Many decision theory problems involve pre-commitment or deciding in advance how you are going to act. This is crucial for game-theory, where an agent that has credibly pre-committed can force other actors to act differently than they would other otherwise acted. It is also important for problems with predictors like Newcomb’s Problem where an agent which pre-commits one-boxing guarantees (or almost guarantees) themselves the million.

Predictors:

There has been significant disagreement about what pre-commitment means for decision theory problems where you are being predicted. In Newcomb’s Problem, two-boxers typically believe that while you could have obtained the million by pre-committing before Omega made their prediction, afterwards is too late. Even though two-boxing only gives you $1000, they claim that the million was never in the box so you never could have gained it. In contrast, one-boxers tend to believe that it is a mistake to think that the million isn’t accessible to you—see Eliezer arguing that you can just do it.