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dlthomas comments on Problematic Problems for TDT - Less Wrong
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I think we could generalise problem 2 to be problematic for any decision theory XDT:
There are 10 boxes, numbered 1 to 10. You may only take one. Omega has (several times) run a simulated XDT agent on this problem. It then put a prize in the box which it determined was least likely to be taken by such an agent - or, in the case of a tie, in the box with the lowest index.
If agent X follows XDT, it has at best a 10% chance of winning. Any sufficiently resourceful YDT agent, however, could run a simulated XDT agent themselves, and figure out what Omega's choice was without getting into an infinite loop.
Therefore, YDT performs better than XDT on this problem.
If I'm right, we may have shown the impossibility of a "best' decision theory, no matter how meta you get (in a close analogy to Godelian incompleteness). If I'm wrong, what have I missed?
I would say that any such problem doesn't show that there is no best decision theory, it shows that that class of problem cannot be used in the ranking.
Edited to add: Unless, perhaps, one can show that an instantiation of the problem with particular choice of (in this case decision theory, but whatever is varied) is particularly likely to be encountered.