  Is the overall value of a world just the sum of values contributed by each
value-bearing entity in that world? Additively separable axiologies (like total
utilitarianism, prioritarianism, and critical level views) say 'yes', but
non-additive axiologies (like average utilitarianism, rank-discounted
utilitarianism, and variable value views) say 'no'. This distinction is
practically important: additive axiologies support 'arguments from astronomical
scale' which suggest (among other things) that it is overwhelmingly important
for humanity to avoid premature extinction and ensure the existence of a large
future population, while non-additive axiologies need not. We show, however,
that when there is a large enough 'background population' unaffected by our
choices, a wide range of non-additive axiologies converge in their implications
with some additive axiology -- for instance, average utilitarianism converges
to critical-level utilitarianism and various egalitarian theories converge to
prioritiarianism. We further argue that real-world background populations may
be large enough to make these limit results practically significant. This means
that arguments from astronomical scale, and other arguments in practical ethics
that seem to presuppose additive separability, may be truth-preserving in
practice whether or not we accept additive separability as a basic axiological
principle.
