On the likelihood of Condorcet's profiles
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  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.  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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Volume (Year): 19 (2002)
Issue (Month): 1 ()
|Note:||Received: 30 April 1999/Accepted: 14 September 2000|
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