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A multidimensional Gini index

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  • Banerjee, Asis Kumar

Abstract

This paper considers the problem of construction of a multidimensional Gini index (MGI) of relative inequality satisfying normatively acceptable conditions. One of the conditions considered is that of Correlation Increasing Majorization (CIM) which has been studied in the existing literature. A new condition called Weighting of Attributes under Unidirectional Comonotonicity (WAUC) is introduced. It requires that, in the case where the allocation of all attributes are comonotonic and attribute i is more unequally distributed than attribute j, a reduction of inequality of i is socially more beneficial than that of inequality of j. An MGI is constructed by taking each individual's well-being to be a weighted average of the attribute levels and applying the univariate Gini formula to the resulting vector of individual well-beings. The weights, same for all individuals, are determined by the attribute levels of all the individuals. It is shown that the suggested MGI satisfies both CIM and WAUC. The existing literature does not seem to contain any other MGI satisfying these two conditions simultaneously.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 60 (2010)
Issue (Month): 2 (September)
Pages: 87-93

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Handle: RePEc:eee:matsoc:v:60:y:2010:i:2:p:87-93

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Web page: http://www.elsevier.com/locate/inca/505565

Related research

Keywords: Multidimensional inequality Gini index;

References

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  1. Thibault Gajdos & John A. Weymark, 2003. "Multidimensional generalized Gini indices," ICER Working Papers - Applied Mathematics Series 16-2003, ICER - International Centre for Economic Research.
  2. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
  3. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
  4. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  5. Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-22, April.
  6. Christian List, 1999. "Multidimensional Inequality Measurement: A Proposal," Economics Series Working Papers 1999-W27, University of Oxford, Department of Economics.
  7. Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
  8. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
  9. Ram, Rati, 1982. "Composite indices of physical quality of life, basic needs fulfilment, and income : A principal component representation," Journal of Development Economics, Elsevier, vol. 11(2), pages 227-247, October.
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Cited by:
  1. Asis Banerjee, 2014. "A multidimensional Lorenz dominance relation," Social Choice and Welfare, Springer, vol. 42(1), pages 171-191, January.

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