The minimal Hilbert basis of the Hammond order cone

Ramses Abul Naga

Economic Theory Bulletin, 2022, vol. 10, issue 2, No 2, 215 pages

Abstract: 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)
Date: 2022
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Working Paper: The Minimal Hilbert Basis of the Hammond Order Cone (2022)
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DOI: 10.1007/s40505-022-00226-2

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