Anonymity and Non-Identity Cases

I argue for the principle of Anonymity, according to which two populations are equally good whenever they have the same anonymous distribution of wellbeing. I first show that, given transitivity of the at-least-as-good-as relation, Anonymity is entailed by the ``Non-Identity Principle'', according to which the consequence of bringing better rather than worse lives into existence is, all else equal, better. I then argue for the Non-Identity Principle on the basis that if it were false, it would follow that we fail to improve the world when we make existing people better off, while at the same time replacing worse-off future people with different better-off future people. Since this is implausible, we should accept the Non-Identity Principle, and therefore Anonymity as well.