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Condorcet's principle and the strong no-show paradoxes

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  • Duddy, Conal

Abstract

We consider two no-show paradoxes, in which a voter obtains a preferable outcome by abstaining from a vote. One arises when the casting of a ballot that ranks a candidate in first causes that candidate to lose the election. The other arises when a ballot that ranks a candidate in last causes that candidate to win. We show that when there are at least four candidates and when voters may express indifference, every voting rule satisfying Condorcet's principle must generate both of these paradoxes.

Suggested Citation

  • Duddy, Conal, 2012. "Condorcet's principle and the strong no-show paradoxes," MPRA Paper 41527, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41527
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    References listed on IDEAS

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    11. Joaqui´n Pérez, 2001. "The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 601-616.
    12. Josep Colomer, 2013. "Ramon Llull: from ‘Ars electionis’ to social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 317-328, February.
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    Cited by:

    1. Brandt, Felix & Geist, Christian & Peters, Dominik, 2017. "Optimal bounds for the no-show paradox via SAT solving," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 18-27.
    2. Eric Kamwa & Issofa Moyouwou, 2021. "Susceptibility to Manipulation by Sincere Truncation: The Case of Scoring Rules and Scoring Runoff Systems," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 275-295, Springer.
    3. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    4. Stensholt, Eivind, 2020. "Anomalies of Instant Runoff Voting," Discussion Papers 2020/6, Norwegian School of Economics, Department of Business and Management Science.
    5. David McCune, 2024. "Single Transferable Vote and Paradoxes of Negative and Positive Involvement," Papers 2406.20045, arXiv.org, revised Nov 2024.
    6. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    7. Hannu Nurmi, 2020. "The Incidence of Some Voting Paradoxes Under Domain Restrictions," Group Decision and Negotiation, Springer, vol. 29(6), pages 1107-1120, December.
    8. 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.
    9. Eric Kamwa & Issofa Moyouwou, 2019. "Susceptibility to Manipulation by Sincere Truncation : the Case of Scoring Rules and Scoring Runoff Systems," Working Papers hal-02185965, HAL.
    10. Eric Kamwa & Vincent Merlin & Faty Mbaye Top, 2023. "Scoring Run-off Rules, Single-peaked Preferences and Paradoxes of Variable Electorate," Working Papers hal-03143741, HAL.
    11. 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.

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    More about this item

    Keywords

    Condorcet; no show; paradox; abstention; voting; participation; positive involvement; negative involvement;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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