This will be my last comment on this thread. I've read Nozick. I've also read much of the current literature on Newcomb's problem. While Omega is sometimes described as a perfect predictor, assuming that Omega is a perfect predictor is not required in order to get an apparently paradoxical result. The reason is that given no backwards causation (more on that below) and as long as Omega is good enough at predicting, CDT and EDT will recommend different decisions. But both approaches are derived from seemingly innocuous assumptions using good reasoning. And that feature -- deriving a contradiction from apparently safe premisses through apparently safe reasoning -- is what makes something a paradox.

Partisans will argue for the correctness or incorrectness of one or the other of the two possible decisions in Newcomb's problem. I have not given any argument. And I'm not going to give one here. For present purposes, I don't care whether one-boxing or two-boxing is the correct decision. All I'm saying is what everyone who works on the problem agrees about. In Newcomb problems, CDT chooses two boxes and that choice has a lower expected value than taking one box. EDT chooses one box, which is strange on its face, since the decision now is presumed to have no causal relevance to the prediction. Yet, EDT recommends the choice with the greater expected value.

The usual story assumes that there is no backwards causation. That is why Nozick asks the reader (in the very passage you quoted, which you really should read more carefully) to: "Suppose we establish or take as given that there is no backwards causality, that what you actually decide to do does not affect what [the predictor] did in the past, that what you actually decide to do is not part of the explanation of why he made the prediction he made." If we don't follow Nozick in making this assumption -- if we assume that there is backwards causation -- CDT does not "reject the case" at all. If there is backwards causation and CDT has that as an input, then CDT will agree with EDT and recommend taking one box. The reason is that in the case of backwards causation, the decision now is causally relevant to the prediction in the past. That is precisely why Nozick ignores backwards causation, and he is utterly explicit about it in the first three sentences of the passage you quoted. So, there is good reason to consider only the case where you know (or believe) that there is no backwards causation because in that case, CDT and EDT paradoxically come apart.

But neither CDT nor EDT excludes any causal structure. CDT and EDT are possible decision theories in worlds with closed time-like curves. They're possible decision theories in worlds that have physical laws that look nothing like our own physical laws. CDT and EDT are theories of decision, not theories of physics or metaphysics.