Coordination in Turnout Games∗

We present a stochastic model of coordination in turnout games. 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 conÞguration 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. The model’s predictions are also consistent with the usual empirical regularities about turnout. We then derive continuum approximation results for large electorates using a partial differential formulation and apply the results to the case of perfectly informative polls. We show that under (perturbed) best response voters are able to spontaneously coordinate their actions on a single state.