A Near-Optimal Mechanism for Impartial Selection

  • Nicolas Bousquet
  • Sergey Norin
  • Adrian Vetta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8877)

Abstract

We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin [5] and Alon et al. [1]. Fischer and Klimm [4] showed that the permutation mechanism is impartial and \(\frac12\)-optimal, that is, it selects an agent who gains, in expectation, at least half the number of votes of the most popular agent. Furthermore, they showed the mechanism is \(\frac{7}{12}\)-optimal if agents cannot abstain in the election. We show that a better guarantee is possible, provided the most popular agent receives at least a large enough, but constant, number of votes. Specifically, we prove that, for any ε > 0, there is a constant Nε (independent of the number n of voters) such that, if the maximum number of votes of the most popular agent is at least Nε then the permutation mechanism is \((\frac{3}{4}-\epsilon)\)-optimal. This result is tight.

Furthermore, in our main result, we prove that near-optimal impartial mechanisms exist. In particular, there is an impartial mechanism that is (1 − ε)-optimal, for any ε > 0, provided that the maximum number of votes of the most popular agent is at least a constant Mε.

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References

  1. 1.
    Alon, N., Fischer, F., Procaccia, A., Tennenholtz, M.: Sum of us: Strategyproof selection from the selectors. In: Proceedings of 13th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), pp. 101–110 (2011)Google Scholar
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    Fischer, F., Klimm, M.: Optimal impartial selection. In: Proceedings of the 15th Conference on Economics and Computation (EC), pp. 803–820 (2014)Google Scholar
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    Procaccia, A., Tennenholtz, M.: Approximate mechanism design without money. ACM Transcactions on Economics and Computing (to appear, 2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nicolas Bousquet
    • 1
    • 3
  • Sergey Norin
    • 1
  • Adrian Vetta
    • 1
    • 2
  1. 1.Department of Mathematics and StatisticsMcGill UniversityCanada
  2. 2.School of Computer ScienceMcGill UniversityCanada
  3. 3.Group for Research in Decision Analysis (GERAD), HECMontréalCanada

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