Climate policies have stochastic consequences that involve a great number of generations. This calls for evaluating social risk (what kind of societies will future people be born into) rather than individual risk (what will happen to people during their own lifetimes). We respond to this call by proposing and axiomatizing probability adjusted rank-discounted critical-level generalized utilitarianism (PARDCLU) through a key axiom ensuring that the social welfare order both is ethical and satisfies first-order stochastic dominance. PARDCLU yields a new useful perspective on intergenerational risks, is ethical in contrast to discounted utilitarianism, and avoids objections that have been raised against other ethical criteria. We show that PARDCLU handles situations with positive probability of human extinction and is linked to decision theory by yielding rank-dependent expected utilitarianism—but with additional structure—in a special case.