If we think
1. it's always better to improve the welfare of an existing person (or someone who would exist anyway) than to bring others into existence, all else equal, and
2. two outcomes are (comparable and) equivalent if they have the same distribution of welfare levels (but possibly different identities) (this is often called Anonymity),
then not only would we reject Mere Addition (the claim that adding good lives, even those which are barely worth living but still worth living, is never bad), but the following would be true:
Given any two nonempty ... (read more)
If welfare is real-valued (specifically from an interval I⊆R), then Maximin (maximize the welfare of the worst off individual) and theories which assign negative value to the addition of individuals with non-maximal welfare satisfy the properties above.
Furthermore, if along with welfare from a real interval and property 1 in the previous comment (2. Anonymity is not necessary), the following two properties also hold:
3. Extended Continuity, a modest definition of continuity for a theory comparing populations with real-valued welfares which must be sa... (read more)