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Diversity as Expected Pairwise Dissimilarity: An axiomatic Characterization

Author

Listed:
  • Charles Figuières

    (Aix Marseille Univ, CNRS, AMSE, Marseille, France)

  • Nicolas Gravel

    (Aix Marseille Univ, CNRS, AMSE, Marseille, 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.

Suggested Citation

  • Charles Figuières & Nicolas Gravel, 2026. "Diversity as Expected Pairwise Dissimilarity: An axiomatic Characterization," AMSE Working Papers 2622, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:2622
    Note: Working paper AMSE 2026-22
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    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics

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