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On the likelihood of single-peaked preferences

Author

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  • Marie-Louise Lackner

    (TU Wien)

  • Martin Lackner

    (University of Oxford)

Abstract

This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can be defined by certain forbidden configurations. This upper bound implies that many domain restrictions (including the single-peaked restriction) are very unlikely to appear in a random election chosen according to the Impartial Culture assumption. For single-peaked elections, this upper bound can be refined and complemented by a lower bound that is asymptotically tight. In addition, we provide exact results for elections with few voters or candidates. Moreover, we consider the Pólya urn model and the Mallows model and obtain lower bounds showing that single-peakedness is considerably more likely to appear for certain parameterizations.

Suggested Citation

  • Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    • Handle: RePEc:spr:sochwe:v:48:y:2017:i:4:d:10.1007_s00355-017-1033-0
    DOI: 10.1007/s00355-017-1033-0
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    Cited by:

    1. Mor Nitzan & Shmuel Nitzan & Erel Segal-Halevi, 2018. "Flexible level-1 consensus ensuring stable social choice: analysis and algorithms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(3), pages 457-479, March.
    2. Alexander Karpov, 2020. "The likelihood of single-peaked preferences under classic and new probability distribution assumptions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 629-644, December.
    3. Asifa Tassaddiq, 2019. "A New Representation of the k-Gamma Functions," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    4. Jiehua Chen & Sven Grottke, 2021. "Small one-dimensional Euclidean preference profiles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 117-144, July.
    5. Alexander Karpov, 2019. "On the Number of Group-Separable Preference Profiles," Group Decision and Negotiation, Springer, vol. 28(3), pages 501-517, June.

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