Electoral Competition with Privately-Informed Candidates

Abstract

We consider a model of elections in which two office-motivated candidates receive private signals about the location of the median voter's ideal point prior to taking policy positions. We show that at most one pure strategy equilibrium exists and provide a sharp characterization, if one exists: After receiving a signal, each candidate locates at the median of the distribution of the median voter's location, conditional on the other candidate receiving the same signal. It follows that a candidate's position, conditional on his/her signal, is a biased estimate of the true median, with candidate positions tending to the extremes of the policy space. We provide sufficient conditions for the existence of a pure strategy equilibrium. Essentially, the pure strategy equilibrium exists if for each signal, the other candidate is sufficiently likely to receive a signal in the same direction that is at least as extreme. Though the electoral game exhibits discontinuous payoffs for the candidates, we prove that mixed strategy equilibria exist generally, that equilibrium expected payoffs are continuous in the parameters of the model, and that mixed strategy equilibria are upper hemicontinuous. We investigate the robustness of the median voter theorem to private information: Pure strategy equilibria may fail to exist in models close to the Downsian model, but mixed strategy equilibria must, and they will be "close" to the Downsian equilibrium. Finally, we provide bounds on the support of mixed strategy equilibria and restrictions on possible atoms of equilibrium mixed strategies.