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IlyaShpitser comments on Causal decision theory is unsatisfactory - LessWrong
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My understanding of the statement of Newcomb is that Omega puts things on boxes only based on what your source code says you will do when faced with input that looks like the Newcomb's problem. Since the agent already preprocessed the source code (possibly using other complicated bits of its own source code) to one box on Newcomb, Omega will populate boxes based on that. Omega does not need to deal with any other part of the agent's source code, including some unspecified complicated part that dealt with preprocessing and rewriting, except to prove to itself that one boxing will happen.
All that matters is that the code currently has the property that IF it sees the Newcomb input, THEN it will one box.
Omega that examines the agent's code before the agent preprocessed will also put a million dollars in, if it can prove the agent will self-modify to one-box before choosing the box.
Phrasing it in terms of source code makes it more obvious that this is equivalent to expecting Omega to be able to solve the halting problem.
This is fighting the hypothetical, Omega can say it will only put a million in if it can find a proof of you one boxing quickly enough.
If Omega only puts the million in if it finds a proof fast enough, it is then possible that you will one-box and not get the million.
(And saying "there isn't any such Omega" may be fighting the hypothetical. Saying there can't in principle be such an Omega is not.)
Yes, it's possible, and serves you right for trying to be clever. Solving the halting problem isn't actually hard for a large class of programs, including the usual case for an agent in a typical decision problem (ie. those that in fact do halt quickly enough to make an actual decision about the boxes in less than a day). If you try to deliberately write a very hard to predict program, then of course omega takes away the money in retaliation, just like the other attempts to "trick" omega by acting randomly or looking inside the boxes with xrays.
The problem requires that Omega be always able to figure out what you do. If Omega can only figure out what you can do under a limited set of circumstances, you've changed one of the fundamental constraints of the problem.
You seem to be thinking of this as "the only time someone won't come to a decision fast enough is if they deliberately stall", which is sort of the reverse of fighting the hypothetical--you're deciding that an objection can't apply because the objection applies to an unlikely situation.
Suppose that in order to decide what to do, I simulate Omega in my head as one of the steps of the process? That is not intentionally delaying, but it still could result in halting problem considerations. Or do you just say that Omega doesn't give me the money if I try to simulate him?