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The Condorcet Efficiency of the Preference Approval Voting and the Probability of Selecting the Condorcet Loser

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  • Eric Kamwa

    () (LC2S - Laboratoire caribéen de sciences sociales - CNRS - Centre National de la Recherche Scientifique - UA - Université des Antilles)

Abstract

Under Approval Voting (AV), each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The Preference Approval Voting (PAV) is a hybrid version of the approval voting first introduced by Brams and Sanver (2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide analytical representations for the probability that PAV elects the Condorcet winner when she exists in three-candidate elections with large electorates. We also provide analytical representations for the probability that PAV elects the Condorcet loser. We perform our analysis by assuming the assumption of the Extended Impartial Culture. This analysis allows us to measure at which extend, PAV performs better than AV both on the propensity of electing the Condorcet loser and on that of the non-election of the Condorcet loser.

Suggested Citation

  • Eric Kamwa, 2019. "The Condorcet Efficiency of the Preference Approval Voting and the Probability of Selecting the Condorcet Loser," Post-Print hal-01786121, HAL.
    • Handle: RePEc:hal:journl:hal-01786121
    Note: View the original document on HAL open archive server: https://hal.univ-antilles.fr/hal-01786121v2
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    1. Eric Kamwa & Fabrice Valognes, 2017. "Scoring Rules and Preference Restrictions: The Strong Borda Paradox Revisited," Revue d'économie politique, Dalloz, vol. 127(3), pages 375-395.
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    6. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2018. "A Note on the Likelihood of the Absolute Majority Paradoxes," Economics Bulletin, AccessEcon, vol. 38(4), pages 1727-1734.
    7. Mostapha Diss & Vincent Merlin & Fabrice Valognes, 2010. "On the Condorcet Efficiency of Approval Voting and Extended Scoring Rules for Three Alternatives," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 255-283, Springer.
    8. William V. Gehrlein & Dominique Lepelley, 2015. "The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules," Group Decision and Negotiation, Springer, vol. 24(2), pages 243-269, March.
    9. Eric Kamwa, 2019. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Group Decision and Negotiation, Springer, vol. 28(3), pages 519-541, June.
    10. Mostapha Diss & William Gehrlein, 2012. "Borda’s Paradox with weighted scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 121-136, January.
    11. Gehrlein, William V. & Lepelley, Dominique & Moyouwou, Issofa, 2016. "A note on Approval Voting and electing the Condorcet loser," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 115-122.
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    Cited by:

    1. Mostapha Diss & Eric Kamwa & Issofa Moyouwou & Hatem Smaoui, 2021. "Condorcet Efficiency of General Weighted Scoring Rules Under IAC: Indifference and Abstention," Studies in Choice and Welfare, in: Mostapha Diss & Vincent Merlin (ed.), Evaluating Voting Systems with Probability Models, pages 55-73, Springer.

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    Keywords

    Probability; Condorcet; Extended Impartial Culture; Ranking; Approval Voting;
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