RT info:eu-repo/semantics/article
T1 Classical inequality indices, welfare and illfare functions, and the dual decomposition
A1 Aristondo, Oihana
A1 García Lapresta, José Luis
A1 Lasso de la Vega, Casilda
A1 Marques Pereira, Ricardo Alberto
K1 Classic inequality indices
K1 Índices de desigualdad clásicos
K1 Aggregation functions
K1 Funciones de agregación
AB In the traditional framework, social welfare functions depend on the mean income and on the income inequality. An alternative illfare framework has been developed to take into account the disutility of unfavorable variables. The illfare level is assumed to increase with the inequality of the distribution. In some social and economic fields, such as those related to employment, health, education, or deprivation, the characteristics of the individuals in the population are represented by bounded variables, which encode either achievements or shortfalls. Accordingly, both the social welfare and the social illfare levels may be assessed depending on the framework we focus on. In this paper we propose a unified dual framework in which welfare and illfare levels can both be investigated and analyzed in a natural way. The dual framework leads to the consistent measurement of achievements and shortfalls, thereby overcoming one important difficulty of the traditional approach, in which the focus on achievements or shortfalls often leads to different inequality rankings. A number of welfare functions associated with inequality indices are OWA operators. Specifically this paper considers the welfare functions associated with the classical inequality measures due to Gini, Bonferroni, and De Vergottini. These three indices incorporate different value judgments in the measurement of inequality, leading to different behavior under income transfers between individuals in the population. In the bounded variables representation, we examine the dual decomposition and the orness degree of the three classical welfare/illfare functions in the standard framework of aggregation functions on the domain. The dual decomposition of each welfare/illfare function into a self-dual central index and an anti-self-dual inequality index leads to the consistent measurement of achievements and shortfalls.
PB Elsevier
SN 0165-0114
YR 2013
FD 2013
LK https://uvadoc.uva.es/handle/10324/50068
UL https://uvadoc.uva.es/handle/10324/50068
LA eng
NO Fuzzy Sets and Systems, 2013, vol. 228, p. 114-136
NO Producción Científica
DS UVaDOC
RD 24-nov-2024