Pre-election polls as strategic coordination devices

In the unique attainable equilibrium of a voting model with one minority candidate and two similarly appealing majority candidates, majority voters are unable to coordinate their support and the minority candidate (Condorcet loser) is elected. Suppose a random sample of voters is asked about their preferences prior to the election. We show that there always exists an equilibrium of this two stage game in which all poll participants are truthful, resulting in a high likelihood of a majority candidate winning the election. This equilibrium is unique if the sample size of the poll is Poisson distributed or fixed and odd.