2019
DOI: 10.1007/s00355-019-01216-3
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A characterization of the single-peaked single-crossing domain

Abstract: We characterize elections that are simultaneously single-peaked and single-crossing (SPSC), by establishing a connection between this domain and that of minimally rich elections, i.e., elections where each candidate is ranked first by at least one voter. Specifically, we show that an election is both single-peaked and single-crossing if and only if it can be obtained from a minimally rich single-crossing election by deleting voters.

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Cited by 12 publications
(11 citation statements)
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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%
“…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%
“…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%
See 1 more Smart Citation
“…Lemma 6.1(Elkind et al (2014),Puppe (2016)). Every regular single-crossing set of preferences is single-peaked.…”
mentioning
confidence: 97%