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Robust Information Aggregation in Committees

Abstract: Numerous theoretical studies have shown that information aggregation through voting is fragile: Since the probability that any agent’s vote influences the committee’s decision becomes arbitrarily small in a large committee, voting behavior is very sensitive to the payoff structure. For example, when agents face payoffs that condition on their individual vote, then these vote-contingent payoffs drive voting behavior in large committees. In this paper, we consider a general model of voting behavior in large committees with vote-contingent payoffs and characterize the set of payoffs lead to a unique equilibrium that aggregates information. Interestingly, we find that the existence of an equilibrium that aggregates information depends only on the ratio of relative payoffs agents receive for voting for the ex-post correct option given that the committee also selects the correct option. However, the uniqueness of the equilibrium that aggregates information depends on payoffs when the committee selects the in- correct option; for information aggregation to be robust, agents must be punished for voting with the committee for the incorrect option.