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The binomial Gini inequality indices and the binomial decomposition of welfare functions

  • Silvia Bortot

    ()

    (Department of Economics and Management, University of Trento)

  • Ricardo Alberto Marques Pereira

    ()

    (Department of Economics and Management, University of Trento)

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    In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the generalized Gini welfare functions and inequality indices for populations of n>=2 individuals, and on the other hand, the Mobius representation framework for Choquet integration, particularly in the case of k-additive symmetric capacities. We recall the binomial decomposition of OWA functions due to Calvo and De Baets [14] and we examine it in the restricted context of generalized Gini welfare functions, with the addition of appropriate S-concavity conditions. We show that the original expression of the binomial decomposition can be formulated in terms of two equivalent functional bases, the binomial Gini welfare functions and the Atkinson-Kolm-Sen (AKS) associated binomial Gini inequality indices, according to Blackorby and Donaldson's correspondence formula. The binomial Gini pairs of welfare functions and inequality indices are described by a parameter j = 1,...,n, associated with the distributional judgements involved. The j-th generalized Gini pair focuses on the (n - j + 1)/n poorest fraction of the population and is insensitive to income transfers within the complementary richest fraction of the population.

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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2013-305.pdf
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    Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 305.

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    Length: 32 pages
    Date of creation: Sep 2013
    Date of revision:
    Handle: RePEc:inq:inqwps:ecineq2013-305
    Contact details of provider: Web page: http://www.ecineq.orgEmail:


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    1. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    2. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    3. Oihana Aristondo & JosŽ Luis Garc’a-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2012. "Classical inequality indices, welfare functions, and the dual decomposition," DISA Working Papers 2012/06, Department of Computer and Management Sciences, University of Trento, Italy, revised Jun 2012.
    4. Ebert, Udo, 1987. "Size and distribution of incomes as determinants of social welfare," Journal of Economic Theory, Elsevier, vol. 41(1), pages 23-33, February.
    5. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-56, February.
    6. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    7. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    8. Rolf Aaberge, 2006. "Gini’s Nuclear Family," Discussion Papers 491, Research Department of Statistics Norway.
    9. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
    10. Oihana Aristondo & José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2011. "The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality," Working Papers 203, ECINEQ, Society for the Study of Economic Inequality.
    11. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, vol. 106(1), pages 190-200, September.
    12. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-36, February.
    13. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    14. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-85, November.
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