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For a prioritarian by contrast to a utilitarian, whether a certain quantity of utility falls within the boundary of one person's life or another's makes the following moral difference: the worse the life of a person who could receive a given benefit, the stronger moral reason we have to confer this benefit on this person. It would seem, therefore, that prioritarianism succeeds, where utilitarianism fails, to ‘take seriously the distinction between persons’. Yet I show that, contrary to these appearances, prioritarianism fails, in ways strikingly parallel to those in which utilitarianism fails, to take this distinction seriously. In so doing, I draw on and develop an earlier critique of prioritarianism by disentangling and pressing two distinct separateness-of-persons objections offered there. One objection is that prioritarianism is insensitive to ‘prudential justifications’. The other is that it is insensitive to the competing claims of different individuals.