13 July 2021This paper provides a generalization of the Hardy-Littlewood-Polya (HLP) Theorem in the following discrete framework: a distribution counts the number of persons having each possible individual outcome –assumed to be finitely divisible– and social welfare improving transfers have the structure of a discrete cone. The generalization is abstract in the sense that individual outcomes can be unidimensional or multidimensional, each dimension can be cardinal or ordinal and no further specification is required for the transfers. It follows that most of the results in the literature, applied to discrete distributions and comparable to the HLP Theorem, are corollaries of our theorem. In addition, our model sheds new light on some surprising results in the literature on social deprivation and, in decision-making under risk, provides new arguments on the key role of the expected utility model.