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Strategyproof social choice when preferences and outcomes may contain ties

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  • Brandt, Felix
  • Saile, Christian
  • Stricker, Christian

Abstract

The Gibbard-Satterthwaite theorem implies that all anonymous, Pareto-optimal, and single-valued social choice functions can be strategically manipulated. In this paper, we investigate whether there exist social choice correspondences (SCCs), that satisfy these conditions under various assumptions about how single alternatives are eventually selected from the choice set. These assumptions include even-chance lotteries as well as resolute choice functions and linear tie-breaking orderings unknown to the agents. We show that (i) all anonymous Pareto-optimal SCCs where ties are broken according to some linear tie-breaking ordering or by means of even-chance lotteries are manipulable, and that (ii) all pairwise Pareto-optimal SCCs are manipulable for any deterministic tie-breaking rule. These results are proved by reducing the statements to finite—yet very large—formulas in propositional logic, which are then shown to be unsatisfiable by a computer.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jetheo:v:202:y:2022:i:c:s0022053122000370
    DOI: 10.1016/j.jet.2022.105447
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    4. Fujun Hou, 2024. "A new social welfare function with a number of desirable properties," Papers 2403.16373, arXiv.org.

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    More about this item

    Keywords

    Gibbard-Satterthwaite theorem; Social choice theory; Strategyproofness; Pareto optimality;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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