In this paper we define and introduce the notion of View the MathML sourceNth degree inequality which is the particular case of View the MathML sourceNth order stochastic dominance which preserves the (N−1)(N−1) first moments. We exhibit that transfer à la Fishburn and Willig (1984) indeed generate decreases in View the MathML sourceNth degree inequality. We then show that whereas Kolm and Atkinson indices are consistent with aversion to any degree of inequality, only a limited class of indices of the generalized entropy family is.