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Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs

Author

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  • Hans Peters

    (Department of Quantitative Economics, School of Business and Economics, Maastricht University, 6200 MD Maastricht, Netherlands)

  • Souvik Roy

    (Economic Research Unit, Indian Statistical Institute, Kolkata, West Bengal 700108, India)

  • Soumyarup Sadhukhan

    (Economic Research Unit, Indian Statistical Institute, Kolkata, West Bengal 700108, India)

Abstract

Finitely many agents have preferences on a finite set of alternatives, single-peaked with respect to a connected graph with these alternatives as vertices. A probabilistic rule assigns to each preference profile a probability distribution over the alternatives. First, all unanimous and strategy-proof probabilistic rules are characterized when the graph is a tree. These rules are uniquely determined by their outcomes at those preference profiles at which all peaks are on leaves of the tree and, thus, extend the known case of a line graph. Second, it is shown that every unanimous and strategy-proof probabilistic rule is random dictatorial if and only if the graph has no leaves. Finally, the two results are combined to obtain a general characterization for every connected graph by using its block tree representation.

Suggested Citation

  • Hans Peters & Souvik Roy & Soumyarup Sadhukhan, 2021. "Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 811-833, May.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:2:p:811-833
    DOI: 10.1287/moor.2020.1089
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    References listed on IDEAS

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    Cited by:

    1. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    2. Felix Brand & Patrick Lederer & Sascha Tausch, 2023. "Strategyproof Social Decision Schemes on Super Condorcet Domains," Papers 2302.12140, arXiv.org.
    3. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    4. Aditya Aradhye & Hans Peters, 2024. "Group strategy-proof rules in multidimensional binary domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 103-124, August.
    5. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).

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