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Inefficiency of Equilibria in Doodle Polls

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11346)


Doodle polls allow people to schedule meetings or events based on 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-theoretic 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 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 find some reasonable conditions under which the quality of the NE (and strong NE) is good.


  • Doodle polls
  • Nash equilibria
  • Approval voting

A 2-page extended abstract of an earlier version of this work was published in [2].

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  1. 1.

    A sample of over 340,000 polls in a 3-month period in 2011 had a median of about 5 respondents and 12 time slots [17].


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Correspondence to Barbara M. Anthony .

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Anthony, B.M., Chung, C. (2018). Inefficiency of Equilibria in Doodle Polls. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham.

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  • Print ISBN: 978-3-030-04650-7

  • Online ISBN: 978-3-030-04651-4

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