Right, but then, are all other variables unchanged? Or are they influenced somehow? The obvious proposal is EDT—assume influence goes with correlation.
I’m not sure why you think there would be a decision theory in that as well. Obviously when BDT decides its output, it will have some theory about how its output nodes propagate. But the hypothesis as a whole doesn’t think about influence. Its just a total probability distribution, and it includes that some things inside it are distributed according to BDT. It doesn’t have beliefs about “if the output of BDT were different”. If BDT implements a mixed strategy, it will have beliefs about what each option being enacted correlates with, but I don’t see a problem if this doesn’t track “real influence” (indeed, in the situations where this stuff is relevant it almost certainly won’t) - its not used in this role.
I’m not sure why you think there would be a decision theory in that as well. Obviously when BDT decides its output, it will have some theory about how its output nodes propagate. But the hypothesis as a whole doesn’t think about influence. Its just a total probability distribution, and it includes that some things inside it are distributed according to BDT. It doesn’t have beliefs about “if the output of BDT were different”. If BDT implements a mixed strategy, it will have beliefs about what each option being enacted correlates with, but I don’t see a problem if this doesn’t track “real influence” (indeed, in the situations where this stuff is relevant it almost certainly won’t) - its not used in this role.