Question

A. Draw the causal network for Newcomb’s Problem with perfect detection and use it to explain why the following argument is valid or not; where the guaranteed money in the clear box is denoted by L and the larger amount of money that might be in the black box is denoted M.

“Once a given amount of money is put into the black box, it is irreversibly fixed no matter how many boxes Adam might open in the future. “So if Eve had put nothing in the black box, and if Adam later opens both boxes, then he will obtain $L compared to $0 if he instead opens only the black box. Likewise, if Eve had already put $M in the black box, and if Adam later opens both boxes, then he will obtain $M + $L compared to obtaining $M if he instead opens only the black box.” “Thus, regardless of what Eve has already done, Adam will obtain an additional $L if he opens both boxes instead of opening only the black box. So Adam is guaranteed to obtain more money by opening both boxes, which therefore must be his rational decision.”

Answer 1

One argument goes as follows: By the time you are asked to choose what to do, the money is already in the boxes. Whatever decision you make, it won’t change what’s in the boxes. So the boxes can be in one of two states:

1. Left box, $0. Right box, $1000.
2. Left box, $1 000 000. Right box, $1000.

Whichever state the boxes are in, you get more money if you take both boxes than if you take one. In game theoretic terms, the strategy of taking both boxes strictly dominates the strategy of taking only one box. You can never lose by choosing both boxes.

The only problem is, you do lose. If you take two boxes then they are in state 1 and you only get $1000. If you only took the left box you would get $1 000 000.

To many people, this may be enough to make it obvious that the rational decision is to take only the left box. If so, you might want to skip the next paragraph.

Taking only the left box didn’t seem rational to me for a long time. It seemed that the reasoning described above to justify taking both boxes was so powerful that the only rational decision was to take both boxes. I therefore saw Newcomb’s Problem as proof that it was sometimes beneficial to be irrational. I changed my mind when I realized that I’d been asking the wrong question. I had been asking which decision would give the best payoff at the time and saying it was rational to make that decision. Instead, I should have been asking which decision theory would lead to the greatest payoff. From that perspective, it is rational to use a decision theory that suggests you only take the left box because that is the decision theory that leads to the highest payoff. Taking only the left box lead to a higher payoff and it’s also a rational decision if you ask, “What decision theory is it rational for me to use?” and then make your decision according to the theory that you have concluded it is rational to follow.