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Are there any nicely structured preference profiles nearby?

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  • Bredereck, Robert
  • Chen, Jiehua
  • Woeginger, Gerhard J.

Abstract

We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted, medium-restricted, or group-separable profiles. We measure this distance by the number of voters or alternatives that have to be deleted to make the profile a nicely structured one. Our results classify the problem variants with respect to their computational complexity, and draw a clear line between computationally tractable (polynomial-time solvable) and computationally intractable (NP-hard) questions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:79:y:2016:i:c:p:61-73
    DOI: 10.1016/j.mathsocsci.2015.11.002
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    Cited by:

    1. Smeulders, B., 2018. "Testing a mixture model of single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 101-113.
    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. 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.
    4. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    5. 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.
    6. Alexander Karpov, 2019. "On the Number of Group-Separable Preference Profiles," Group Decision and Negotiation, Springer, vol. 28(3), pages 501-517, June.
    7. Nathann Cohenn & Edith Elkind & Foram Lakhani, 2019. "Single-crossing Implementation," Papers 1906.09671, arXiv.org.

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