Condorcet's paradox and the likelihood of its occurrence: Different perspectives on balanced preferences

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with...

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Bibliographic Details
Published inTheory and decision Vol. 52; no. 2; pp. 171 - 199
Main Author GEHRLEIN, William V
Format Journal Article
LanguageEnglish
Published Dordrecht Springer 01.03.2002
Springer Nature B.V
Subjects
Applied sciences
Candidates
Decision theory
Decision theory. Utility theory
Elections
Electoral behaviour
Electoral systems
Exact sciences and technology
Majority rule
Operational research and scientific management
Operational research. Management science
Preferences
Probability
Rational choice
Studies
Voter behavior
Voters
Voting
Decision theory
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Summary:Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with the assumptions of: Impartial Culture, Impartial Anonymous Culture, Maximal Culture, Dual Culture and Uniform Culture. Results are included for the likelihood that there is a strong winner by PMR, a weak winner by PMR, and the probability that a specific candidate is among the winners by PMR. Closed form representations are developed for some of these probabilities for Impartial Anonymous Culture and for Maximal Culture. Consistent results are obtained for all cultures. In particular, very different behaviors are observed for odd and even numbers of voters. The limiting probabilities as the number of voters increases are reached very quickly for odd numbers of voters, and quite slowly for even numbers of voters. The greatest likelihood of observing Condorcet's Paradox typically occurs for small numbers of voters. Results suggest that while examples of Condorcet's Paradox are observed, one should not expect to observe them with great frequency in three candidate elections. [PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0040-5833
1573-7187
DOI:10.1023/A:1015551010381