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On the Number of Group-Separable Preference Profiles

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  • Alexander Karpov

    (National Research University Higher School of Economics
    Russian Academy of Science)

Abstract

The paper studies group-separable preference profiles. Such a profile is group-separable if for each subset of alternatives there is a partition in two parts such that each voter prefers each alternative in one part to each alternative in the other part. We develop a parenthesization representation of group-separable domain. The precise formula for the number of group-separable preference profiles is obtained. The recursive formula for the number of narcissistic group-separable preference profiles is obtained. Such a profile is narcissistic group-separable if it is group-separable and each alternative is preferred the most by exactly one voter.

Suggested Citation

  • Alexander Karpov, 2019. "On the Number of Group-Separable Preference Profiles," Group Decision and Negotiation, Springer, vol. 28(3), pages 501-517, June.
    • Handle: RePEc:spr:grdene:v:28:y:2019:i:3:d:10.1007_s10726-019-09621-w
    DOI: 10.1007/s10726-019-09621-w
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    References listed on IDEAS

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    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
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    4. Bredereck, Robert & Chen, Jiehua & Woeginger, Gerhard J., 2016. "Are there any nicely structured preference profiles nearby?," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 61-73.
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    Cited by:

    1. 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.
    2. Niclas Boehmer & Piotr Faliszewski & Rolf Niedermeier & Stanis{l}aw Szufa & Tomasz Wk{a}s, 2022. "Understanding Distance Measures Among Elections," Papers 2205.00492, arXiv.org.

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