On single-peaked domains and min–max rules

Achuthankutty, Gopakumar; Roy, Souvik

doi:10.1007/s00355-018-1137-1

Cited by 10 publications

(3 citation statements)

References 45 publications

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“…However, in our case, there can be more than one preference with the same top-ranked alternative, and hence, tops-onlyness is required to be proved additionally. Weymark (2011) shows that the maximal single-peaked domain on a line is tops-only, and recently, Achuthankutty and Roy (2018) generalize this result for arbitrary (that is, not necessary maximal) singlepeaked domains on a line. 9 Chatterji and Sen (2011) provide a sufficient condition on a domain for it to be tops-only.…”

Section: Schummer and Vohra (2002)mentioning

confidence: 69%

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

2021

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In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.

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Section: Schummer and Vohra (2002)mentioning

confidence: 69%

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

2021

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“…When choosing a single alternative from a finite set (of alternatives), strategy-proofness and voter-sovereignty characterize, on the domain of strict preferences, a class of functions similar to the class of efficient generalized median rules (Barberà et al 1993). Moreover, the admissible preferences of all agents being top-connected 6 characterizes the maximal domain in which (i) every strategy-proof and unanimous function is a generalized median rule, and (ii) every generalized median rule is strategy-proof (Achuthankutty and Roy 2018).…”

Section: Related Literaturementioning

confidence: 99%

On strategy-proofness and single-peakedness: median-voting over intervals

Klaus

Protopapas

2020

Int J Game Theory

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We study correspondences that choose an interval of alternatives when agents have single-peaked preferences over locations and ordinally extend their preferences over intervals. We extend the main results of Moulin (Public Choice 35:437–455, 1980) to our setting and show that the results of Ching (Soc Choice Welf 26:473–490, 1997) cannot always be similarly extended. First, strategy-proofness and peaks-onliness characterize the class of generalized median correspondences (Theorem 1). Second, this result neither holds on the domain of symmetric and single-peaked preferences, nor can in this result min/max continuity substitute peaks-onliness (see counter-Example 3). Third, strategy-proofness and voter-sovereignty characterize the class of efficient generalized median correspondences (Theorem 2).

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“…Our motivations for this research began with the random assignment problem (Fujishige et al 2018). Single-peakedness is important to keep required properties for further generalization (Achuthankutty and Roy 2018;Bade 2019;Moulin 1980Moulin , 2017Savaglio and Vannucci 2019). Having a better understanding of the structure of single-peaked domains leads to the simple recursive construction provided in the following.…”

Section: Introductionmentioning

confidence: 99%

A simple construction of complete single-peaked domains by recursive tiling

Zhan

2019

Math Meth Oper Res

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Single-peakedness was introduced by Black (J Political Econ 56:23-34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published in recent years, and some observations of known results and examples by the author. The underlying basic structure of tiling type and properties of single-peaked domains provided here give a good visualization and make further developments on single-peakedness more easy.

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On single-peaked domains and min–max rules

Cited by 10 publications

References 45 publications

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

On strategy-proofness and single-peakedness: median-voting over intervals

A simple construction of complete single-peaked domains by recursive tiling

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