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Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders

Published online by Cambridge University Press:  02 September 2013

Bradford Jones ,
Benjamin Radcliff ,
Charles Taber  and
Richard Timpone
Bradford Jones
Affiliation:
University of Arizona
Benjamin Radcliff
Affiliation:
University of Notre Dame
Charles Taber
Affiliation:
State University of New York, Stony Brook
Richard Timpone
Affiliation:
State University of New York, Stony Brook
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Abstract

That individual preferences may he aggregated into a meaningful collective decision using the Condorcet criterion of majority choice is one of the central tenets of democracy. But that individual preferences may not yield majority winners is one of the classic findings of the social choice literature. Given this problem, social choice theorists have attempted to estimate the probability of Condorcet winners, given certain empirical or theoretical conditions. We shall estimate the probabilities of Condorcet winners and intransitive aggregate orders for various numbers of individuals with strong or weak preference orders across various numbers of alternatives. We find, using computer simulation, a stark contrast between these estimates assuming strong individual preferences and the estimates allowing for individuals' indifference between pairs of alternatives. In contrast to earlier work, which depends on the strong-preference assumption, we suggest that the problem is most acute for small committee decision making and least acute for mass elections with few alternatives.

Information

Type
Research Notes
Information
American Political Science Review , Volume 89 , Issue 1 , March 1995 , pp. 137 - 144
Copyright
Copyright © American Political Science Association 1995

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