Sequential dominance and weighted utilitarianism

One well-known way to make heterogeneous welfare comparisons - comparing distributions in which households differ in both income and needs - is Atkinson and Bourguignon's [Atkinson, A.B., Bourguignon, F., 1987. Income distribution and differences in needs. In: Feiwel, G.R. (Ed.), Arrow and the Foundations of the Theory of Economic Policy. Macmillan, London, pp. 350-370] sequential generalized Lorenz dominance criterion. We show that it suffices to be a weighted utilitarian, with higher weights for the more needy, to accept the sequential generalized Lorenz dominance criterion.