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The gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality
Author(s) -
Aristondo Oihana,
GarcíaLapresta José Luis,
Lasso de la Vega Casilda,
Pereira Ricardo Alberto Marques
Publication year - 2012
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21517
Subject(s) - inequality , dual (grammatical number) , index (typography) , measure (data warehouse) , econometrics , mathematics , poverty , operator (biology) , decomposition , decomposition method (queueing theory) , mathematical economics , economics , statistics , computer science , economic growth , data mining , literature , art , mathematical analysis , ecology , biochemistry , chemistry , repressor , biology , world wide web , transcription factor , gene
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, 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 ordered weighted averaging (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. © 2011 Wiley Periodicals, Inc.