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Abstract The class of rank-additive social welfare orders (RA SWOs) includes rank-weighted utilitarian, generalized utilitarian, and rank-discounted generalized utilitarian rules; it is a flexible framework for population ethics. This paper axiomatically characterizes RA SWOs and studies their properties in two frameworks: the actualist framework (which only tracks the utilities of people who actually exist) and the possibilist framework (which also assigns zero utilities to people who don’t exist). The axiomatizations and properties are quite different in the two frameworks. For example, actualist RA SWOs can simultaneously evade the Repugnant Conclusion and promote equality, whereas in the possibilist framework, there is a trade-off between these two desiderata. On the other hand, possibilist RA SWOs satisfy the Positive expansion and Negative expansion axioms, whereas the actualist ones don’t.