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The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences

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  • Joaqui´n Pérez

    (Departamento de Fundamentos de Economía e Historia Económica, Universidad de Alcalá, Plaza de la Victoria, 28802 Alcalá de Henares Spain)

Abstract

The No Show Paradox (there is a voter who would rather not vote) is known to affect every Condorcet voting function. This paper analyses two strong versions of this paradox in the context of Condorcet voting correspondences. The first says that there is a voter whose favorite candidate loses the election if she votes honestly, but gets elected if she abstains. The second says that there is a voter whose least preferred candidate gets elected if she votes honestly, but loses the election if she abstains. All Condorcet correspondences satisfying some weak domination properties are shown to be affected by these strong forms of the paradox. On the other hand, with the exception of the Simpson-Cramer Minmax and the Young rule, all the Condorcet correspondences that (to the best of our knowledge) are proposed in the literature suffer from these two paradoxes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:18:y:2001:i:3:p:601-616
    Note: Received: 30 November 1999/Accepted: 27 March 2000
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    Cited by:

    1. Leonardo Matone & Ben Abramowitz & Nicholas Mattei & Avinash Balakrishnan, 2024. "DeepVoting: Learning Voting Rules with Tailored Embeddings," Papers 2408.13630, arXiv.org.
    2. 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.
    3. Eivind Stensholt, 2013. "What shall we do with the cyclic profile?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 229-262, January.
    4. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    5. Joaquín Pérez & José L. Jimeno & Estefanía García, 2012. "No Show Paradox in Condorcet k-voting Procedures," Group Decision and Negotiation, Springer, vol. 21(3), pages 291-303, May.
    6. Holliday, Wesley H., 2024. "An impossibility theorem concerning positive involvement in voting," Economics Letters, Elsevier, vol. 236(C).
    7. Núñez, Matías & Sanver, M. Remzi, 2017. "Revisiting the connection between the no-show paradox and monotonicity," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 9-17.
    8. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    9. Jimeno, José L. & García, Estefanía & Pérez, Joaquín, 2011. "Extensions of the Young and Levenglick result about the inconsistency of Condorcet voting correspondences," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 25-27, July.
    10. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    11. Estefanía García & José L. Jimeno & Joaquín Pérez, 2013. "New Voting Correspondences Obtained from a Distance-Based Framework," Group Decision and Negotiation, Springer, vol. 22(3), pages 379-388, May.
    12. Dan S. Felsenthal & Hannu Nurmi, 2016. "Two types of participation failure under nine voting methods in variable electorates," Public Choice, Springer, vol. 168(1), pages 115-135, July.
    13. Nurmi, Hannu, 2005. "Aggregation problems in policy evaluation: an overview," European Journal of Political Economy, Elsevier, vol. 21(2), pages 287-300, June.
    14. 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.
    15. Joaquín Pérez & José L. Jimeno & Estefanía García, 2015. "No Show Paradox and the Golden Number in Generalized Condorcet Voting Methods," Group Decision and Negotiation, Springer, vol. 24(3), pages 497-513, May.
    16. Stefano Vannucci, 2006. "The Proportional Lottery Protocol is Strongly Participatory and VNM-Strategy-Proof," Department of Economics University of Siena 490, Department of Economics, University of Siena.
    17. Dan S. Felsenthal & Hannu Nurmi, 2019. "The No-Show Paradox Under a Restricted Domain," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(4), pages 277-293, April.
    18. Hannu Nurmi & Madeleine O. Hosli, 2003. "Which Decision Rule for the Future Council?," European Union Politics, , vol. 4(1), pages 37-50, March.
    19. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    20. Guillaume Chèze, 2017. "Topological aggregation, the twin paradox and the No Show paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 707-715, April.

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