My second observation is closely related to the first. It is true that the state of box 2 is not causally dependent upon my act, in Newcomb’s problem. But another kind of dependence relation obtains which is at least as important as causal independence and which seems to take clear precedence in the limit case. If I am completely certain that the being has predicted correctly, then the state of box 2 depends logically upon my current beliefs together with my act. That is, from the relevant propositions about the setup of the problem (including the proposition that the being has correctly predicted
my choice) together with the proposition that I choose both boxes, it follows that I get $1,000. And from those relevant propositions together with the proposition that I choose only box 2, it follows that I get $1 million. (This logical dependence, of course, is the reason why the two-box choice seems patently irrational in the limit case.)
ETA: I realised that this might require context (otherwise it looks a little like I’m just randomly presenting a quote which makes a point that the community has heard often before). I thought that the quote was interesting because it’s an example of philosophers who think that some concept of logical dependence should be more important than causal dependence in relation to rational choice. This view seems to be interestingly linked to the views of various people on LW.
A quote for those of you who are interested in decision theory, taken from Counterfactuals and Newcomb’s Problem (sorry, though: gated link):
ETA: I realised that this might require context (otherwise it looks a little like I’m just randomly presenting a quote which makes a point that the community has heard often before). I thought that the quote was interesting because it’s an example of philosophers who think that some concept of logical dependence should be more important than causal dependence in relation to rational choice. This view seems to be interestingly linked to the views of various people on LW.