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The minimal Hilbert basis of the Hammond order cone

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  • Ramses H. Abul Naga

    (Universidad de Málaga
    University of Aberdeen
    Pan African Scientific Research Council)

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.

Suggested Citation

  • Ramses H. Abul Naga, 2022. "The minimal Hilbert basis of the Hammond order cone," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 191-215, October.
    • Handle: RePEc:spr:etbull:v:10:y:2022:i:2:d:10.1007_s40505-022-00226-2
    DOI: 10.1007/s40505-022-00226-2
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    1. Alain Chateauneuf & Patrick Moyes, 2002. "Non-welfarist approaches to inequality measurement," Post-Print hal-00156671, HAL.
    2. Magdalou, Brice, 2021. "A model of social welfare improving transfers," Journal of Economic Theory, Elsevier, vol. 196(C).
    3. Suman Seth & Gaston Yalonetzky, 2021. "Assessing Deprivation with an Ordinal Variable: Theory and Application to Sanitation Deprivation in Bangladesh," The World Bank Economic Review, World Bank, vol. 35(3), pages 793-811.
    4. Bénédicte Apouey & Jacques Silber & Yongsheng Xu, 2020. "On Inequality‐Sensitive and Additive Achievement Measures Based on Ordinal Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(2), pages 267-286, June.
    5. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
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