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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. 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.
    2. 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.
    3. 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.
    4. repec:eee:matsoc:v:90:y:2017:i:c:p:9-17 is not listed on IDEAS
    5. 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.
    6. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, pages 275-285.
    7. 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.
    8. Nurmi, Hannu, 2005. "Aggregation problems in policy evaluation: an overview," European Journal of Political Economy, Elsevier, vol. 21(2), pages 287-300, June.
    9. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, pages 275-285.
    10. 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.

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