How Bad is Selfish Doodle Voting?

Doodle polls allow people to schedule meetings or events based on the time preferences of participants. Each participant indicates on a web-based poll form which time slots they find acceptable and a time slot with the most votes is chosen. This is a social choice mechanism known as approval voting, in which a standard assumption is that all voters vote sincerely-no one votes no on a time slot they prefer to a time slot they have voted yes on. We take a game theoretical approach to understanding what happens in Doodle polls assuming participants vote sincerely. First we characterize Doodle poll instances where sincere pure Nash Equilibria (NE) exist, both under lexicographic tie-breaking and randomized tie-breaking. We then study the quality of such NE voting profiles in Doodle polls, showing that the price of anarchy and price of stability are both unbounded, even when a time slot that many participants vote yes for is selected. Finally, we give some conditions under which the quality of the NE (and strong NE) is good.