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Ordering Distributions on a Finitely Generated Cone

Author

Listed:
  • Ramses H. Abul Naga

    (Departamento de Teoría e Historia Económica, Universidad de Málaga and Faculté de Gou- vernance, sciences économiques et sociales, Université Mohammed VI Polytechnique.)

Abstract

One large class of relations used in the measurement of social welfare and risk consists of relations induced by finitely generated cones. Within this class, we develop a general approach to investigate the ordering of distributions-an approach that does not require the prior derivation of a numerical representation of the order relation. We provide an equivalence between the statement that two distributions x and y are ordered, and (1) the possibility of expressing x - y as a positive combination of a subset of linearly independent vectors from the generators of the cone, (2) the existence of a relation defined on a simplicial cone such that x and y are ordered by this latter relation, and (3) the existence of a generalized inverse G of the matrix whose columns generate the underlying cone, such that the product of G and the vector x - y results in a non-negative vector. The results are illustrated in the context of distributional comparisons on socioeconomic data.

Suggested Citation

  • Ramses H. Abul Naga, 2024. "Ordering Distributions on a Finitely Generated Cone," Working Papers 2024-02, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    • Handle: RePEc:mal:wpaper:2024-2
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