We analyze two-candidate elections in which voters are uncertain about the realization of a state variable that affects the utility of all voters. Each voter has noisy private information about the state variable. We show that the fraction of voters whose vote depends on their private information goes to zero as the size of the electorate goes to infinity. Nevertheless elections fully aggregate information in the sense that the chose candidate would not change if all private information were common knowledge among voters. We also show that the equilibrium voting behavior is to a large extent determined by the electoral rule, i.e., if a candidate is required to get at least x percent of the vote in order to win the election then in equilibrium this candidate gets very close to x percent of the vote with probability close to one.
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