A characterization of the single-peaked single-crossing domain

Elkind, Edith; Faliszewski, Piotr; Skowron, Piotr

doi:10.1007/s00355-019-01216-3

Cited by 12 publications

(11 citation statements)

References 32 publications

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“…Recall that single-crossingness implies single-peakedness for narcissist domains, i.e., under the assumption that each candidate is ranked top at least once Elkind et al [2020]. Since for narcissist domains a single peaked profile is also single-top-peaked, we get a related result: that singlepeakedness is equivalent to single-top-crossingness assuming narcissist preferences.…”

Section: Top Monotonic Preferencesmentioning

confidence: 92%

Core-Stable Committees under Restricted Domains

Grzegorz¹,

Skowron²

2021

Preprint

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We study the setting of committee elections, where a group of individuals needs to collectively select a given size subset of available objects. This model is relevant for a number of real-life scenarios including political elections, participatory budgeting, and facility-location. We focus on the core-the classic notion of proportionality, stability and fairness. We show that for a number of restricted domains including voter-interval, candidate-interval, single-peaked, and single-crossing preferences the core is non-empty and can be found in polynomial time. We show that the core might be empty for strict top-monotonic preferences, yet we introduce a relaxation of this class, which guarantees non-emptiness of the core. Our algorithms work both in the randomized and discrete models. We also show that the classic known proportional rules do not return committees from the core even for the most restrictive domains among those we consider (in particular for 1D-Euclidean preferences). We additionally prove a number of structural results that give better insights into the nature of some of the restricted domains, and which in particular give a better intuitive understanding of the class of top-monotonic preferences.

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Section: Top Monotonic Preferencesmentioning

confidence: 92%

Core-Stable Committees under Restricted Domains

Grzegorz¹,

Skowron²

2021

Preprint

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“…As an application of the interval property and sign representation, we show the characterization of single-peaked preferences by Puppe [9,18].…”

Section: Sign Representation Of Single-peaked Preferencesmentioning

confidence: 99%

“…Singlepeakedness preserves strategy-proofness in assignments [16]. The structure and characterization of single-peaked domains have been researched extensively [9,18], see also a review paper [15]. Recently, single-peakedness is studied in various topics, for applications in matching and assignment [2], counting and distribution [13], construction by tiling [20], forbidden configuration [3], and finding optimal committees under proportional approval voting [17].…”

Section: Introductionmentioning

confidence: 99%

“…The operations based on the sign representation which specify the structure of Bruhat orders are also provided. The sign representation and operations can be used to characterize the minimal richness and semi-connectedness of single-peaked domains [9,18] in a different way. The procedural intervals and sign representation are useful in designing algorithms related to the single-peakedness [2].…”

Section: Introductionmentioning

confidence: 99%

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Sign representation of single-peaked preferences and Bruhat orders

Zhan¹

2022

Preprint

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Single-peaked preferences and domains are extensively researched in social science and economics. In this study, we examine the interval property as well as combinatorial structure of single-peaked preferences on a fixed Left-Right social axis. We introduce a sign representation of singlepeaked preferences; consequently, some cardinalities of single-peaked domains are easily obtained. Basic operations on the sign representation, which completely define the Bruhat poset, are also provided. The applications to known results and an isomorphic relation with associated rhombus tiling are given. Finally, we some discussions of related topics.

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“…Lemma 6.1(Elkind et al (2014),Puppe (2016)). Every regular single-crossing set of preferences is single-peaked.…”

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confidence: 97%

On single-peaked domains and min–max rules

Achuthankutty

Roy

2018

Soc Choice Welf

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We consider social choice problems where different agents can have different sets of admissible single-peaked preferences. We show every unanimous and strategy-proof social choice function on such domains satisfies Pareto property and tops-onlyness. Further, we characterize all domains on which (i) every unanimous and strategy-proof social choice function is a min-max rule, and (ii) every min-max rule is strategy-proof. As an application of our result, we obtain a characterization of the unanimous and strategy-proof social choice functions on maximal single-peaked domains (Moulin (1980), Weymark (2011)), minimally rich single-peaked domains (Peters et al. (2014)), maximal regular single-crossing domains (Saporiti (2009), Saporiti (2014)), and distance based single-peaked domains.

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A characterization of the single-peaked single-crossing domain

Cited by 12 publications

References 32 publications

Core-Stable Committees under Restricted Domains

Core-Stable Committees under Restricted Domains

Sign representation of single-peaked preferences and Bruhat orders

On single-peaked domains and min–max rules

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