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Preference Restrictions in Computational Social Choice: A Survey

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  • Edith Elkind
  • Martin Lackner
  • Dominik Peters

Abstract

Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and computational problems can be solved more efficiently. In this survey, we give a thorough overview of many classic and modern restricted preference domains and explore their properties and applications. We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures as well. Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard to compute if preferences are unrestricted.

Suggested Citation

  • Edith Elkind & Martin Lackner & Dominik Peters, 2022. "Preference Restrictions in Computational Social Choice: A Survey," Papers 2205.09092, arXiv.org.
    • Handle: RePEc:arx:papers:2205.09092
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    Cited by:

    1. Klas Markstrom & S{o}ren Riis & Bei Zhou, 2024. "Arrow's single peaked domains, richness, and domains for plurality and the Borda count," Papers 2401.12547, arXiv.org.
    2. Demange, Gabrielle, 2024. "Stable outcomes in simple cooperative games," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Isaac Lara & Sergio Rajsbaum & Armajac Ravent'os-Pujol, 2024. "A Generalization of Arrow's Impossibility Theorem Through Combinatorial Topology," Papers 2402.06024, arXiv.org, revised Jul 2024.
    4. Edith Elkind & Svetlana Obraztsova & Nicholas Teh, 2023. "Temporal Fairness in Multiwinner Voting," Papers 2312.04417, arXiv.org, revised Dec 2023.
    5. Bruno Escoffier & Olivier Spanjaard & Magdaléna Tydrichová, 2024. "Euclidean preferences in the plane under $$\varvec{\ell _1},$$ ℓ 1 , $$\varvec{\ell _2}$$ ℓ 2 and $$\varvec{\ell _\infty }$$ ℓ ∞ norms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 125-169, August.
    6. Yang, Yongjie & Dimitrov, Dinko, 2023. "Group control for consent rules with consecutive qualifications," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 1-7.
    7. Duv{s}an Knop & v{S}imon Schierreich, 2023. "Host Community Respecting Refugee Housing," Papers 2302.13997, arXiv.org, revised Mar 2023.
    8. Alexander Karpov & Klas Markstrom & S{o}ren Riis & Bei Zhou, 2023. "Bipartite peak-pit domains," Papers 2308.02817, arXiv.org, revised Jan 2024.

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