players holding a belief induced by the cognitive hierarchy. Contrary to the previous models, however, players are allowed to consider the presence of opponents at their own level of cognitive hierarchy. This extension is shown to eradicate the incompatibility of cognitive hierarchy models in the classes of games. We employ the model to explain voting behavior in information aggregation problems of the Condorcet Jury Theorem. Behavioral assumption of the strategic thinking turns out to be a crucial factor in whether the asymptotic efficiency is obtained or not. We conducted laboratory experiments which show that the endogenous cognitive hierarchy model provides significant improvements upon symmetric Bayesian Nash equilibrium and the previous cognitive hierarchy models in explaining the observed behavior of voters. 1