Must Prioritarians be Antiegalitarian?

Abstract It has been argued that Prioritarianism violates Risky Non-Antiegalitarianism , a condition stating roughly that an alternative is socially better than another if it both makes everyone better off in expectation and leads to more equality. I show that Risky Non-Antiegalitarianism is in fact compatible with Prioritarianism as ordinarily defined, but that it violates some other conditions that may be attractive to prioritarians. While I argue that the latter conditions are not core principles of Prioritarianism, the choice between these conditions and Risky Non-Antiegalitarianism nonetheless constitutes an important intramural debate for prioritarians.