We establish an equivalence theorem between (i) dominance of one society by another, according to a finite sequence of social welfare improving transfers and (ii) dominance according to a class of social welfare functions, in the following framework: individual outcomes are multidimensional but finitely divisible in each dimension, a distribution simply counts the number of individuals having each possible outcome, and the considered set of transfers has the structure of a discrete cone. This framework encompasses most of the social welfare improving transfers investigated in the literature such as, for instance, Pigou-Dalton pro- gressive transfers. As by-products, our model sheds new light on some surprising results in the literature on social deprivation, and provides new arguments on the key role of the expected utility model in decision-making under risk.