Utilitarianism is the most prominent social welfare function in economics. We present three new axiomatic characterizations of utilitarian (that is, additively-separable) social welfare functions in a setting where there is risk over both population size and individuals' welfares. We first show that, given uncontroversial basic axioms, Blackorby et al.'s (1998) Expected Critical-Level Generalized Utilitarianism is equivalent to a new axiom holding that it is better to allocate higher utility-conditional-on-existence to possible people who have a higher probability of existence. The other two characterizations extend and clarify classic axiomatizations of utilitarianism from settings with either social risk or variable-population, considered alone.
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