Even if you don’t believe such a situation can exist, you can make inferences for how you should act in such a case, base on how you should act in realistic cases.
Like AdamBell said, you can consider a more realistic scenario where someone simply has a good chance of guessing what you do.
Then take it a step further: write your decision theory as a function of how accurate the guesser is. Presumably, for the “high but not 100%” accuracy cases, you’ll want to one-box. So, in order to have a decision theory that doesn’t have some sort of discontinuity, you will have to set it so that it would imply that on a 100% guesser-accuracy case, you should one-box as well.
In short, it’s another case of Belief in the Implied Invisible, or implied optimal, as is the case here. While you may not be in a position to test claim X directly, it falls out as an implication of the best theories, which are directly testable.
(I should probably write an article justifying the importance of Newcomb’s problem and why it has real implications for our lives—there are many other ways it’s important, such as in predicting the output of a process.)
Even if you don’t believe such a situation can exist, you can make inferences for how you should act in such a case, base on how you should act in realistic cases.
Like AdamBell said, you can consider a more realistic scenario where someone simply has a good chance of guessing what you do.
Then take it a step further: write your decision theory as a function of how accurate the guesser is. Presumably, for the “high but not 100%” accuracy cases, you’ll want to one-box. So, in order to have a decision theory that doesn’t have some sort of discontinuity, you will have to set it so that it would imply that on a 100% guesser-accuracy case, you should one-box as well.
In short, it’s another case of Belief in the Implied Invisible, or implied optimal, as is the case here. While you may not be in a position to test claim X directly, it falls out as an implication of the best theories, which are directly testable.
(I should probably write an article justifying the importance of Newcomb’s problem and why it has real implications for our lives—there are many other ways it’s important, such as in predicting the output of a process.)