Most discussion in population ethics has concentrated on how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as.” This field has been riddled with “paradoxes” and impossibility theorems which purport to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. It is natural to think that the axiological impossibility results directly translates into impossibility results for normative theories since this part of our morality—our theory of beneficence—is consequentialist in nature and thus must be based on an ordering of outcomes in regard to their “welfarist” goodness. However, it is all too hasty to conclude that the axiological impossibility results directly translate into normative ones for two reasons: one can reject the transitivity of “better than” and one can reject consequentialism. The latter idea is that we should turn to theories that take welfare into account in a nonconsequentialist manner, that is, theories that take welfare into account directly on the normative level instead of taking the route over an ordering of outcomes in regard to their goodness. Since transitivity of “better than” plays an important role in the axiological paradoxes, and since there is no convincing analog to transitivity on the normative level, the paradoxes will not reappear on the normative level, or so it is claimed. This chapter shows that this claim is unfortunately false. As a corollary, it shows how we can prove the axiological impossibility theorems without an appeal to the transitivity of “better than.”