Coordination and turnout in large elections

Competitive elections are frequently decided by which side can generate larger turnout on polling day. When decided on whether to turn out voters are assumed to balance the cost of going to the polls with the prospect of making a difference in the election outcome. We present a stochastic model of turnout where voters receive information about current turnout propensities of the voting populus through opinion polls. Voters then decide on whether to vote or not by maximizing their expected utility based on the (potentially noisy) polling information as well as the costs and benefits of participation. We prove the existence of a unique limiting distribution for the process and show that even in large electorates substantial expected turnout is possible if voting factions are sufficiently similar in size. A key requirement for substantial turnout is that polls never provide precise feedback on the current state of the electorate. The effect of noise, however, is non-monotonic: no noise or too much noise results in vanishing turnout, while moderate noise may result in substantial turnout. Our model also can account for known empirical regularities about turnout identified in the political science literature.