On the combinatorial structure of the approval-voting polytope

Jean Paul Doignon; Michel Regenwetter

doi:10.1006/jmps.2001.1411

On the combinatorial structure of the approval-voting polytope

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Abstract

Falmagne and Regenwetter (1996) proposed a probabilistic choice model of approval voting called the size-independent model. This model was investigated geometrically by Doignon and Regenwetter (1997), who introduced the approval-voting polytope associated with the choice model. In an effort to get closer to a full linear description of the polytope, we provide all edges, two-dimensional faces, and a large group of combinatorial automorphisms. Despite the new insights gathered from these results, the main challenge of listing all facets remains an open problem.

Original language	English (US)
Pages (from-to)	554-563
Number of pages	10
Journal	Journal of Mathematical Psychology
Volume	46
Issue number	5
DOIs	https://doi.org/10.1006/jmps.2001.1411
State	Published - Oct 2002

Keywords

Adjacency
Approval-voting polytope
Combinatorial automorphism
Facet
Probabilistic choice model

ASJC Scopus subject areas

Psychology(all)
Applied Mathematics

Online availability

10.1006/jmps.2001.1411

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title = "On the combinatorial structure of the approval-voting polytope",

abstract = "Falmagne and Regenwetter (1996) proposed a probabilistic choice model of approval voting called the size-independent model. This model was investigated geometrically by Doignon and Regenwetter (1997), who introduced the approval-voting polytope associated with the choice model. In an effort to get closer to a full linear description of the polytope, we provide all edges, two-dimensional faces, and a large group of combinatorial automorphisms. Despite the new insights gathered from these results, the main challenge of listing all facets remains an open problem.",

keywords = "Adjacency, Approval-voting polytope, Combinatorial automorphism, Facet, Probabilistic choice model",

author = "Doignon, {Jean Paul} and Michel Regenwetter",

note = "Funding Information: Both authors thank the Fuqua School of Business, Duke University, for supporting their collaboration, as well as the National Science Foundation for Grant 98-18756 to Regenwetter and Pekecˇ that was instrumental for the collaboration. The authors thank Mathieu Koppen, Reinhard Suck, and an anonymous referee for their remarks on a previous version. These remarks led to a significant improvement in the presentation. J.-P. D. thanks Michel Dehon for his advice on the Magma software. M. R. thanks the National Science Foundation for grant 97-30076 to Regenwetter. This research was carried out while M. R. was a faculty member at the Fuqua School of Business, Duke University.",

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AU - Regenwetter, Michel

N1 - Funding Information: Both authors thank the Fuqua School of Business, Duke University, for supporting their collaboration, as well as the National Science Foundation for Grant 98-18756 to Regenwetter and Pekecˇ that was instrumental for the collaboration. The authors thank Mathieu Koppen, Reinhard Suck, and an anonymous referee for their remarks on a previous version. These remarks led to a significant improvement in the presentation. J.-P. D. thanks Michel Dehon for his advice on the Magma software. M. R. thanks the National Science Foundation for grant 97-30076 to Regenwetter. This research was carried out while M. R. was a faculty member at the Fuqua School of Business, Duke University.

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N2 - Falmagne and Regenwetter (1996) proposed a probabilistic choice model of approval voting called the size-independent model. This model was investigated geometrically by Doignon and Regenwetter (1997), who introduced the approval-voting polytope associated with the choice model. In an effort to get closer to a full linear description of the polytope, we provide all edges, two-dimensional faces, and a large group of combinatorial automorphisms. Despite the new insights gathered from these results, the main challenge of listing all facets remains an open problem.

AB - Falmagne and Regenwetter (1996) proposed a probabilistic choice model of approval voting called the size-independent model. This model was investigated geometrically by Doignon and Regenwetter (1997), who introduced the approval-voting polytope associated with the choice model. In an effort to get closer to a full linear description of the polytope, we provide all edges, two-dimensional faces, and a large group of combinatorial automorphisms. Despite the new insights gathered from these results, the main challenge of listing all facets remains an open problem.

KW - Adjacency

KW - Approval-voting polytope

KW - Combinatorial automorphism

KW - Facet

KW - Probabilistic choice model

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On the combinatorial structure of the approval-voting polytope

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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