The decomposition of strategy-proof random social choice functions on dichotomous domains

Gaurav, Abhishek; Picot, Jérémy; Sen, Arunava

doi:10.1016/j.mathsocsci.2017.03.004

Cited by 3 publications

(2 citation statements)

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“…In this section, we investigate the decomposability property of RSCFs. Decomposability is an important property of unanimous and strategy-proof RSCFs and has been established in a large class of domains, e.g., the complete domain of Gibbard (1977), the single-peaked domain of Peters et al (2014) and Pycia and Ünver (2015) and the dichotomous domain of Gaurav et al (2017). We say that a unanimous and strategy-proof RSCF is decomposable if it can be expressed as a mixture (equivalently, a convex combination) of finitely many unanimous and strategy-proof DSCFs.…”

Section: Decomposability Of Anonymous Pfbrsmentioning

confidence: 99%

Probabilistic Fixed Ballot Rules and Hybrid Domains

Chatterji¹,

Roy²,

Sadhukhan³

et al. 2021

Preprint

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We characterize a class of preference domains called hybrid * domains. These are specific collections of preferences that are single-peaked at the "extremes" and unrestricted in the "middle". They are characterized by the familiar properties of minimal richness, diversity and no-restoration. We also study the structure of strategy-proof and unanimous Random Social Choice Functions on these domains. We show them to be special cases of probabilistic fixed ballot rules (or PFBR). These PFBRs are not necessarily decomposable, i.e., cannot be written as a convex combination of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous PFBRs.

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Section: Decomposability Of Anonymous Pfbrsmentioning

confidence: 99%

Probabilistic Fixed Ballot Rules and Hybrid Domains

Chatterji¹,

Roy²,

Sadhukhan³

et al. 2021

Preprint

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“…Separable preferences have been used in multi-dimensional voting(Border and Jordan (1983),Barberà et al (1991),Breton and Sen (1999)), in combinatorial auctions(Hart and Nisan (2017), Hart and Reny (2015)), multi-dimensional screening(Carroll (2017)) and matching(Kurino (2014)). Dichotomous preferences have been employed in voting(Bogomolnaia et al (2005),Gaurav et al (2017)), auctions(Mishra and Roy (2013)) and matching(Bogomolnaia and Moulin (2004),Roth et al (2005)).…”

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confidence: 99%

Matching with partners and projects

Nicolò

Sen

Yadav

2019

Journal of Economic Theory

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We propose a model where agents are matched in pairs in order to undertake a project. Agents have preferences over both the partner and the project they are assigned to. These preferences over partners and projects are separable and dichotomous. Each agent partitions the set of partners into friends and outsiders, and the set of projects into good and bad ones. Friendship is mutual and transitive. In addition, preferences over projects among friends are correlated (homophily). We define a suitable notion of the weak core and propose an algorithm, the minimum demand priority algorithm (MDPA) that generates an assignment in the weak core. In general, the strong core does not exist but the MDPA assignment satisfies a limited version of the strong core property when only friends can be members of the blocking coalition. The MDPA is also strategy-proof. Finally we show that our assumptions on preferences are indispensable. We show that the weak core may fail to exist if any of the assumptions of homophily, separability and dichotomous preferences are relaxed.

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