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Bakkot comments on Prisoner's Dilemma (with visible source code) Tournament - LessWrong
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Point. Not sure how to fix that.
Maybe defined the Reasonable' set of programs to be the maximal Reasonable set? That is, a set is Reasonable if it has the property as described, then take the maximal such set to be the Reasonable' set (I'm pretty sure this is guaranteed to exist by Zorn's Lemma, but it's been a while...)
Zorn's lemma doesn't give you uniqueness either. Also, maximal under which partial order? If you mean maximal under inclusion, then my one-element set seems to be already maximal :-)