An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains

Peters, Hans; Roy, Souvik; Sadhukhan, Soumyarup; Storcken, Ton

doi:10.1016/j.jmateco.2017.01.003

Cited by 9 publications

(3 citation statements)

References 19 publications

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“…Inspired by this, many works in the literature express RSCFs as convex combinations of DSCFs [27,26,28,25,29]. The Lemma 2 provides such a characterization of all the unanimous and strategy-proof RSCFs by proving that they are equivalent to random min-max rules.…”

Section: Extreme Point Characterization (Epc)mentioning

confidence: 99%

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

Sreedurga¹,

Sadhukhan²,

Roy³

et al. 2022

Preprint

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We study fairness in social choice settings under single-peaked preferences. Construction and characterization of social choice rules in the single-peaked domain has been extensively studied in prior works. In fact, in the single-peaked domain, it is known that unanimous and strategy-proof deterministic rules have to be min-max rules and those that also satisfy anonymity have to be median rules. Further, random social choice rules satisfying these properties have been shown to be convex combinations of respective deterministic rules. We non-trivially add to this body of results by including fairness considerations in social choice. Our study directly addresses fairness for groups of agents. To study group-fairness, we consider an existing partition of the agents into logical groups, based on natural attributes such as gender, race, and location. To capture fairness within each group, we introduce the notion of group-wise anonymity. To capture fairness across the groups, we propose a weak notion as well as a strong notion of fairness. The proposed fairness notions turn out to be natural generalizations of existing individual-fairness notions and moreover provide non-trivial outcomes for strict ordinal preferences, unlike the existing group-fairness notions. We provide two separate characterizations of random social choice rules that satisfy group-fairness: (i) direct characterization (ii) extreme point characterization (as convex combinations of fair deterministic social choice rules). We also explore the special case where there are no groups and provide sharper characterizations of rules that achieve individual-fairness.

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Section: Extreme Point Characterization (Epc)mentioning

confidence: 99%

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

Sreedurga¹,

Sadhukhan²,

Roy³

et al. 2022

Preprint

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“…For instance, Ehlers et al [18] have shown the existence of attractive strategyproof SDSs on the domain of single-peaked preference profiles [see also 36,37]. The existence of strategyproof and non-imposing SDSs other than random dictatorships has also been investigated for a variety of other domains [34,35,40]. Following a more general approach, Chatterji et al [14] and Chatterji and Zeng [15] identify criteria for deciding whether a domain admits such SDSs.…”

Section: Related Workmentioning

confidence: 99%

Strategyproof Social Decision Schemes on Super Condorcet Domains

Brand¹,

Lederer²,

Tausch³

2023

Preprint

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One of the central economic paradigms in multi-agent systems is that agents should not be better off by acting dishonestly. In the context of collective decision-making, this axiom is known as strategyproofness and turns out to be rather prohibitive, even when allowing for randomization. In particular, Gibbard's random dictatorship theorem shows that only rather unattractive social decision schemes (SDSs) satisfy strategyproofness on the full domain of preferences. In this paper, we obtain more positive results by investigating strategyproof SDSs on the Condorcet domain, which consists of all preference profiles that admit a Condorcet winner. In more detail, we show that, if the number of voters is odd, every strategyproof and non-imposing SDS on the Condorcet domain can be represented as a mixture of dictatorial SDSs and the Condorcet rule (which chooses the Condorcet winner with probability 1). Moreover, we prove that the Condorcet domain is a maximal connected domain that allows for attractive strategyproof SDSs if is odd as only random dictatorships are strategyproof and nonimposing on any sufficiently connected superset of it. We also derive analogous results for even by slightly extending the Condorcet domain. Finally, we also characterize the set of group-strategyproof and non-imposing SDSs on the Condorcet domain and its supersets. These characterizations strengthen Gibbard's random dictatorship theorem and establish that the Condorcet domain is essentially a maximal domain that allows for attractive strategyproof SDSs.

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“…Ehlers et al (2002) characterize the unanimous and strategy-proof random rules on single-peaked domains, and Peters et al (2014) show that such a rule is a convex combination of min-max rules. In a recent work, Peters et al (2017) characterize the unanimous and strategy-proof RSCFs on single-dipped domains and show that they are convex combinations of unanimous and strategy-proof DSCFs on those domains. However, to the best of our knowledge, the unanimous and strategy-proof RSCFs on single-crossing domains are not characterized yet.…”

Section: Introductionmentioning

confidence: 99%

A unified characterization of the randomized strategy-proof rules

Roy

Sadhukhan

2021

Journal of Economic Theory

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This paper presents a unified characterization of the unanimous and strategy-proof random rules on a class of domains that are based on some prior ordering over the alternatives. It identifies a condition called top-richness so that, if a domain satisfies top-richness, then an RSCF on it is unanimous and strategy-proof if and only if it is a convex combination of tops-restricted min-max rules. Well-known domains like single-crossing, single-peaked, singledipped etc. satisfy top-richness. This paper also provides a characterization of the random min-max domains. Furthermore, it offers a characterization of the tops-only and strategyproof random rules on top-rich domains satisfying top-connectedness. Finally, it presents a characterization of the unanimous (tops-only) and group strategy-proof random rules on those domains.

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An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains

Cited by 9 publications

References 19 publications

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences

Strategyproof Social Decision Schemes on Super Condorcet Domains

A unified characterization of the randomized strategy-proof rules

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