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Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser

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  • Eric Kamwa

    () (Université des Antilles, Faculté de Droit et d’Economie de la Martinique)

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 (in: Brams, Gehrlein, Roberts (eds) The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. (in: Laslier and Sanver (eds) Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley (Group Decis Negot 24:243–269, 2015).

Suggested Citation

  • Eric Kamwa, 2019. "Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser," Theory and Decision, Springer, vol. 87(3), pages 299-320, October.
  • Handle: RePEc:kap:theord:v:87:y:2019:i:3:d:10.1007_s11238-019-09716-5
    DOI: 10.1007/s11238-019-09716-5
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    1. William Gehrlein & Dominique Lepelley, 2010. "On the probability of observing Borda’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 1-23, June.
    2. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
    3. 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.
    4. 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.
    5. 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.
    6. 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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