 Ordering Distributions on a Finitely Generated ConeNo 2024-02, Working Papers from Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center 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. Keywords: Measurement of social welfare and inequality; order rela- tions induced by convex cones; Carathéodory's theorem; Farkas lemma; generalized inverses. (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:mal:wpaper:2024-2 Access Statistics for this paper More papers in Working Papers from Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center Contact information at EDIRC. |
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