The Minimal Hilbert Basis of the Hammond Order Cone

Ramses Abul Naga

No 2022-02, Working Papers from Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center

Abstract: We characterize the minimal Hilbert basis of the Hammond order cone, and present several novel applications of the resulting basis. From the basis, we extract an invertible matrix, that provides a numerical representation of the Hammond order relation. The basis also enables the construction of a space—that we call the Hammond order lattice—where order-extensions of the Hammond order (i.e. more complete relations) may be derived. Finally, we introduce a class of maximal linearly independent Hilbert bases, in which the specific results derived in relation to the Hammond order cone, are shown to hold more generally.

Keywords: Measurement of social welfare; order relations induced by convex cones; Hammond order; Hilbert bases. (search for similar items in EconPapers)
Pages: 30 pages
Date: 2022-07
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Journal Article: The minimal Hilbert basis of the Hammond order cone (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:mal:wpaper:2022-2

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