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Fair Mixing: The Case of Dichotomous Preferences

Haris Aziz, Anna Bogomolnaia () and Herve Moulin ()
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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

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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.

Date: 2020-10
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Published in ACM Transactions on Economics and Computation, Association for Computing Machinery (ACM), 2020, 8 (4), pp.Article No.: 18. ⟨10.1145/3417738⟩

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Related works:
Working Paper: Fair Mixing: The Case of Dichotomous Preferences (2020)
Working Paper: Fair Mixing: the Case of Dichotomous Preferences (2019)
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DOI: 10.1145/3417738

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