An instability in Newcomb one-boxing

Consider Newcomb’s Paradox, and assume the predictor has a high accuracy but is nonetheless fallible. Suppose you have the character of a one-boxer and you know it. Then you also know that the predictor has predicted your choosing one box and hence you know that there is money in both boxes. It is now quite obvious that you should go for two boxes! Of course, like the predictor, you predict that you won’t do it. But there is nothing unusual about a situation where you predict you won’t do the rational thing: weakness of the will is a sadly common phenomenon. Similarly, if you have the character of a two-boxer and you know it, the rational thing to do is to go for two boxes. For in this case you know the predictor put money only in the clear box, and it would be stupid to just go for the opaque box and get nothing.

None of what I said above should be controversial. If you know what the predictor did, you should take both boxes. It’s like Drescher’s Transparent Newcomb Problem where the boxes are clear and it seems obvious you should take both. (That said, some do endorse one-boxing in Transparent Newcomb!) Though you should be sad that you are the sort of person who takes both.

This means that principles that lead to one-boxing suffer from an interesting instability: if you find out you are firmly committed to acting in accordance with these principles, it is irrational for you to act in accordance with them. Not so for the principles that lead to two-boxing. Even when you find out you are firmly committed to them, it’s rational to act in accordance with them.

This instability is a kind of flip of the usual observation that if one expects to be faced with Newcomb situations, and one has two-boxing principles, then it becomes rational to regret having one-boxing principles. That, too, is an odd kind of inconsistency. But this inconsistency does not seem particularly telling. Take any correct rational principle R. There are situations where it becomes rational to regret having R, e.g., if a madman is going around torturing all the people who have R. (This is similar to the example that Xenophon attributes to Socrates that being wise can harm you because it can lead to your being kidnapped by a tyrant to serve as his advisor.)