Full Information Equivalence in Large Elections

Abstract

We study the problem of aggregation of private information in common-value elections with two or more alternatives and with general state and signal spaces. We provide conditions on the environment for which there exists a strategy that aggregates information efficiently as the electorate grows large. Drawing upon McLennan (1998), we show that whenever aggregation is feasible in the above sense, there also exists a sequence of Nash equilibria that aggregates information. Our approach explores the geometry of partitions on the simplex of distributions over private signals induced by the common state-dependent utility of the voters. In broad terms, information can be aggregated in equilibrium when states with the same top-ranked alternative generate similar signal distributions, where similarity is captured by specific convex partitions of the simplex. This is met generically when the signal space is rich enough relative to the state space, and fails robustly when the state space is rich relative to the signal space. Our results hold for a variety of popular voting rules, and our feasibility results also apply to the non-common-value case.