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Condorcet Consistency and the strong no show paradoxes

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  • Kasper, Laura
  • Peters, Hans
  • Vermeulen, Dries

Abstract

We identify the maximal voting correspondence which is Condorcet Consistent and satisfies two participation conditions, namely the Top Property and the Bottom Property — thereby extending a result in Pérez (2001). The former participation condition says that if an alternative is in the chosen set at a profile of rankings and a ranking is added with that alternative on top, then it remains to be a member of the chosen set. The latter says that if an alternative is not in the chosen set at a profile of rankings and a ranking is added with that alternative at bottom, then the alternative is again not in the chosen set. In particular, voting functions (single-valued voting correspondences) with these three properties 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, 2019. "Condorcet Consistency and the strong no show paradoxes," Mathematical Social Sciences, Elsevier, vol. 99(C), pages 36-42.
    • Handle: RePEc:eee:matsoc:v:99:y:2019:i:c:p:36-42
    DOI: 10.1016/j.mathsocsci.2019.03.002
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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. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
    3. Szybowski, Jacek & Kułakowski, Konrad & Prusak, Anna, 2020. "New inconsistency indicators for incomplete pairwise comparisons matrices," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 138-145.
    4. 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.
    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.

    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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