The Interpersonal Addition Theorem, due to John Broome, states that, given certain seemingly innocuous assumptions, the overall utility of an uncertain prospect can be represented as the sum of its individual utilities. Given ‘Bernoulli's hypothesis’ according to which individual utility coincides with individual welfare, this result appears to be incompatible with the Priority View. On that view, due to Derek Parfit, the benefits to the worse off should count for more, in the overall evaluation, than the comparable benefits to the (...) better off. Pace Broome, the paper argues that prioritarians should meet this challenge not by denying Bernoulli's hypothesis, but by rejecting one of the basic assumptions behind the addition theorem: that a prospect is better overall if it is better for everyone. This conclusion follows if one interprets the priority weights that are imposed by prioritarians as relevant only to moral, but not to prudential, evaluations of prospects. (shrink)