Question: is there a proof that strategies that follow “always doing what you would have precommitted to doing” always dominate strategies that do not, in some sense? Or perhaps “adding a precommittment stage always improves utility”?
No—if the universe punishes you for behaving some way (e.g. adding a precomittment stage), then doing that is dominated. There are no dominant strategies against all possible states of the universe.
Fair enough, but perhaps there proofs that it dominates unless you are punished specifically for doing it?
How sure are people that “do what you would have precommitted to doing” is a good strategy? Wanting to build it into the decision theory seems to suggest very high certainty.
Well, it seems obvious that it’s true—but tricky to formalise. Subtle problems like agent simulates predictor (when you know more than Omega) and maybe some diagonal agents (who apply diagonal reasoning to you) seem to be relatively believable situations. It’s a bit like Godel’s theorem—initially, the only examples were weird and specifically constructed, but then people found more natural examples.
But “do what you would have precommitted to doing” seems to be much better than other strategies, even if it’s not provably ideal.
Question: is there a proof that strategies that follow “always doing what you would have precommitted to doing” always dominate strategies that do not, in some sense? Or perhaps “adding a precommittment stage always improves utility”?
No—if the universe punishes you for behaving some way (e.g. adding a precomittment stage), then doing that is dominated. There are no dominant strategies against all possible states of the universe.
Fair enough, but perhaps there proofs that it dominates unless you are punished specifically for doing it?
How sure are people that “do what you would have precommitted to doing” is a good strategy? Wanting to build it into the decision theory seems to suggest very high certainty.
Well, it seems obvious that it’s true—but tricky to formalise. Subtle problems like agent simulates predictor (when you know more than Omega) and maybe some diagonal agents (who apply diagonal reasoning to you) seem to be relatively believable situations. It’s a bit like Godel’s theorem—initially, the only examples were weird and specifically constructed, but then people found more natural examples.
But “do what you would have precommitted to doing” seems to be much better than other strategies, even if it’s not provably ideal.