Ordering Distributions on a Finitely Generated Cone

Ramses Abul Naga

No 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)
Pages: 24 pages
Date: 2024-03
References: Add references at CitEc
Citations:

Downloads: (external link)
https://theeconomics.uma.es/malagawpseries/Papers/METCwp2024-2.pdf First version, 2024 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

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.
Bibliographic data for series maintained by Ascension Andina ().