Multidimensional Generalized Gini Indices
Working Paper No. 03-W11R
Thibault Gajdos and John A. Weymark
ABSTRACT [article]
The axioms used to 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.
Keywords and Phrases: Generalized Gini, multidimensional inequality
JEL Classification Number: D63