Persuasion and Information Aggregation in Large Elections

This paper studies the Bayes correlated equilibria of large majority elections in a general environment with heterogeneous, private preferences. Voters have exogeneous private signals and a version of the Condorcet Jury Theorem holds when voters do not receive additional information (Feddersen & Pesendorfer, 1997). We show that any state-contingent outcome can be implemented in some Bayes-Nash equilibrium by an expansion of the exogenous private signal structure. We interpret the result in terms of the possibility of persuasion by a biased sender who provides additional information to voters who also have noisy private information from other sources. The additional information can be an almost public signal that almost reveals the state truthfully. The same additional information is shown to be effective uniformly across environments so that persuasion does not require detailed knowledge of the distribution of the voters' private information and preferences. In a numerical example with uniform voter types, we show the effects of persuasion with already 17 or more voters.