  The Gini's mean difference was defined as the expected absolute difference
between a random variable and its independent copy. The corresponding
normalized version, namely Gini's index, denotes two times the area between the
egalitarian line and the Lorenz curve. Both are dispersion indices because they
quantify how far a random variable and its independent copy are. Aiming to
measure dispersion in the multivariate case, we define and study new Gini's
indices. For the bivariate case we provide several results and we point out
that they are "dependence-dispersion" indices. Covariance representations are
exhibited, with an interpretation also in terms of conditional distributions.
Further results, bounds and illustrative examples are discussed too.
Multivariate extensions are defined, aiming to apply both indices in more
general settings. Then, we define efficiency Gini's indices for any
semi-coherent system and we discuss about their interpretation. Empirical
versions are considered in order as well to apply multivariate Gini's indices
to data.
