Choice'. 1 The problem involves a chooser and a predictor. The chooser is shown two boxes. One box is transparent and contains one thousand dollars. The other is opaque and contain:~ one million dollars just in case the predictor has long ago predicted that the chooser will take only the opaque box. However, the chooser also knows that the predictor is highly successful at predicting the chooser's decision. Maya Bar-Hillel and Avishai Margalit suggest that the chooser might know this from having played the same game with the predictor many times before for points instead of money. 2 Newcomb's problem is the problem of determining whether the rational chooser decides to take only the opaque box or decides to take both boxes.
Nozick points out that Newcomb's problem seems to show that two principles of choice can conflict. If the chooser follows the principle of maximizing expected utility, then he will take only the opaque box since its expected utility is nearly a million dollars whereas the expected utility of taking both boxes is not much more than one thousand dollars. If" the chooser follows the dominance principle, then he will take both boxes. If the million is in the opaque box, then the two-boxer has a million plus a thousand dollars while the one-boxer has only a million dollars. If the opaque box is empty, then the two-boxer has a thousand dollars while the one-boxer has nothing. In either case, the two boxer has more money.
Reservations have been expressed about the dominance argument since the dominance principle does not apply when the decision itself has a bearing on the probabilities of the alternative states. In 'The Unpredictability of Free Choices', George Schlesinger uses a different argument. 3 Suppose Smith is a perfect well-wisher of mine who always advises me to do what is in my own best interests. Smith can see whether there is any money in the ,opaque box. If he sees that there is a million dollars in the opaque box, then Smith surely Theory and Decision 15 (1983) 399-404.