Senior Researcher / Lead, FutureLab on Game Theory and Networks of Interacting Agents @ Potsdam Institute for Climate Impact Research.
I’m a mathematician working on collective decision making, game theory, formal ethics, international coalition formation, and a lot of stuff related to climate change. Here’s my professional profile.
Take a possible world in which the predictor is perfect (meaning: they were able to make a prediction, and there was no possible extension of that world’s trajectory in which what I will actually do deviates from what they have predicted). In that world, by definition, I no longer have a choice. By definition I will do what the predictor has predicted. Whatever has caused what I will do lies in the past of the prediction, hence in the past of the current time point. There is no point in asking myself now what I should do as I have no longer causal influence on what I will do. I can simply relax and watch myself doing what I have been caused to do some time before. I can of course ask myself what might have caused my action and try to predict myself from that what I will do. If I come to believe that it was myself who decided at some earlier point in time what I will do, then I can ask myself what I should have decided at that earlier point in time. If I believe that at that earlier point in time I already knew that the predictor would act in the way it did, and if I believe that I have made the decision rationally, then I should conclude that I have decided to one-box.
The original version of Newcomb’s paradox in Nozick 1969 is not about a perfect predictor however. It begins with (1) “Suppose a being in whose power to predict your choices you have enormous confidence.… You know that this being has often correctly predicted your choices in the past (and has never, so far as you know, made an incorrect prediction about your choices), and furthermore you know that this being has often correctly predicted the choices of other people, many of whom are similar to you, in the particular situation to be described below”. So the information you are given is explicitly only about things from the past (how could it be otherwise). It goes on to say (2) “You have a choice between two actions”. Information (2) implies that what I will do has not been decided yet and I still have causal influence on what I will do. Hence the information what I will do cannot have been available to the predictor. This implies that the predictor cannot have made a perfect prediction about my behaviour. Indeed nothing in (1) implies that they have, the information given is not about my future action at all. After I will have made my decision, it might turn out, of course, that it happens to coincides with what the predictor has predicted. But that is irrelevant for my choice as it would only imply that the predictor will have been lucky this time. What should I make of information (1)? If I am confident that I still have a choice, that question is of no significance for the decision problem at hand and I should two-box. If I am confident that I don’t have a choice but have decided already, the reasoning of the previous paragraph applies and I should hope to observe that I will one-box.
What if I am unsure whether or not I still have a choice? I might have the impression that I can try to move my muscles this way or that way, without being perfectly confident that they will obey. What action should I then decide to try? I should decide to try two-boxing. Why? Because that decision is the dominant strategy: if it turns out that indeed I can decide my action now, then we’re in a world where the predictor was not perfect but merely lucky and in that world two-boxing is dominant; if it instead turns out that I was not able to override my earlier decision at this point, then we’re in a world where what I try now makes no difference. In either case, trying to two-box is undominated by any other strategy.