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The impartial culture maximizes the probability of majority cycles

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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.

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Correspondence to Ilia Tsetlin.

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All three authors thank the Fuqua School of Business for supporting their research collaboration. Regenwetter and Grofman gratefully acknowledge the precious support of the National Science Foundation through grant #SBR-9730076 on Probabilistic Models of Social Choice (Methodology, Measurement and Statistics program). We are grateful to the referees and we thank Saša Pekeč for critical comments on an earlier draft. Grofman thanks Scott L. Feld for numerous reminders about the implausibility of the impartial culture assumption which helped lead to this paper.

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Tsetlin, I., Regenwetter, M. & Grofman, B. The impartial culture maximizes the probability of majority cycles. Soc Choice Welfare 21, 387–398 (2003).

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