Doodle poll games - Obraztsova, S; Rabinovich, Z; Polukarov, M; Elkind, E (Association for Computing Machinery, 2017)
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. [18] 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.