Coordinations and Turnouts in Large Elections

We present a stochastic model of coordination in turnout games with boundedly rational voters. In each period a randomly selected voter receives information about current play through noisy polls and then, based on this information, forms expectations about the current configuration of play and chooses a best response. 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 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 is consistent with the usual empirical regularities about turnout. Continuum results for large electorates are presented.