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On the likelihood of Condorcet's profiles

Listed author(s):
  • 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.

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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 19 (2002)
Issue (Month): 1 ()
Pages: 193-206

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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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