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Public Choice (2014) 160:313326
DOI 10.1007/s11127-014-0180-4
Dan S. Felsenthal Nicolaus Tideman
Received: 4 September 2013 / Accepted: 17 April 2014 / Published online: 13 May 2014 Springer Science+Business Media New York 2014
Abstract A strong Condorcet winner (SCW) is an alternative, x, that a majority of voters rank higher than z, for every other alternative, z. A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW. There has been some confusion in the voting/social choice literature as to whether particular voting rules that are SCW-consistent are also WCW-consistent. The purpose of this paper is to revisit this issue, clear up the confusion that has developed, and determine whether three additional SCW-consistent voting rulesthat as far as we know have not been investigated to date regarding their possible WCW consistencyare indeed WCW-consistent.
Keywords Condorcet winner Voting methods Voting rules
Weak Condorcet winner
JEL Classication D71 D72
1 Introduction
Given n voters with strict rankings over m candidates, we can determine the majority ranking relation for any pair of candidates. If a majority of voters rank candidate x higher than candidate y, we say that x beats y (in a head-to-head comparison). A candidate who beats every other candidate is commonly called a (strong) Condorcet Winner (SCW) and a
D. S. Felsenthal (&)
School of Political Sciences, University of Haifa, 31905 Haifa, Israel e-mail: [email protected]; [email protected]
N. Tideman
Department of Economics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, USAe-mail: [email protected]
Weak Condorcet winner(s) revisited
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314 Public Choice (2014) 160:313326
voting rule that always selects the Condorcet winner when one exists is said to satisfy (strong) Condorcet consistency.
A strong Condorcet winner may fail to exist for either of two reasons. First, there may be an instance of the Condorcet paradox (Condorcet 1785), where the majority ranking of the candidates cycles, such that, for example, candidate x beats y, y beats z, and z beats x, with the result that every candidate is beaten and the criterion of strong Condorcet consistency is inapplicable. Second, if the number of voters is even, ties may occur in the majority ranking of the candidates so that x does not beat y and y...