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Fair Mixing: The Case of Dichotomous Preferences

Author

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  • Haris Aziz

    (UNSW - University of New South Wales [Sydney], CSIRO - Data61 [Canberra] - ANU - Australian National University - CSIRO - Commonwealth Scientific and Industrial Research Organisation [Canberra])

  • Anna Bogomolnaia

    (University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Hervé Moulin

    (University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a setting in which agents vote to choose a fair mixture of public outcomes. The agents have dichotomous preferences: each outcome is liked or disliked by an agent. We discuss three outstanding voting rules. The Conditional Utilitarian rule, a variant of the random dictator, is strategyproof and guarantees to any group of like-minded agents an influence proportional to its size. It is easier to compute and more efficient than the familiar Random Priority rule. Its worst case (resp. average) inefficiency is provably (resp. in numerical experiments) low if the number of agents is low. The efficient Egalitarian rule protects individual agents but not coalitions. It is excludable strategyproof: I do not want to lie if I cannot consume outcomes I claim to dislike. The efficient Nash Max Product rule offers the strongest welfare guarantees to coalitions, who can force any outcome with a probability proportional to their size. But it even fails the excludable form of strategyproofness.

Suggested Citation

  • Haris Aziz & Anna Bogomolnaia & Hervé Moulin, 2020. "Fair Mixing: The Case of Dichotomous Preferences," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03047386, HAL.
    • Handle: RePEc:hal:cesptp:hal-03047386
    DOI: 10.1145/3417738
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    Cited by:

    1. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2020. "Truthful fair division without free disposal," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 523-545, October.
    2. Brandl, Florian & Brandt, Felix & Greger, Matthias & Peters, Dominik & Stricker, Christian & Suksompong, Warut, 2022. "Funding public projects: A case for the Nash product rule," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    3. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    4. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    5. Xiaohui Bei & Xinhang Lu & Warut Suksompong, 2021. "Truthful Cake Sharing," Papers 2112.05632, arXiv.org, revised Feb 2022.
    6. Haris Aziz & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen & Toby Walsh, 2023. "Best-of-Both-Worlds Fairness in Committee Voting," Papers 2303.03642, arXiv.org, revised Dec 2023.
    7. Florian Brandl & Felix Brandt & Matthias Greger & Dominik Peters & Christian Stricker & Warut Suksompong, 2020. "Funding Public Projects: A Case for the Nash Product Rule," Papers 2005.07997, arXiv.org, revised Oct 2021.
    8. Xiaohui Bei & Guangda Huzhang & Warut Suksompong, 2018. "Truthful Fair Division without Free Disposal," Papers 1804.06923, arXiv.org, revised Apr 2020.
    9. Bentert, Matthias & Boehmer, Niclas & Heeger, Klaus & Koana, Tomohiro, 2023. "Stable matching with multilayer approval preferences: Approvals can be harder than strict preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 508-526.
    10. Freeman, Rupert & Pennock, David M. & Peters, Dominik & Wortman Vaughan, Jennifer, 2021. "Truthful aggregation of budget proposals," Journal of Economic Theory, Elsevier, vol. 193(C).

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