The impartial culture maximizes the probability of majority cycles

Many papers have studied the probability of majority cycles, also called the Condorcet paradox, using the impartial culture or related distributional assumptions. While it is widely acknowledged that the impartial culture is unrealistic, conclusions drawn from the impartial culture are nevertheless...

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Bibliographic Details
Published in:Social choice and welfare 2003-12, Vol.21 (3), p.387-398
Main Authors: Tsetlin, Ilia, Regenwetter, Michel, Grofman, Bernard
Format: Article
Language:English
Subjects:
Ambivalence
Candidates
Distribution
Electoral sociology
Electoral systems
Electorate
Infinity
Majority rule
Mathematical minima
Paradoxes
Political candidates
Political culture
Preferences
Probability
Probability distributions
Public choice
Sampling distributions
Social choice
Social theory
Theorems
Voting Behavior
Voting behaviour
Voting paradox
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Summary:Many papers have studied the probability of majority cycles, also called the Condorcet paradox, using the impartial culture or related distributional assumptions. While it is widely acknowledged that the impartial culture is unrealistic, conclusions drawn from the impartial culture are nevertheless still widely advertised and reproduced in textbooks. We demonstrate that the impartial culture is the worst case scenario among a very broad range of possible voter preference distributions. More specifically, any deviation from the impartial culture over linear orders reduces the probability of majority cycles in infinite samples unless the culture from which we sample is itself inherently intransitive. We prove this statement for the case of three candidates and we provide arguments for the conjecture that it extends to any number of candidates.
ISSN:0176-1714
1432-217X
DOI:10.1007/s00355-003-0269-z