When do utilitarianism and egalitarianism agree on evaluation? An intersection approach

We examine the range of the agreement between the utilitarian social welfare ordering (SWO) and leximin SWO by analyzing the intersection of them. We characterize the intersection (in terms of subrelation) using the strong version of Pigou-Dalton equity and a new axiom on the composition of rank-preserving progressive and regressive utility transfers. Then, adding separability and cardinal full comparability, we jointly characterize the leximin SWO and the lexicographic composition of the utilitarian and leximin SWOs that applies the utilitarian SWO first. We also jointly characterize these two SWOs and the utilitarian SWO using the weak version of Pigou-Dalton equity.