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On the likelihood of Condorcet's profiles


  • Fabrice Valognes

    () (Department of Economics, The University of Namur, Rempart de la Vierge 8, B-5000 Namur, Belgium)

  • Vincent Merlin

    () (GEMMA-CREME and CNRS, MRSH-SH230, Université de Caen, Esplanade de la Paix, F-14032 Caen Cedex, France)

  • Monica Tataru

    () (Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730 USA)


Consider a group of individuals who have to collectively choose an outcome from a finite set of feasible alternatives. A scoring or positional rule is an aggregation procedure where each voter awards a given number of points, wj, to the alternative she ranks in jth position in her preference ordering; The outcome chosen is then the alternative that receives the highest number of points. A Condorcet or majority winner is a candidate who obtains more votes than her opponents in any pairwise comparison. Condorcet [4] showed that all positional rules fail to satisfy the majority criterion. Furthermore, he supplied a famous example where all the positional rules select simultaneously the same winner while the majority rule picks another one. Let P* be the probability of such events in three-candidate elections. We apply the techniques of Merlin et al. [17] to evaluate P* for a large population under the Impartial Culture condition. With these assumptions, such a paradox occurs in 1.808% of the cases.

Suggested Citation

  • Fabrice Valognes & Vincent Merlin & Monica Tataru, 2002. "On the likelihood of Condorcet's profiles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 193-206.
  • Handle: RePEc:spr:sochwe:v:19:y:2002:i:1:p:193-206
    Note: Received: 30 April 1999/Accepted: 14 September 2000

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    Cited by:

    1. Eric Kamwa & Vincent Merlin, 2019. "The Likelihood of the Consistency of Collective Rankings Under Preferences Aggregation with Four Alternatives Using Scoring Rules: A General Formula and the Optimal Decision Rule," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1377-1395, April.
    2. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    3. Eyal Baharad & Shmuel Nitzan, 2011. "Condorcet vs. Borda in light of a dual majoritarian approach," Theory and Decision, Springer, vol. 71(2), pages 151-162, August.
    4. Aaron Meyers & Michael Orrison & Jennifer Townsend & Sarah Wolff & Angela Wu, 2014. "Generalized Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 11-27, June.
    5. Aleksandras KRYLOVAS & Natalja KOSAREVA & Edmundas Kazimieras ZAVADSKAS, 2016. "Statistical Analysis of KEMIRA Type Weights Balancing Methods," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 19-39, September.
    6. 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.
    7. William v. Gehrlein & Dominique Lepelley, 2009. "A note on Condorcet's other paradox," Economics Bulletin, AccessEcon, vol. 29(3), pages 2000-2007.
    8. Eric Kamwa & Vincent Merlin, 2018. "The Likelihood of the Consistency of Collective Rankings under Preferences Aggregation with Four Alternatives using Scoring Rules: A General Formula and the Optimal Decision Rule," Working Papers hal-01757742, HAL.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations


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