Population axiology concerns how to rank populations by the relation “is socially preferred to”. So far, population ethicists have (with important exceptions) focused less on the question of how to rank population prospects, that is, alternatives that contain uncertainty as to which population they will bring about. Most public policy choices, however, are decisions under uncertainty, including policy choices that affect the size of a population (such as climate policy choices). Here, we shall address the question of how to rank population prospects by the relation “is socially preferred to”. We start by illustrating how well-known population axiologies can be extended to population prospect axiologies. And we show that new problems arise when extending population axiologies to prospects. In particular, traditional population axiologies lead to prospect-versions of the problems that they are praised for avoiding in the risk-free settings. Moreover, we show how the axiom of State-Wise Dominance allow us to extend any impossibility theorem in population axiology to impossibility theorems for non-trivial population prospects, that is, prospects that confer probabilities strictly between zero and one on different populations. Finally, we formulate impossibility results that only involve probabilistic axioms.