A multidimensional Gini index
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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- Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-122, April.
- Thibault Gajdos & John Weymark, 2005.
"Multidimensional generalized Gini indices,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
- Thibault Gajdos & John A. Weymark, 2003. "Multidimensional Generalized Gini Indices," Vanderbilt University Department of Economics Working Papers 0311, Vanderbilt University Department of Economics, revised Jul 2003.
- Thibault Gajdos & John Weymark, 2005. "Multidimensional Generalized Gini Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085881, HAL.
- Thibault Gajdos & John A. Weymark, 2003. "Multidimensional generalized Gini indices," ICER Working Papers - Applied Mathematics Series 16-2003, ICER - International Centre for Economic Research.
- Thibault Gadjos & John A, Weymark, 2003. "Multidimensional Generalized Gini Indices," Working Papers 2003-16, Centre de Recherche en Economie et Statistique.
- 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.
- Patrick Moyes & Nicolas Gravel, 2010. "Ethically robust comparisons of distributions of two individual attributes," Post-Print hal-00796074, HAL.
- Patrick Moyes & Nicolas Gravel, 2007. "Ethically robust comprisons of distributions of two individual attributes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00389601, HAL.
- Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
- Udo Ebert & Patrick Moyes, 2002. "Equivalence scales reconsidered," Post-Print hal-00156680, HAL.
- Udo Ebert & Patrick Moyes, 2003. "Equivalence scales reconsidered," Post-Print hal-00156453, HAL.
- Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
- WEYMARK, John A., "undated". "Generalized Gini inequality indices," CORE Discussion Papers RP 453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
- Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
- Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 1-13.
- 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. Full references (including those not matched with items on IDEAS)