  For the comparison of inequality and welfare in multiple attributes the use
of generalized Gini indices is proposed. Individual endowment vectors are
summarized by using attribute weights and aggregated in a spectral social
evaluation function. Such functions are based on classes of spectral functions,
ordered by their aversion to inequality. Given a spectrum and a set $P$ of
attribute weights, a multivariate Gini dominance ordering, being uniform in
weights, is defined. If the endowment vectors are comonotonic, the dominance is
determined by their marginal distributions; if not, the dependence structure of
the endowment distribution has to be taken into account. For this, a set-valued
representative endowment is introduced that characterizes the welfare of a
$d$-dimensioned distribution. It consists of all points above the lower border
of a convex compact in $\R^d$, while the set ordering of representative
endowments corresponds to uniform Gini dominance. An application is given to
the welfare of 28 European countries. Properties of $P$-uniform Gini dominance
are derived, including relations to other orderings of $d$-variate
distributions such as convex and dependence orderings. The multi-dimensioned
representative endowment can be efficiently calculated from data. In a sampling
context, it consistently estimates its population version.
