Small nitpick: If you’ve really pre-committed to one-boxing, there is no decision to be made once Omega has set up the boxes. In fact, the thought of making a decision won’t even cross your mind. If it does cross your mind, you should two-box. But if you two-box, you now know that you haven’t really pre-committed to one-boxing. Actually, even if you decide to (mistakenly) one-box, you’ll still know you haven’t really pre-committed, or you wouldn’t have had to decide anything on the spot.
In other words, Newcomb’s problem can only ever involve a single true decision. If you’re capable of pre-commitment (that is, if you know about Newcomb-like problems in advance and if you have the means to really pre-commit), it’s the decision to pre-commit, which precludes any ulterior decision. If you aren’t capable of pre-commitment (that is, if at least one of the above conditions is false), it’s the on-the-spot decision.
Small nitpick: If you’ve really pre-committed to one-boxing, there is no decision to be made once Omega has set up the boxes. In fact, the thought of making a decision won’t even cross your mind. If it does cross your mind, you should two-box. But if you two-box, you now know that you haven’t really pre-committed to one-boxing. Actually, even if you decide to (mistakenly) one-box, you’ll still know you haven’t really pre-committed, or you wouldn’t have had to decide anything on the spot.
In other words, Newcomb’s problem can only ever involve a single true decision. If you’re capable of pre-commitment (that is, if you know about Newcomb-like problems in advance and if you have the means to really pre-commit), it’s the decision to pre-commit, which precludes any ulterior decision. If you aren’t capable of pre-commitment (that is, if at least one of the above conditions is false), it’s the on-the-spot decision.