@MISC{Merlin00onthe, author = {V. Merlin and M. Tataru and F. Valognes}, title = {On the likelihood of Condorcet’s profiles ∗}, year = {2000} }

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Abstract

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, 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. 1