From unidimensional to multidimensional inequality: a review

We review results concerning the representation of partial orders of univariate distributions via stochastic orders and investigate their applications to some classes of stochastic dominance conditions applied in inequality and welfare measurement. The results obtained in an unidimensional framework are extended to multidimensional analysis. We discuss difficulties arising from aggregation of multidimensional distributions into synthetic indicators that value both inequality in the distribution of each attribute and the association between the attributes. We explore the potential for multidimensional evaluations that are based on the partial orders induced by different criteria of majorization and organize related and equivalent inequality and welfare representations.