The article presents a new model for social welfare improving transfers based on the Hardy-Littlewood-Polya Theorem. This model applies to situations where distributions count the number of people with different outcomes, and transfers have a specific structure. The model can be used for both one-dimensional and multi-dimensional outcomes, whether they are numerical or ranked. Many existing results in the field are actually natural consequences of this new theorem. The model also offers insights into social deprivation and highlights the importance of expected utility in decision-making under risk.