In the situation I presented, the decision theory had no effect on the utility other than through its effect on the choice. In that case, the expected utility of the decision theory and the expected utility of the choice reduce to the same thing, so your proposal doesn't seem to help. Do you agree with that, or am I misapplying the idea somehow?
I'm not sure that they reduce to the same thing. In e.g. Newcomb's problem, if you reduce your two options to "P(full box A) U(full Box A)" versus "P(full box A) U(full box A) + U(full box B)", where U(x) is the utility of x, then you end up two-boxing, that's causal decision theory.
It's only when you consider the utility of different decision theories, that you end up one boxing, because then you're effectively considering U(any decision theory in which I one-box) vs U(any decision theory in which I two-box) and you see that the exp...
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