2018
DOI: 10.1609/aaai.v32i1.11461
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On Recognising Nearly Single-Crossing Preferences

Abstract: If voters' preferences are one-dimensional, many hard problems in computational social choice become tractable. A preference profile can be classified as one-dimensional if it has the single-crossing property, which requires that the voters can be ordered from left to right so that their preferences are consistent with this order. In practice, preferences may exhibit some one-dimensional structure, despite not being single-crossing in the formal sense. Hence, we ask whether one can identify preference profiles… Show more

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Cited by 4 publications
(2 citation statements)
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“…Besides, a local version of the new measure (where, instead of the sum, we minimize the maximum over the voters of the number of forbidden triples), together with a comparison to local versions of V D and GS, might be investigated. Also, it would be interesting to undertake the same type of approach, based on the very definition of a restricted domain, for defining distance measures to other domains, such as the single-crossing domain [16], or single-peaked preferences on a graph [18].…”
Section: Discussionmentioning
confidence: 99%
“…Besides, a local version of the new measure (where, instead of the sum, we minimize the maximum over the voters of the number of forbidden triples), together with a comparison to local versions of V D and GS, might be investigated. Also, it would be interesting to undertake the same type of approach, based on the very definition of a restricted domain, for defining distance measures to other domains, such as the single-crossing domain [16], or single-peaked preferences on a graph [18].…”
Section: Discussionmentioning
confidence: 99%
“…Lastly, a different-yet intuitively related-task on domain restrictions, pioneered by Faliszewski, Hemaspaandra, and Hemaspaandra (2014) and so far only explored on domains of total orders, is about recognising profiles that nearly enjoy a given structure (Elkind and Lackner 2014;Erdélyi, Lackner, and Pfandler 2017;Jaeckle, Peters, and Elkind 2018), according to some distance metric. This is very natural area to investigate for dichotomous preferences as well, but this is a topic for another paper.…”
Section: Introductionmentioning
confidence: 99%