An extreme point characterization of random strategy-proof social choice functions: The two alternative case

Picot, Jérémy; Sen, Arunava

doi:10.1016/j.econlet.2011.11.008

Cited by 12 publications

(6 citation statements)

References 6 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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“…By Theorem 3,

{scriptQ}^{normalmrex}

consists of qualified majority voting rules and the constant voting rule that selects b at all type profiles. Picot and Sen (2012) show that

{scriptQ}^{normalmex}

consists of the same set of voting rules 4 . Hence, we can conclude that

{scriptQ}^{normalmex} = {scriptQ}^{normalmrex}

.…”

Section: Monotone Reduced‐form Implementationmentioning

confidence: 99%

Symmetric reduced‐form voting

Lang,

Mishra

2024

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We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probability can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti‐majority. We also provide analogous results by requiring implementation by a symmetric monotone (strategy‐proof) voting rule and by a symmetric unanimous voting rule. We apply our results to show that an ex ante Rawlsian rule is a convex combination of a pair of qualified majority rules.

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“…Closely related papers are Larsson and Svensson (2006) and Picot and Sen (2012). Larsson and Svensson (2006) include a characterization of all strategy-proof surjective deterministic rules for the case of two alternatives with indifferences allowed.…”

Section: Introductionmentioning

confidence: 99%

“…Their Theorem 3 is close to our Theorem 3.9-our theorem is slightly more general since we allow for more than two alternatives. Picot and Sen (2012) show that every probabilistic rule is a convex combination of deterministic rules if there are only two alternatives and no indifferences are allowed.…”

Section: Introductionmentioning

confidence: 99%

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

Peters

Roy

Sadhukhan

et al. 2017

Journal of Mathematical Economics

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An extreme point characterization of random strategy-proof social choice functions: The two alternative case

Cited by 12 publications

References 6 publications

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

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

Symmetric reduced‐form voting

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

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