But I don't have a general theory which replies "Yes" [to a counterfactual mugging].

You don't? I was sure you'd handled this case with Timeless Decision Theory.

I will try to write up a sketch of my idea, which involves using a Markov State Machine to represent world states that transition into one another. Then you distinguish evidence about the structure of the MSM, from evidence of your historical path through the MSM. And the best decision to make in a world state is defined as the decision which is part of a policy that maximizes expected utility for the whole MSM.

OK, I just tried for four hours but couldn't successfully describe a useful formalism that provides a good analysis of counterfactual mugging. Will keep trying later.