On strategy-proofness and semilattice single-peakedness

Bonifacio, Agustín G.; Massó, Jordi

doi:10.1016/j.geb.2020.08.005

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…is an anonymous, tops-only and strategy-proof rule. The characterization of all anonymous, tops-only and strategy-proof rules on the semi-single-peaked domain can be established according to Theorem 1 of Bonifacio and Massó (2020). 27 Although Statement (ii) of the Theorem is an impossibility statement for designing, its proof shows that an (a, b)-semi-hybrid domain D on a tree T A admits the following tops-only and strategy-proof rule, called the hybrid rule: given a voter i ∈ N , for all P ∈ D n ,…”

Section: A Classification Of Non-dictatorial Domainsmentioning

confidence: 99%

“…The seeming paradox is of course not a paradox: the non-tops-only rules for a semi-single-peaked domain continue to be strategy-proof for the single-peaked domain, except that they become topsonly when restricted to the single-peaked domain and are thus subsumed in the usual known class of strategy-proof rules for single-peaked domains. For instance, in the case of two voters, on the singlepeaked domain, the characterization theorem ofMoulin (1980) implies that the number of tops-only and strategy-proof rules that in addition satisfies anonymity equals the number of alternatives, while on the semi-single-peaked domain, this number reduces to be one according to Corollary 1 ofBonifacio and Massó (2020).…”

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confidence: 99%

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A Taxonomy of Non-dictatorial Unidimensional Domains

Chatterji¹,

Zeng²

2022

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A preference domain is called a non-dictatorial domain if it allows the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof; otherwise it is called a dictatorial domain. We study a class of preference domains called unidimensional domains and establish that within this class, the unique seconds property (introduced by Aswal, Chatterji, and Sen ( 2003)) separates non-dictatorial domains from dictatorial domains. The principal contribution of the paper is the subsequent exhaustive classification of all non-dictatorial unidimensional domains based on a simple property of two-voter rules called invariance. The preference domains that constitute the classification are semi-single-peaked domains (introduced by Chatterji, Sanver, and Sen ( 2013)) and semi-hybrid domains (introduced here) which are two appropriate weakenings of single-peaked domains and which, importantly, are shown to allow strategy-proof rules to depend on non-peak information of voters' preferences. As a refinement of the classification, single-peaked domains and hybrid domains emerge as the only unidimensional domains that force strategy-proof rules to be determined completely by the peaks of voters' preferences.

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Section: A Classification Of Non-dictatorial Domainsmentioning

confidence: 99%

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confidence: 99%

A Taxonomy of Non-dictatorial Unidimensional Domains

Chatterji¹,

Zeng²

2022

Preprint

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“…The analysis of strategy-proof deterministic social choice functions on single-peaked domains was initiated by Moulin (1980) and developed further by Barberà et al (1993), Ching (1997) and Weymark (2011). In the deterministic setting, Nehring and Puppe (2007), Chatterji et al (2013), Reffgen (2015), Chatterji and Massó (2018), Achuthankutty and Roy (2020) and Bonifacio and Massó (2020) analyze the structure of unanimous and strategy-proof social choice functions on domains closely related to single-peakedness.…”

Section: Relationship With the Literaturementioning

confidence: 99%

Probabilistic Fixed Ballot Rules and Hybrid Domains

Chatterji¹,

Roy²,

Sadhukhan³

et al. 2021

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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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