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On the probability of observing Borda’s paradox

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  • William Gehrlein
  • Dominique Lepelley

Abstract

Previous studies have shown that, when voters' preferences become more internally consistent or mutually coherent, the probability of observing Condorcet's Paradox of cyclic majorities is reduced and tends to zero, in accordance with intuition. The current study shows that the impact of an increasing degree of mutual coherence among voters' preferences on the likelihood of observing Borda's Paradox is much more subtle and more difficult to analyze. The degree of the impact in this case depends both on the measure of mutual coherence that is considered and on the voting rule that is used. In some circumstances, the probability that Borda's Paradox will occur actually increases when voters' preferences become more internally consistent.
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  • 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.
    • Handle: RePEc:spr:sochwe:v:35:y:2010:i:1:p:1-23
    DOI: 10.1007/s00355-009-0415-3
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    References listed on IDEAS

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    1. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    2. Thom Bezembinder, 1996. "The plurality majority converse under single peakedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 365-380.
    3. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    4. Saari, Donald G. & Valognes, Fabrice, 1999. "The geometry of Black's single peakedness and related conditions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 429-456, December.
    5. William Gehrlein & Dominique Lepelley, 2009. "The Unexpected Behavior of Plurality Rule," Theory and Decision, Springer, vol. 67(3), pages 267-293, September.
    6. Van Newenhizen, Jill, 1992. "The Borda Method Is Most Likely to Respect the Condorcet Principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 69-83, January.
    7. Lepelley, Dominique, 1993. "On the probability of electing the Condorcet," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 105-116, February.
    8. William Gehrlein, 2005. "Probabilities of election outcomes with two parameters: The relative impact of unifying and polarizing candidates," Review of Economic Design, Springer;Society for Economic Design, vol. 9(4), pages 317-336, December.
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    Cited by:

    1. Daniela Bubboloni & Mostapha Diss & Michele Gori, 2020. "Extensions of the Simpson voting rule to the committee selection setting," Public Choice, Springer, vol. 183(1), pages 151-185, April.
    2. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    3. 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.
    4. 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.
    5. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.
    6. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    7. 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.
    8. Winfried Bruns & Bogdan Ichim & Christof Söger, 2019. "Computations of volumes and Ehrhart series in four candidates elections," Annals of Operations Research, Springer, vol. 280(1), pages 241-265, September.
    9. Eric Kamwa, 2018. "On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules," Working Papers hal-01786590, HAL.

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