Diversity as Expected Pairwise Dissimilarity: An axiomatic Characterization

Charles Figuières and Nicolas Gravel
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Charles Figuières: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique
Nicolas Gravel: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique

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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)
Date: 2026-07-21
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