What if you have some uncertainty about which program our universe corresponds to? In that case, we have to specify preferences for the entire set of programs that our universe may correspond to. If your preferences for what happens in one such program is independent of what happens in another, then we can represent them by a probability distribution on the set of programs plus a utility function on the execution of each individual program. More generally, we can always represent your preferences as a utility function on vectors of the form where E1 is an execution history of P1, E2 is an execution history of P2, and so on.
In this case I’m assuming preferences for program executions that aren’t independent of each other, so it falls into the “more generally” category.
It’s from this paragraph of http://lesswrong.com/lw/15m/towards_a_new_decision_theory/ :
In this case I’m assuming preferences for program executions that aren’t independent of each other, so it falls into the “more generally” category.
Got an example?
You originally seemed to suggest that represented some set of preferences.
Now you seem to be saying that it is a bunch of vectors representing possible universes on which some unspecified utility function might operate.