Nonmyopic voting dynamics: An optimistic approach

Iterative voting has presented, in the past few years, a voting model in which a player participates in an election poll, and can change his vote at any time to influence the result. Several extensions for this model have been considered, including some attempts to handle the uncertainty that players may face. However, all those extensions retained the myopic assumption—that is, players change their vote only when they believe that their move will have an immediate effect on the outcome. In this paper, we address this assumption by allowing for certain non-myopic dynamics. Specifically, the outlook is optimistic to a certain extent, a horizon, as players change their vote if they believe that if some other players also move, the outcome can change. We show that players with the same horizon of optimism would converge to a Nash equilibrium under Plurality, and for Veto, even players with varying horizons of optimism always converge. However, such non-myopic behavior is not necessarily a positive feature—as we demonstrate, in some cases it is better for the player to stick to myopic moves.