Information Aggregation in Two-Candidate Elections

Abstract

Many interesting political institutions, such as campaigning, polls, and sequences of elections cannot be understood in the context of standard spatial competition models of elections with fully informed candidates and voters. To fill this void, we introduce a model of elections in which candidates are privately and asymmetrically informed about the electorate. This model differs from other incomplete information models, such as the rational expectations model, in that a full range of sequential strategic behavior is considered. We begin with a model in which candidates can constantly revise their positions before the election. In this case, one might expect each to "invert" the other's strategies and infer the other's private information, as is done in equilibrium with rational expectations. However, we find that each candidate, knowing the other will try to make such inferences, will follow a strategy which is not invertible. No information will leak from one candidate to the other. The outcome will be identical to a single-move election with incomplete information and no information aggregation will occur. The introduction of a public poll changes the results in an interesting way. Candidates still use pooling strategies (strategies that are constant on their private information) to avoid leaking anything to the opponent but, contrary to the case without the poll, candidates learn about the electorate before the election. In equilibrium, candidates use mixed strategies (pure strategy equilibria do not exist) and the better informed player cannot prevent the lesser informed from learning from the poll. No private information is leaked but information aggregation occurs. We conclude with an examination of the effect on information aggregation of a sequence of elections. In the previous results, candidates moves were "free" in the sense that revisions were costless as in a "cheap talk" model. Now moves are not free and hiding information today in order to improve one's chances of winning tomorrow may lower one's chances today. We show that information aggregation may occur both through the results of the election (as with the poll) and through the leakage of private information. We also provide an example in which the strategic choices of the candidates are skewed away from the rational expectations equilibrium. Because of the asymmetric information and the strategic issues surrounding information leakage, behavior is different than would be observed in simple one-shot elections.

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