Doodle Poll Games.

In Doodle polls, each voter approves a subset of the available alternatives according to his preferences. While such polls can be captured by the standard models of Approval voting, Zou et al. (2015) analyse real-life Doodle poll data and conclude that poll participants' behaviour seems to be affected by considerations other than their intrinsic preferences over the alternatives. To capture this phenomenon, they propose a model of social voting, where voters approve their top alternatives as well as additional `safe' choices so as to appear cooperative. The predictions of this model turn out to be consistent with the real-life data. However, Zou et al. do not attempt to rationalise the voters' behaviour in the context of social voting: they explicitly describe the voters' strategies rather than explain how these strategies arise from voters' preferences. In this paper, we complement the work of Zou et al. by putting forward a model in which the behaviour described by Zou et al. arises as an equilibrium strategy. In our model, a voter derives a bonus from approving each additional alternative, up to a certain cap. We show that trembling hand perfect Nash equilibria of our model behave consistently with the model of Zou et al. Importantly, placing a cap on the total bonus is an essential component of our model: in the absence of the cap, all Nash equilibria are very far from the behaviour observed in Doodle polls.