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cousin_it comments on What a reduction of "could" could look like - Less Wrong
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Um, the obvious generalization to many strategies must "privilege" one of the strategies apriori, the same way as your algorithm "privileges" cooperation. Otherwise, what single statement would the proof checker be trying to prove? I don't see a way around that.
Ah, sorry, now I understand what's going on. You are saying "there's an obvious generalization, but then you'd have to pick a 'fair' strategy profile that it would privilege." I'm saying "there's no obvious generalization which preserves what's interesting about the two-strategy case." So we're in agreement already.
(I'm not entirely without hope; I have a vague idea that we could order the possible somehow, and if we can prove a higher utility for strategy X than for any strategy that is below X in the ordering, then the agent can prove it will definitely choose X or a strategy that is above it in the ordering. Or something like that. But need to look at the details much more closely.)