Abstract
This paper gives an axiomatic characterization of the Gini index of segregation. We use some standard axioms along with an independence axiom that is related to the dual independence axiom of Yaari’s dual theory of choice under risk.
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Notes
This axiom first appeared in James and Taeuber (1985).
This property was originally proposed by Jahn et al. (1947).
The expected utility axiom states that if there are two lotteries G, and \(G^{\prime },\) such that \(G\succeq G^{\prime }\), then for any other lottery H and any \(\alpha \in [0,1]\) , \(\alpha G+(1-\alpha )H\) \(\succeq \alpha G^{\prime } +(1-\alpha )H\). The assumption that X and Y have the same girl populations is analogous to the assumption of a constant weight \(\alpha \) on G and \(G^{\prime },\) as shown in the next section.
In Frankel and Volij (2011) this axiom is called the neighborhood division property. It is applied to two or more ethnic groups.
The transfer principle is the translation to the context of segregation of the Pigou Dalton transfer principle from the context of income inequality.
In fact, the segregation curve of a society can be interpreted as the Lorenz curve of an income distribution, in which boys and girls, respectively, play the roles of population and income.
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We are very grateful to Oscar Volij, whose useful suggestions have contributed to improve the paper. We are also grateful to two anonymous referees for their helpful comments. This research is supported by the Spanish Ministerio de Economía y Competitividad and the European Regional Development Fund under project ECO2015-67519-P (MINECO/FEDER) and by funding from the Basque Government for Grupos Consolidados IT 568-13.
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Puerta, C., Urrutia, A. A characterization of the Gini segregation index. Soc Choice Welf 47, 519–529 (2016). https://doi.org/10.1007/s00355-016-0980-1
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DOI: https://doi.org/10.1007/s00355-016-0980-1