  For the comparison of inequality in multiple attributes the use of
generalized Gini indices is proposed. Spectral social evaluation functions are
used in the multivariate setting, and Gini dominance orderings are introduced
that are uniform in attribute weights. Classes of spectral evaluators are
considered that are parameterized by their aversion to inequality. Then a
set-valued representative endowment is defined that characterizes
$d$-dimensioned inequality. It consists of all points above the lower border of
a convex compact in $R^d$, while the pointwise ordering of such endowments
corresponds to uniform Gini dominance. Properties of uniform Gini dominance are
derived, including relations to other orderings of $d$-variate distributions
such as usual multivariate stochastic order and convex order. The
multi-dimensioned representative endowment can be efficiently calculated from
data; in a sampling context, it consistently estimates its population version.
