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Multidimensional Pigou-Dalton Transfers and Social Evaluation Functions

Author

Listed:
  • Marcello Basili

    (University of Siena)

  • Paulo Casaca

    (Federal University of Minas Gerais)

  • Alain Chateauneuf

    (Centre d'Economie de la Sorbonne)

  • Maurizio Franzini

    (University of Rome La Sapienza)

Abstract

We axiomatize, in the multidimensional case, a social evaluation function that can accommodate a natural Pigou-Dalton principle and correlation increasing majorization. This is performed by building upon a simple class of inframodular functions proposed by Müller and Scarsini under risk

Suggested Citation

  • Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2016. "Multidimensional Pigou-Dalton Transfers and Social Evaluation Functions," Documents de travail du Centre d'Economie de la Sorbonne 16043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:16043
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    1. Carmen Herrero & Ricardo Martínez & Antonio Villar, 2010. "Multidimensional Social Evaluation: An Application To The Measurement Of Human Development," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(3), pages 483-497, September.
    2. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
    3. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
    4. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    5. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    6. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    7. Eduardo Zambrano, 2014. "An axiomatization of the human development index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 853-872, April.
    8. François Bourguignon & Satya R. Chakravarty, 2019. "The Measurement of Multidimensional Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 83-107, Springer.
    9. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    10. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    11. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons with Discrete Indicators of Well-being," Cahiers de recherche 0628, CIRPEE.
    12. Massimo Marinacci & Luigi Montrucchio, 2005. "Ultramodular Functions," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 311-332, May.
    13. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    14. Müller, Alfred & Scarsini, Marco, 2012. "Fear of loss, inframodularity, and transfers," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1490-1500.
    15. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
    16. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    17. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
    18. Boland, Philip J. & Proschan, Frank, 1988. "Multivariate arrangement increasing functions with applications in probability and statistics," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 286-298, May.
    19. Bosmans, Kristof & Lauwers, Luc & Ooghe, Erwin, 2009. "A consistent multidimensional Pigou-Dalton transfer principle," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1358-1371, May.
    20. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    21. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda," World Bank Economic Review, World Bank Group, vol. 20(1), pages 91-113.
    22. Milorad Kovacevic, 2010. "Measurement of Inequality In Human Development - A Review," Human Development Research Papers (2009 to present) HDRP-2010-35, Human Development Report Office (HDRO), United Nations Development Programme (UNDP).
    23. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    24. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    25. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    26. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 1-13.
    27. Shaked, Moshe, 1982. "A general theory of some positive dependence notions," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 199-218, June.
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    Cited by:

    1. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.

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    More about this item

    Keywords

    multidimensional inequality; Pigou-Dalton transfer; increasing majorization; inframodular functions; Human Development Index;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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