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. Lastly, it can be important for agents who are aware that they are likely to make a bad decision in the moment.
There has been significant disagreement about what pre-commitment means for decision theory problems where you are being predicted by a sufficiently high quality predictor. 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 - in other words that if you one-box you will always find that the million always was accessible to you.
If you have to pre-commit in advance the question naturally arises - what counts as pre-commitment? Is it sufficient to just decide in advance what you are going to do as long as you are committed to following through or do you have to commit more substantially by setting up a penalty sufficient to dissuade yourself from changing your mind? Having raised this question, the answer seems clear - a pre-commitment is valid in terms of obtaining you the million so long as it is legible to Omega and it is valid in terms of binding you to the action so long as you actually follow through.
One distinction that it might be useful to make is between formal and effective pre-commitment. Formal pre-commitment is when you take specific legible actions to commit yourself like talking about it in public, handing over money as a deposit or rewriting your source-code. On the other hand, effective pre-commitment is the notion that in a deterministic universe whatever action you take you are pre-committed to and that an agent that knew the environment and your state in sufficient detail would be able to predict what action you would take. In this view, the only difference is that formal pre-commitment is easier to predict.
One issue that arises with predictors is that some scenarios may be conditionally inconsistent (or just plain inconsistent when we're dealing with logical uncertainty and oracles). Oddly enough, it seems as though it might make sense to allow pre-commitments in relation to these scenarios, although this involves pre-committing to taking an action when receiving input representing such a potentially inconsistent scenario rather than pre-committing to take an action in a particular scenario itself.
In game theory, commitment is often considered purely from the perspective of incentives. From this view, you are considered to have pre-committed youself to an action if any benefit you would gain from it is outweighed by the penalty you would pay.
Pre-commitment can also be important from a psychological perspective. Suppose you have an assignment to work on. You know that you need to work on it tomorrow, but you also know that you won't feel like it on the day. By deciding in advance to work on the assignment tomorrow you are providing yourself an additional reason (keeping your commitments to yourself) to work on it.
Related Pages: Commitment Mechanisms, Assurance contracts