Utilitarianism is the most prominent family of social welfare functions. 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 the welfares of individuals. First, we show that, given uncontroversial basic axioms, Blackorby et al.'s (1998) Expected Critical-Level Generalized Utilitarianism (ECLGU) 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 novel characterizations extend classic axiomatizations of utilitarianism from settings with either social risk or variable-population, considered alone. By considering both social risk and variable population together, we clarify the fundamental normative considerations underlying utilitarian policy evaluation.