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twanvl comments on A model of UDT without proof limits - Less Wrong
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Another thing is that I don't think spurious proofs can have influence on the decision in any case.
Take the simpler algorithm B:
A spurious proof is one for b where B()≠b.
By definition, the result returned in step 2 will be B(). Therefore B() is the best b found in step 1. Since B()=b for the best b, this can not be from a spurious proof. If for any other b' there is a spurious proof, then the proved utilities must be worse, since otherwise B() would equal c. Therefore the existence of spurious proofs does not affect B at all.
It's sort of inspiring that you make all the expected mistakes someone would make when studying this problem for the first time, but you progress through them really fast. Maybe you'll soon get to the leading edge? That would be cool!
In this comment the mistake is thinking that "the best b found in step 1" is indeed the best b for the given problem. For example, in the problem given in the post, B could find a correct proof that B()=1 implies U()=5 and a spurious proof that B()=2 implies U()=0. Then B will go on to return 1, thus making the spurious proof also correct because its premise is false.
Ah, I think I get it. By returning 1, B makes B()=2 false, and therefore it can no longer proof anything about the cases where it would have returned 2. In essence, counter-factual reasoning becomes impossible.
However, these problems only happen if B does not find a proof of "B()=2 implies U()=10". If it does find such a proof then it would correctly return 2. This reminds me of bounded rationality. If B searches for all proofs up to some length L, then for large enough L it will also find the non-spurious ones.
Counter-factuals were my reason for writing U=U'(A). By allowing the argument to U' to be different from A you can examine counter-factual cases. But perhaps then you end up with just CDT.
Right, and the non-spurious proofs will "kill" the spurious ones. That was the idea in the reduction of "could" post, linked from the current one. Nice work! Please continue thinking, maybe you'll find something that we missed.