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On the Indecisiveness of Kelly-Strategyproof Social Choice Functions

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  • Felix Brandt
  • Martin Bullinger
  • Patrick Lederer

Abstract

Social choice functions (SCFs) map the preferences of a group of agents over some set of alternatives to a non-empty subset of alternatives. The Gibbard-Satterthwaite theorem has shown that only extremely restrictive SCFs are strategyproof when there are more than two alternatives. For set-valued SCFs, or so-called social choice correspondences, the situation is less clear. There are miscellaneous - mostly negative - results using a variety of strategyproofness notions and additional requirements. The simple and intuitive notion of Kelly-strategyproofness has turned out to be particularly compelling because it is weak enough to still allow for positive results. For example, the Pareto rule is strategyproof even when preferences are weak, and a number of attractive SCFs (such as the top cycle, the uncovered set, and the essential set) are strategyproof for strict preferences. In this paper, we show that, for weak preferences, only indecisive SCFs can satisfy strategyproofness. In particular, (i) every strategyproof rank-based SCF violates Pareto-optimality, (ii) every strategyproof support-based SCF (which generalize Fishburn's C2 SCFs) that satisfies Pareto-optimality returns at least one most preferred alternative of every voter, and (iii) every strategyproof non-imposing SCF returns the Condorcet loser in at least one profile. We also discuss the consequences of these results for randomized social choice.

Suggested Citation

  • Felix Brandt & Martin Bullinger & Patrick Lederer, 2021. "On the Indecisiveness of Kelly-Strategyproof Social Choice Functions," Papers 2102.00499, arXiv.org, revised Mar 2022.
  • Handle: RePEc:arx:papers:2102.00499
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    References listed on IDEAS

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    Cited by:

    1. Brandt, Felix & Lederer, Patrick & Suksompong, Warut, 2023. "Incentives in social decision schemes with pairwise comparison preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 266-291.
    2. Hayrullah Dindar & Jean Lainé, 2023. "Vote swapping in irresolute two-tier voting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 221-262, August.
    3. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).

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