In the least convenient possible world, the TDT agent doesn't care intrinsically about any counterfactual process, only about the result on the real world.
Saying you can get an agent with one DT to follow the output of another DT by changing its utility function is not interesting.
Saying you can get an agent with one DT to follow the output of another DT by changing its utility function is not interesting.
If the mapping is natural enough, it establishes relative expressive power of the decision theories, perhaps even allowing to get the same not-a-priori-obvious conclusions from studying one theory as the other. But granted, as I described in this post, the step forward made in UDT/ADT, as compared to TDT, is that causal graph doesn't need to be given as part of problem statement, dependencies get inferred from utility/action definition.
Omega kidnapps you and an alien from FarFarAway Prime, and gives you the choice: either the alien dies and you go home with your memory wiped, or you lose an arm, and you both go home with your memories wiped. Nobody gets to remember this. Oh and Omega flipped a coin to see who got to choose. What is your choice?
As usual, Omega is perfectly reliable, isn't hiding anything, and goes away afterwards. You also have no idea what the alien's values are, where it lives, what it would choose, nor what is the purpose of that organ that pulsates green light.
(This is my (incorrect) interpretation of counterfactual mugging, which we were discussing on the #lesswrong channel; Boxo pointed out that it's Prisonner's Dilemma where a random player is forced to cooperate, and isn't that similar to counterfactual mugging.)