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The impact of voters’ preference diversity on the probability of some electoral outcomes

Author

Listed:
  • William V. Gehrlein

    (University of Delaware [Newark])

  • Issofa Moyouwou

    (MASS - Université de Yaoundé I [Yaoundé])

  • Dominique Lepelley

    () (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

Abstract

Voting rules are known to exhibit various paradoxical or problematic behaviors, typically in the form of their failure to meet the Condorcet criterion or in their vulnerability to strategic voting. Our basic premise is that a decrease in the number of coalitions of voters that exist with similar preference rankings should generally lead to a reduced propensity of voting rules to yield undesired results. Surprisingly enough, conclusions that are reported by Felsenthal et al. (1990) in an early study do not corroborate this intuition. This study reconsiders and extends the Felsenthal et al. analysis by using a modified Impartial Anonymous Culture (IAC) model. It turns out that the results obtained with this probabilistic assumption are much more consistent with the stated intuitive premise.

Suggested Citation

  • William V. Gehrlein & Issofa Moyouwou & Dominique Lepelley, 2013. "The impact of voters’ preference diversity on the probability of some electoral outcomes," Post-Print hal-01243417, HAL.
    • Handle: RePEc:hal:journl:hal-01243417
    DOI: 10.1016/j.mathsocsci.2013.07.007
    Note: View the original document on HAL open archive server: https://hal.univ-reunion.fr/hal-01243417
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    References listed on IDEAS

    as
    1. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    2. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 503-512.
    3. Gehrlein, William V. & Lepelley, Dominique, 2001. "The Condorcet efficiency of Borda Rule with anonymous voters," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 39-50, January.
    4. Lepelley, Dominique & Mbih, Boniface, 1987. "The proportion of coalitionally unstable situations under the plurality rule," Economics Letters, Elsevier, vol. 24(4), pages 311-315.
    5. Geoffrey Pritchard & Mark Wilson, 2007. "Exact results on manipulability of positional voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 487-513, October.
    6. 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.
    7. Gehrlein, William V., 1982. "Condorcet efficiency and constant scoring rules," Mathematical Social Sciences, Elsevier, vol. 2(2), pages 123-130, March.
    8. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
    9. Davide Cervone & William Gehrlein & William Zwicker, 2005. "Which Scoring Rule Maximizes Condorcet Efficiency Under Iac?," Theory and Decision, Springer, vol. 58(2), pages 145-185, March.
    10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Mostapha Diss & Boris Tsvelikhovskiy, 2019. "Manipulable outcomes within the class of scoring voting rules," Papers 1911.09173, arXiv.org, revised Sep 2020.
    2. Moyouwou, Issofa & Tchantcho, Hugue, 2017. "Asymptotic vulnerability of positional voting rules to coalitional manipulation," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 70-82.
    3. William Gehrlein & Dominique Lepelley & Issofa Moyouwou, 2015. "Voters’ preference diversity, concepts of agreement and Condorcet’s paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2345-2368, November.
    4. 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.
    5. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    6. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    7. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.

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