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endoself comments on The Empty White Room: Surreal Utilities - Less Wrong
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What's wrong with the surreals? It's not like we have reason to keep our sets small here. The surreals are prettier, don't require an arbitrary nonconstructive ultrafilter, are more likely to fall out of an axiomatic approach, and can't accidently end up being too small (up to some quibbles about Grothendieck universes).
I agree with all of that, but I think we should work out what decision theory actually needs and then use that. Surreals will definitely work, but if hyperreals also worked then that would be a really interesting fact worth knowing, because the hyperreals are so much smaller. (Ditto for any totally ordered affine set).