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AndyCossyleon comments on Problematic Problems for TDT - Less Wrong
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Someone may already have mentioned this, but doesn't the fact that these scenarios include self-referencing components bring Goedel's Incompleteness Theorem into play somehow? I.e. As soon as we let decision theories become self-referencing, it is impossible for a "best" decision theory to exist at all.
There was some discussion of much the same point in this comment thread
One important thing to consider is that there may be a sensible way to define "best" that is not susceptible to this type of problem. Most notably, there may be a suitable, solvable, and realistic subclass of problems over which to evaluate performance. Also, even if there is no "best", there can still be better and worse.
Self-reference and the like is necessary for Goedel sentences but not sufficient. It's certainly plausible that this scenario could have a Goedel sentence, but whether the current problem is isomorphic to a Goedel sentence is not obvious, and seems unlikely.
Perhaps referring directly to Goedel was not apt. What Goedel showed was that Hilbert/Russell's efforts were futile. And what Hilbert and Russell were trying to do was create a formal system where actual self-reference was impossible. And the reason he was trying to do that, finally, was that self-reference creates paradoxes which reduce to either incompleteness or inconsistency. And the same is true of these more advanced decision theories. Because they are self-referencing, they create an infinite regress that precludes the existence of a "best" decision theory at all.
So, finding a best decision theory is impossible once self-reference is allowed, because of the nature of self-reference, but not quite because of Goedel's theorems, which are the stronger declaration that any formal system by necessity contains self-referential aspects that make it incomplete or inconsistent.