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Social Choice and Welfare

Erschienen in:

20.03.2019 | Original Paper

A note on the decomposability of inequality measures

verfasst von: Frédéric Chantreuil, Sébastien Courtin, Kevin Fourrey, Isabelle Lebon

Erschienen in: Social Choice and Welfare | Ausgabe 2/2019

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Abstract

We propose a decomposition of inequality measures. By taking the example of the decomposition of income inequality by components, we show that this decomposition fits the definition of two elements: the sum of pure marginal contributions of income components and the sum of the pairwise interactions of all income components. This decomposition relies on the Shapley function and remains valid for a decomposition by subgroups and by components.

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See also Murofushi and Soneda (1993), Grabish (1996, 1997), Grabish et al. (2000), and Kojadinovic (2002, 2004, 2005).

For instance, if there are two components (\(m=2\)), the coalition considered to evaluate the interaction between i and j only includes these two components (\(t=0\)). Thus, in this particular case, the weight of this interaction is \(\frac{(2-0-2)!(0+1)!}{2!} = \frac{0!1!}{2!} = \frac{1}{2}\). Both components will have an importance equals to their PMC, plus half of value of their interaction.

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Titel: A note on the decomposability of inequality measures
verfasst von: Frédéric Chantreuil
Sébastien Courtin
Kevin Fourrey
Isabelle Lebon
Publikationsdatum: 20.03.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 2/2019
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-019-01183-9

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