A Class of Dissimilarity Semimetrics for Preference Relations

Hiroki Nishimura () and Efe A. Ok ()
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Hiroki Nishimura: Department of Economics, University of California Riverside, Riverside, California 92507
Efe A. Ok: Department of Economics, New York University, New York, New York 10003; Courant Institute of Mathematical Sciences, New York University, New York, New York 10012

Mathematics of Operations Research, 2024, vol. 49, issue 4, 2249-2270

Abstract: We propose a class of semimetrics for acyclic preference relations, any one of which is an alternative to the classical Kemeny-Snell-Bogart metric. These semimetrics are based solely on the implications of preferences for choice behavior and thus appear more suitable in economic contexts and choice experiments. We obtain a fairly simple axiomatic characterization for the class we propose. The apparently most important member of this class, which we dub the “ top-difference semimetric ,” is characterized separately. We also obtain alternative formulae for it and, relative to this particular metric, compute the diameter of the space of complete and transitive preferences, as well as the best transitive extension of a given acyclic preference relation.

Keywords: Primary: 06A06; 06A75; Secondary: 06A07; 30L05; metrics for preorders; Kemeny-Snell metric; weighted Kendall metrics; finite metric spaces; transitive closure (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:4:p:2249-2270

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