Atlantis Press Paper Details: The Gini index and the consistent measurement of inequality among the poor

In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor.

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title:		The Gini index and the consistent measurement of inequality among the poor
publication:		EUSFLAT
part of series:		Advances in Intelligent Systems Research
pages:		33 - 40
DOI:		To be assigned soon (how to use a DOI)
author(s):		O. Aristondo, J.L. Garc¨ªa-Lapresta, C. Lasso, R.A. Marques
publication date:		July 2011
keywords:		Aggregation functions, OWA operators, Gini index, achievement and shortfall inequality, dual decomposition.
abstract:		In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		eusflatlfa2011_S1_6.pdf (2408 K)