Condorcet Jury Theorem and Cognitive Hierarchies: Theory and Experiments

An information aggregation problem of the Condorcet Jury Theorem is considered with cognitive hierarchy models in which players would best respond holding heterogeneous beliefs on cognitive level of the other players. Whether the players are aware of the presence of opponents at their own cognitive level turns out to be a key factor for asymptotic properties of the deviation from the Nash behavior, and thence for asymptotic efficiency of the group decision. Our laboratory experiments provide evidence for the self-awareness condition. We obtain an analytical result showing that the difference from the standard cognitive hierarchy models arises when the best-reply functions are asymptotically expanding.