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MrMind comments on Decision Theories: A Less Wrong Primer - Less Wrong
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See mine and orthonormal's comments on the PD on this post for my view of that.
The point I'm struggling to express is that I don't think we should worry about the thought experiment, because I have the feeling that Omega is somehow impossible. The suggestion is that Newcomb's problem makes a problem with CDT clearer. But I argue that Newcomb's problem makes the problem. The flaw is not with the decision theory, but with the concept of such a predictor. So you can't use CDT's "failure" in this circumstance as evidence that CDT is wrong.
Here's a related point: Omega will never put the money in the box. Smith act like a one-boxer. Omega predicts that Smith will one-box. So the million is put in the opaque box. Now Omega reasons as follows: "Wait though. Even if Smith is a one-boxer, now that I've fixed what will be in the boxes, Smith is better off two-boxing. Smith is smart enough to realise that two-boxing is dominant, once I can't causally affect the contents of the boxes." So Omega doesn't put the money in the box.
Would one-boxing ever be advantageous if Omega were reasoning like that? No. The point is Omega will always reason that two-boxing dominates once the contents are fixed. There seems to be something unstable about Omega's reasoning. I think this is related to why I feel Omega is impossible. (Though I'm not sure how the points interact exactly.)
That line of reasoning is though available to Smith as well, so he can choose to one-boxing because he knows that Omega is a perfect predictor. You're right to say that the interplay between Omega-prediction-of-Smith and Smith-prediction-of-Omega are in a meta-stable state, BUT: Smith has to decide, he is going to make a decision, and so whatever algorithm it implements, if it ever goes down this line of meta-stable reasoning, must have a way to get out and choose something, even if it's just bounded computational power (or the limit step of computation in Hamkins infinite Turing machine). But since Omega is a perfect predictor, it will know that and choose accordingly. I have the feeling that Omega existence is something like an axiom, you can refuse or accept it and both stances are coherent.