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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 (“information aggregation”). We show that any state-contingent outcome can be implemented in Bayes-Nash equilibrium by some expansion of the given private signal structure.
We interpret the result in terms of the possibility of persuasion of privately informed voters by a biased sender. We show that persuasion does not require detailed knowledge of the distribution of voters’ preferences. An implication of our result is that an outside analyst who only knows that voters receive at least the information assumed in the Condorcet Jury Theorem cannot make a robust prediction on the election outcome.
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