Prioritarians, unlike utilitarians, believe that well-being has diminishing marginal moral value. This difference is captured in the Pigou-Dalton axiom: a transfer of well-being from a better-off person to a worse-off person, which (a) is non-leaky in the sense that the worse-off one gains exactly what the better-off one loses, (b) still leaves the better-off one at least as well off as the worse-off one, and (c) affects no one else, is a moral improvement. Prioritarianism satisfies the Pigou-Dalton axiom, while utilitarianism does not. Prioritarianism also satisfies the Pareto axioms and an axiom of Anonymity. The axiom cluster Pareto, Pigou-Dalton, and Anonymity can be defended with reference to individuals’ “claims across outcomes.” A claim is a tripartite relation between an individual and two outcomes, which is valenced in terms of her well-being. The moral ranking of two outcomes, in turn, depends upon the valence and strength of individuals’ claims between them. The claims-across-outcome framework helps make the case for prioritarianism as against utilitarianism and other outcome-ranking criteria that fail to satisfy the combination of Pareto, Pigou-Dalton, and Anonymity. Can the claims-across-outcomes framework be extended to the case of variable population, in which the individuals who exist in a given outcome x need not be identical to those who exist in another outcome y? This chapter argues that the framework can be thus extended and that it supports generalized versions of the Pareto, Pigou-Dalton and Anonymity axioms. These axioms, in turn, have implications for a range of topics in population ethics.