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A Solution to the Predictor Paradox

Published online by Cambridge University Press:  01 June 1976

Michael F. Stack
Michael F. Stack*
Affiliation:
University of Manitoba
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Extract

William Newcomb and Robert Nozick have provided us with the following problem in rational decision-making. There are two boxes, A and B. A contains either a million dollars (M) or nothing (0). B contains a thousand dollars (T). I come into the room in which we have the boxes, closed. I must make one of two choices. Either I open A and take whatever money is present, M or O, or I open both and take whatever money is present, M + T or O + T. What is the rational choice for me to make?

Nothing unusual is meant by “rational” in this context. We assume that a person making the choice desires as much money as possible. We assume that he will take into account all relevant available information as to what decision will lead to more money. If he believes that doing X will, or is likely to, lead to more money than doing not-X, then he will do X.

In the above case, it would seem that the rational choice is both. T is there for the taking, whether or not I get M, and I might as well try for both.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 7 , Issue 1 , March 1977 , pp. 147 - 154
Copyright
Copyright © The Authors 1977

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References

1 This paper was first presented at the meetings of the Western Canadian Philosophical Association in Calgary in November, 1975. I am grateful to Leon Ellsworth, Ken Warmrod, and the editors of this journal for comments and suggestions.

2 Nozick, Robert “Newcomb's Problem and Two Principles of Choice', in Rescher, Nicholas et al. (eds.), Essays in Honor of Carl Hempel, G. Dordrecht, Reidel, 1969Google Scholar. See also “Mathematical Games” in Scientific American, March 1974. For different solutions, see Schlesinger, G. “The Unpredictability of Free Choices”, The British journal for the Philosophy of Science, 25,1974CrossRefGoogle Scholar, and Levi, Isaac “Newcomb's Many Problems”, Theory and Decision, 6, 1975.CrossRefGoogle Scholar

3 Such conditions should take care of Isaac Levi's point that merely a lot of successful prediction is not enough.

4 I owe this point to Vic Tennant, who has in general been very helpful in discussions of the problem, despite the fact that he is a firm one-box man.

5 The difficulty with this rational choice can be made starker. Suppose we leave the thousand dollars in B, but in A there either is or is not a certificate guaranteeing eternal happiness, the alternative being eternal damnation. I wonder if any of us, including me, would have the courage to be rational.