First, Mahtani argues that both in the game The Mug and in the Sleeping Beauty we should not defer to a trusted person under a particular designation if they do not self-identify under this designation. This invites a more complex Reflection Principle. I respond that there are more parsimonious ways to avoid the challenges posed to the Reflection Principle. Second, Mahtani argues that preferences create a hyperintensional context, which poses a challenge to the Ex-Ante Pareto Principle that can be averted by supervaluation. I respond that such an appeal to supervaluation would block randomization as a fair allocation device.

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.