An Introduction to Decision Theory

The focus of this chapter is on the role of causal processes in decision making. In some decision problems, beliefs about causal processes play a significant role in determining what we intuitively think it is rational to do. However, it has turned out to be very difficult to give a convincing account of what role beliefs about causal process should be allowed to play. Much of the discussion has focused on a famous example known as Newcomb's problem. We shall begin by taking a look at this surprisingly deep problem.

Newcomb's Problem

Imagine a being who is very good at predicting other people's choices. Ninety-nine percent of all predictions made by the being so far have been correct. You are offered a choice between two boxes, B1 and B2. Box B1 contains $1,000 and you know this, because it is transparent and you can actually see the money inside. Box B2 contains either a million dollars or nothing. This box is not transparent, so you cannot see its content. You are now invited to make a choice between the following pair of alternatives: You either take what is in both boxes, or take only what is in the second box. You are told that the predictor will put $1 million in box B2if and only if she predicts that you will take just box B2, and nothing in it otherwise. The predictor knows that you know this. Thus, in summary, the situation is as follows. First the being makes her prediction, then she puts either $1 million or nothing in the second box, according to her prediction, and then you make your choice. What should you do?

Alternative 1 Take box B1 ($1,000) and box B2 (either $0 or $1 m).

Alternative 2 Take only box B2 (either $0 or $1 m).

This decision problem was first proposed by the physicist William Newcomb in the 1960s. It has become known as Newcomb's problem, or the predictor's paradox. Philosopher Robert Nozick was the first author to discuss it in print. (According to legend, he learned about the problem from a mutual friend of his and Newcomb's at a dinner party.) Nozick identified two different, but contradictory, ways of reasoning about the problem.