On the likelihood of Condorcet's profiles
AbstractConsider 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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Bibliographic InfoArticle provided by Springer in its journal Social Choice and Welfare.
Volume (Year): 19 (2002)
Issue (Month): 1 ()
Note: Received: 30 April 1999/Accepted: 14 September 2000
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- 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.
- William v. Gehrlein & Dominique Lepelley, 2009. "A note on Condorcet's other paradox," Economics Bulletin, AccessEcon, vol. 29(3), pages 2000-2007.
- Eyal Baharad & Shmuel Nitzan, 2011.
"Condorcet vs. Borda in light of a dual majoritarian approach,"
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- Eyal Baharad & Shmuel Nitzan, 2010. "Condorcet vs. Borda in Light of a Dual Majoritarian Approach," Working Papers 2010-07, Department of Economics, Bar-Ilan University.
- 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.
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