This paper considers the problem of comparing two income distributions with different numbers of income recipients. The approach eschews the “replication of populations” of Dalton’s Population Principle which has been a fixture of the literature on income inequality since its inception. We start from a preorder which is a generalization of majorization, construct the “better-than” set and characterize the order-preserving welfare functions in a unified framework. The fixed population case falls off as a particular case.