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A characterization of the single-crossing domain

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  • Robert Bredereck
  • Jiehua Chen
  • Gerhard Woeginger

Abstract

We characterize single-crossing preference profiles in terms of two forbidden substructures, one of which contains three voters and six (not necessarily distinct) alternatives, and one of which contains four voters and four (not necessarily distinct) alternatives. We also provide an efficient way to decide whether a preference profile is single-crossing. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Robert Bredereck & Jiehua Chen & Gerhard Woeginger, 2013. "A characterization of the single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 989-998, October.
    • Handle: RePEc:spr:sochwe:v:41:y:2013:i:4:p:989-998
    DOI: 10.1007/s00355-012-0717-8
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    References listed on IDEAS

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    Cited by:

    1. Edith Elkind & Piotr Faliszewski & Piotr Skowron, 2020. "A characterization of the single-peaked single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 167-181, January.
    2. Matheus Costa & Paulo Henrique Ramos & Gil Riella, 2020. "Single-crossing choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 69-86, January.
    3. 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.
    4. Jiehua Chen & Martin Nollenburg & Sofia Simola & Anais Villedieu & Markus Wallinger, 2022. "Multidimensional Manhattan Preferences," Papers 2201.09691, arXiv.org.
    5. Jiehua Chen & Kirk R. Pruhs & Gerhard J. Woeginger, 2017. "The one-dimensional Euclidean domain: finitely many obstructions are not enough," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 409-432, February.
    6. 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.
    7. repec:awi:wpaper:0610 is not listed on IDEAS
    8. 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.
    9. Felix Brand & Patrick Lederer & Sascha Tausch, 2023. "Strategyproof Social Decision Schemes on Super Condorcet Domains," Papers 2302.12140, arXiv.org.
    10. Nathann Cohenn & Edith Elkind & Foram Lakhani, 2019. "Single-crossing Implementation," Papers 1906.09671, arXiv.org.
    11. Slinko, Arkadii & Wu, Qinggong & Wu, Xingye, 2021. "A characterization of preference domains that are single-crossing and maximal Condorcet," Economics Letters, Elsevier, vol. 204(C).

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