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On the probability of observing Borda’s paradox

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  • William Gehrlein

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  • Dominique Lepelley

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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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Suggested Citation

  • 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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    File URL: http://hdl.handle.net/10.1007/s00355-009-0415-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    5. 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.
    6. Lepelley, Dominique, 1993. "On the probability of electing the Condorcet," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 105-116, February.
    7. William Gehrlein & Dominique Lepelley, 2009. "The Unexpected Behavior of Plurality Rule," Theory and Decision, Springer, vol. 67(3), pages 267-293, September.
    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. Mostapha Diss & Abdelmonaim Tlidi, 2018. "Another perspective on Borda’s paradox," Theory and Decision, Springer, vol. 84(1), pages 99-121, January.

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