Condorcet Domains of Degree at most Seven

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Tác giả: Dolica Akello-Egwell, Charles Leedham-Green, Alastair Litterick, Klas Markström, Søren Riis

Ngôn ngữ: eng

Ký hiệu phân loại: 512.4 Rings

Thông tin xuất bản: 2023

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 197597

Comment: Typos corrected, some open problems, a conjecture, and a new figure has been added in the latest versionIn this paper we give the first explicit enumeration of all maximal Condorcet domains on $n\leq 7$ alternatives. This has been accomplished by developing a new algorithm for constructing Condorcet domains, and an implementation of that algorithm which has been run on a supercomputer. We follow this up by the first survey of the properties of all maximal Condorcet domains up to degree 7, with respect to many properties studied in the social sciences and mathematical literature. We resolve several open questions posed by other authors, both by examples from our data and theorems. We give a new set of results on the symmetry properties of Condorcet domains which unify earlier works. Finally we discuss connections to other domain types such as non-dictatorial domains and generalisations of single-peaked domains. All our data is made freely available for other researches via a new website.
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