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Random mechanism design on multidimensional domains

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  • Chatterji, Shurojit
  • Zeng, Huaxia

Abstract

We study random mechanism design in an environment where the set of alternatives has a Cartesian product structure. We first show that all generalized random dictatorships are sd-strategy-proof on a minimally rich domain if and only if all preferences are top-separable. We call a domain satisfying top-separability a multidimensional domain, and furthermore generalize the notion of connectedness (Monjardet, 2009) to a broad class of multidimensional domains: connected+domains. We show that in the class of minimally rich and connected+ domains, the multidimensional single-peakedness restriction is necessary and sufficient for the design of a flexible random social choice function that is unanimous and sd-strategy-proof. Such a flexible random social choice function allows for a systematic notion of compromise. We prove an analogous result for deterministic social choice functions satisfying anonymity. Our characterization remains valid for a problem of voting under constraints where not all alternatives are feasible (Barberà et al., 1997).

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  • Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    • Handle: RePEc:eee:jetheo:v:182:y:2019:i:c:p:25-105
    DOI: 10.1016/j.jet.2019.04.003
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    Cited by:

    1. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    2. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    3. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    4. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2023. "Committee formation under constraints through randomized voting rules on separable domains," Journal of Economic Theory, Elsevier, vol. 209(C).
    6. Shurojit Chatterji & Huaxia Zeng, 2023. "Decomposability and Strategy-proofness in Multidimensional Models," Papers 2303.10889, arXiv.org, revised Nov 2023.
    7. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "Formation of committees under constraints through random voting rules," MPRA Paper 110873, University Library of Munich, Germany.

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    More about this item

    Keywords

    Generalized random dictatorships; Top-separability; Separability; Multidimensional single-peakedness; Connected+ domains; Voting under constraints;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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