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ygert comments on Dark Arts of Rationality - LessWrong
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Agreed. But here is what I think Hofstadter was saying: The assumption that is used can be weaker than the assumption that the two players have an identical method. Rather, it just needs to be that they are both "smart". And this is almost as strong a result as the true zero knowledge scenario, because most agents will do their best to be smart.
Why is he saying that "smart" agents will cooperate? Because they know that the other agent is the same as them in that respect. (In being smart, and also in knowing what being smart means.)
Now, there are some obvious holes in this, but it does hold a certain grain of truth, and is a fairly powerful result in any case. (TDT is, in a sense, a generalization of exactly this idea.)
Have you seen this explored in mathematical language? Cause it's all so weird that there's no way I can agree with Hofstadter to that extent. As yet, I don't know really know what "smart" means.
Yeah, I agree, it is weird. And I think that Hofstadter is wrong: With such a vague definition of being "smart", his conjecture fails to hold. (This is what you were saying: It's rather vague and undefined.)
That said, TDT is an attempt to put a similar idea on firmer ground. In that sense, the TDT paper is the exploration in mathematical language of this idea that you are asking for. It isn't Hofstadterian superrationality, but it is inspired by it, and TDT puts these amorphous concepts that Hofstadter never bothered solidifying into a concrete form.