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cousin_it comments on Prisoner's Dilemma (with visible source code) Tournament - LessWrong
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I'm not sure your definition defines a unique "reasonable" subset of programs. There are many different cliques of mutually cooperating programs. For example, you could say the "reasonable" subset consists of one program that cooperates only with exact copies of itself, and that would be consistent with your definition, unless I'm missing something.
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 :-)