Diversity as Expected Pairwise Dissimilarity: An axiomatic Characterization

Charles Figuières and Nicolas Gravel
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Charles Figuières: Aix Marseille Univ, CNRS, AMSE, Marseille, France
Nicolas Gravel: Aix Marseille Univ, CNRS, AMSE, Marseille, France

No 2622, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: We provide an axiomatic characterization of a family of criteria for comparing distributions of individuals into categories. The characterized family consists in all rankings that compare distributions based on the expectation of the pairwise dissimilarities between categories for some numerical valuation of these dissimilarities. In the context of biological diversity measurement, such criteria are sometimes referred to as Rao (1982) quadratic entropy. Beside the ordinal characterization of the family of all these criteria that produce quasiconcave rankings of distributions, this paper also singles out with an additional axiom the specific member of this family that considers all distinct categories to be equally dissimilar. This criterion turns out to be the ranking of distributions induced by the comparison of their Herfindahl (1950)-Hirschman (1945)-Simpson (1949) index.

Keywords: Axioms; Herfindahl-Hirschman-Simpson; Rao Quadratic Entropy; Mixture Symmetry; Quasi-Concavity; Diversity (search for similar items in EconPapers)
JEL-codes: C65 D63 Q57 (search for similar items in EconPapers)
Date: 2026-07-21
Note: Working paper AMSE 2026-22
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Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:2622

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