Doodle Poll Games

In Doodle polls, each voter may approve 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. [17] analyse reallife Doodle poll data and conclude that poll participants’ behaviour seems to be affected by considerations other than their intrinsic preferences over the alternatives. In particular, they propose a model of social voting, where participants approve their top alternatives as well as additional ‘safe’ choices so as to appear cooperative. The appeal of their model is that it appears to be consistent with the real-life data. However, Zou et al. explicitly describe the voters’ strategies rather than attempt to rationalise them in terms of 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. We do so by formally modelling the bonus that voters derive from approving additional alternatives. We consider two scenarios: one where this bonus is accumulated over all approved alternatives, and one where it is capped by a certain threshold. The former model turns out to be easier to analyse, but its predictions do not appear realistic; in contrast, trembling hand perfect Nash equilibria of the latter model behave consistently with the model of Zou et al.