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The likelihood of single-peaked preferences under classic and new probability distribution assumptions

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Abstract

The paper offers new results about the probabilities of single-peaked preference profiles according to the impartial culture, impartial anonymous culture, impartial anonymous neutral culture, uniform culture, dual culture, and maximal culture assumptions. Two new probabilistic assumptions are studied. The uniform plurality culture assumption developed in the paper preserves uniformly distributed plurality votes, and it is easier than other culture assumptions. The case of abstention of voters is discussed.

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Notes

  1. Statements of Theorem 11, Theorem 12(ii) and (iii) (Lackner and Lackner 2017) are obtained in (Durand 2003, pp. 581–585); Statement of Proposition 13 (i) (Lackner and Lackner 2017) is obtained in (Durand 2003, p. 584) in more compact representation; Statement of Proposition 13 (iii) (Lackner and Lackner 2017) is obtained in (Lepelley 1993, p. 111).

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Authors and Affiliations

  1. National Research University Higher School of Economics, 20 Myasnitskaya str, Moscow, 10100, Russia

    Alexander Karpov

  2. Institute of Control Science, Russian Academy of Science, 65 Profsoyuznaya Str, Moscow, 117997, Russia

    Alexander Karpov

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  1. Alexander Karpov
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Alexander Karpov: The author is grateful to Clemens Puppe, Fuad Aleskerov and an anonymous reviewer for their very valuable comments, which improved the quality of the paper. This article is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University).

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Karpov, A. The likelihood of single-peaked preferences under classic and new probability distribution assumptions. Soc Choice Welf 55, 629–644 (2020). https://doi.org/10.1007/s00355-020-01258-y

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