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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 N ε (independent of the number n of voters) such that, if the maximum number of votes of the most popular agent is at least N ε 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 M ε .

Keywords

Directed Graph Random Permutation Sampling Phase Approximation Guarantee Election Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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    de Clippel, G., Moulin, H., Tideman, N.: Impartial division of a dollar. Journal of Economic Theory 139, 176–191 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
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    Dekel, O., Fischer, F., Procaccia, A.: Incentive compatible regression learning. Journal of Computer and System Sciences 76(8), 759–777 (2013)CrossRefMathSciNetGoogle 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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    Holzman, R., Moulin, H.: Impartial nominations for a prize. Econometrica 81(1), 173–196 (2013)CrossRefzbMATHMathSciNetGoogle 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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