On the likelihood of Condorcet's profiles

Vincent Merlin, Monica Tataru, Fabrice Valognes
2002 Social Choice and Welfare  
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, w j , to the alternative she ranks in j th 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
more » ... parison. 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, Tataru and Valognes [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. * The authors are indebted to Ashley Piggins for his careful reading.
doi:10.1007/s355-002-8332-y fatcat:5j4ydnweqng3tm7tgrtqgz6yzi