Having thought about it a little more, I think I have pinpointed my problem with building a decision theory in which real outcomes are allowed to depend on the outcomes of counterfactuals:
The output of your algorithm in a given situation will need to depend on your prior distribution and not just on your posterior distribution.
In CDT, your choice of actions depends only on the present state of the universe. Hence you can make your decision based solely on your posterior distribution on the present state of the universe.
If you need to deal with counterfactuals though, the output of your algorithm in a given situation should depend not only on the state of the universe in that situation, but on the probability that this situation appears in a relevant counterfactual and upon the results thereof. I cannot just consult my posterior and ask about the expected results of my actions. I also need to consult my prior and compute the probability that my payouts will depend on a counterfactual version of this situation.
Having thought about it a little more, I think I have pinpointed my problem with building a decision theory in which real outcomes are allowed to depend on the outcomes of counterfactuals:
The output of your algorithm in a given situation will need to depend on your prior distribution and not just on your posterior distribution.
In CDT, your choice of actions depends only on the present state of the universe. Hence you can make your decision based solely on your posterior distribution on the present state of the universe.
If you need to deal with counterfactuals though, the output of your algorithm in a given situation should depend not only on the state of the universe in that situation, but on the probability that this situation appears in a relevant counterfactual and upon the results thereof. I cannot just consult my posterior and ask about the expected results of my actions. I also need to consult my prior and compute the probability that my payouts will depend on a counterfactual version of this situation.