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Symmetry and impartial lotteries

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  • Mackenzie, Andrew

Abstract

A prize is to be awarded, so each candidate designates one of his peers on a ballot. The ballots determine the lottery that selects the winner, and impartiality requires that no candidate's choice of designee impacts his own chance of winning, removing incentives for strategic ballot submission. The primary results are (1) a characterization of all impartial rules that treat agents symmetrically as voters, and (2) a characterization of all impartial rules that treat agents symmetrically as candidates. Each rule in either class may be represented as a randomization over a finite set of simple rules. These results have immediate interpretation in a second context: the division of surplus among team members. Corollaries include the constant rule impossibility of Holzman and Moulin (2013), a new dictatorship impossibility, and the first axiomatic characterization of uniform random dictatorship.

Suggested Citation

  • Mackenzie, Andrew, 2015. "Symmetry and impartial lotteries," Games and Economic Behavior, Elsevier, vol. 94(C), pages 15-28.
    • Handle: RePEc:eee:gamebe:v:94:y:2015:i:c:p:15-28
    DOI: 10.1016/j.geb.2015.08.007
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Pablo Amorós, 2020. "Aggregating experts’ opinions to select the winner of a competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 833-849, September.
    2. Amorós, Pablo, 2021. "Using supermajority rules to aggregate judgments of possibly biased experts," Economics Letters, Elsevier, vol. 207(C).
    3. Edelman, Paul H. & Por, Attila, 2021. "A new axiomatic approach to the impartial nomination problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 443-451.
    4. Matthew Olckers & Toby Walsh, 2022. "Manipulation and Peer Mechanisms: A Survey," Papers 2210.01984, arXiv.org, revised May 2024.
    5. Javier Cembrano & Felix Fischer & Max Klimm, 2023. "Optimal Impartial Correspondences," Papers 2301.04544, arXiv.org.
    6. Axel Niemeyer & Justus Preusser, 2023. "Simple Allocation with Correlated Types," CRC TR 224 Discussion Paper Series crctr224_2023_486, University of Bonn and University of Mannheim, Germany.
    7. Bloch, Francis & Dutta, Bhaskar & Dziubiński, Marcin, 2023. "Selecting a winner with external referees," Journal of Economic Theory, Elsevier, vol. 211(C).
    8. Amorós, Pablo, 2022. "Implementation in dominant strategies of quota rules to choose one candidate," Economics Letters, Elsevier, vol. 216(C).
    9. Andrew Mackenzie, 2020. "An axiomatic analysis of the papal conclave," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 713-743, April.
    10. Amorós, Pablo, 2020. "Using sub-majoritarian rules to select the winner of a competition," Economics Letters, Elsevier, vol. 190(C).
    11. Mackenzie, Andrew, 2018. "A Game of the Throne of Saint Peter," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    12. Ruben Juarez & Kohei Nitta & Miguel Vargas, 2020. "Profit-sharing and efficient time allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 817-846, October.
    13. Javier Cembrano & Felix Fischer & Max Klimm, 2023. "Improved Bounds for Single-Nomination Impartial Selection," Papers 2305.09998, arXiv.org.
    14. Cembrano, Javier & Fischer, Felix & Hannon, David & Klimm, Max, 2024. "Impartial selection with additive guarantees via iterated deletion," Games and Economic Behavior, Elsevier, vol. 144(C), pages 203-224.

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    More about this item

    Keywords

    Symmetry; Impartiality; Name independence; Voter anonymity; Candidate neutrality;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • M52 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Compensation and Compensation Methods and Their Effects

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