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Condorcet Consistency and the strong no show paradoxes

Author

Listed:
  • Kasper, Laura
  • Peters, Hans

    (RS: GSBE ETBC, QE Math. Economics & Game Theory)

  • Vermeulen, Dries

    (RS: GSBE ETBC, QE Operations research)

Abstract

We consider voting correspondences that are, besides Condorcet Consistent, immune against the two strong no show paradoxes. That is, it cannot happen that if an additional voter ranks a winning alternative on top then that alternative becomes loosing, and that if an additional voter ranks a loosing alternative at bottom then that alternative becomes winning. This immunity is called the Top Property in the first case and the Bottom Property in the second case. We establish the voting correspondence satisfying Condorcet Consistency and the Top Property, which is maximal in the following strong sense: it is the union of all smaller voting correspondences with these two properties. The result remains true if we add the Bottom Property but not if we replace the Top Property by the Bottom Property. This voting correspondence contains the Minimax Rule but it is strictly larger. In particular, voting functions (single-valued voting correspondences) that are Condorcet Consistent and immune against the two paradoxes must select from this maximal correspondence, and we demonstrate several ways in which this can or cannot be done.

Suggested Citation

  • Kasper, Laura & Peters, Hans & Vermeulen, Dries, 2017. "Condorcet Consistency and the strong no show paradoxes," Research Memorandum 017, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2017017
    DOI: 10.26481/umagsb.2017017
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    Cited by:

    1. Diss, Mostapha & Dougherty, Keith & Heckelman, Jac C., 2023. "When ties are possible: Weak Condorcet winners and Arrovian rationality," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 128-136.
    2. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    3. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
    4. Szybowski, Jacek & KuĊ‚akowski, Konrad & Prusak, Anna, 2020. "New inconsistency indicators for incomplete pairwise comparisons matrices," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 138-145.
    5. Wesley H. Holliday & Eric Pacuit, 2023. "Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers," Public Choice, Springer, vol. 197(1), pages 1-62, October.
    6. Wesley H. Holliday & Eric Pacuit, 2020. "Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers," Papers 2004.02350, arXiv.org, revised Nov 2023.

    More about this item

    JEL classification:

    • 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

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