Add to ORKGThis paper explores the implications of using multidimensional majorization criteria to derive inequality measures, without taking into consideration the idea behind the Pigou-Dalton principle, in the sense that if a richer person transfers something of at least one attribute to a poorer person the inequality falls. A new and basic criterion proposed by Fleurbaey and Trannoy (2003) which generalizes this idea to the multidimensional framework is explored, and its logical relationships with the dominance criteria that exist in the literature are analyzed. The paper also surveys the existent multidimensional inequality indices in order to see whether they meet this new criterion.