Multidimensional Generalized Gini Indices

Thibault Gajdos (1, 2) , John A. Weymark (3)

1 CREST - Centre de Recherche en Économie et Statistique
2 EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative
3 Department of Economics

The axioms that characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.

Mots clés: Generalized Gini; multidimensional inequality

Domaines: Economies et finances

Thibault Gajdos, John A. Weymark. Multidimensional Generalized Gini Indices. Economic Theory, 2005, 26 (3), pp.471-496. ⟨10.1007/s00199-004-0529-x⟩. ⟨halshs-00085881⟩