I disagree. I am not saying that Omega is a godlike intelligence that stands outside time and space. Omega just records the position and momentum of every atom in an initial state, feeds them into a computer, and computes a prediction for your decision.
When you say a Laplacian superintelligence, I presume I can turn to the words of Laplace:
An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
I'm not saying that Omega is outside of time and space- it still exists in space and acts at various times- but its omniscience is complete at all times.
I am quite sure that with the standard meaning of "cause", here the causal diagram
Think of causes this way: if we change X, what also changes? If the world were such that I two-boxed, Omega would not have filled the second box. We change the world such that I one-box. This change requires a physical difference in the world, and that difference propagates both backwards and forwards in time. Thus, the result of that change is that Omega would have filled the second box. Thus, my action causes Omega's action, because Omega's action is dependent on its prediction, and its prediction is dependent on my action.
Do not import the assumption that causality cannot flow backwards in time. In the presence of Omega, that assumption is wrong, and "two-boxing" is the result of that defective assumption, not any trouble with CDT.
and no causal arrow goes from your decision to the prediction.
In your model, the only way to alter my decision, which is deterministically determined by the "initial state of atoms", is to alter the initial state of atoms. That's the node you should focus on, and it clearly causes both my decision and Omega's prediction, and so if I can alter the state of the universe such that I will be a one-boxer, I should. If I don't have that power, there's no decision problem.
Well, I think this is becoming a dispute over the definition of "cause", which is not a worthwhile topic. I agree with the substance of what you say. In my terminology, if an event X is entangled deterministically with events before it and events after it, it causes the events after it, is caused by the events before it, and (in conjunction with the laws of nature) logically implies both the events before and after it. You prefer to say that it causes all those events, prior or future, that we must change if we assume a change in X. Fine, then CD...
I stumbled upon this paper by Andy Egan and thought that its main result should be shared. We have the Newcomb problem as counterexample to CDT, but that can be dismissed as being speculative or science-fictiony. In this paper, Andy Egan constructs a smoking lesion counterexample to CDT, and makes the fascinating claim that one can construct counterexamples to CDT by starting from any counterexample to EDT and modifying it systematically.
The "smoking lesion" counterexample to EDT goes like this:
EDT implies that she should not smoke (since the likely outcome in a world where she doesn't smoke is better than the likely outcome in a world where she does). CDT correctly allows her to smoke: she shouldn't care about the information revealed by her preferences.
But we can modify this problem to become a counterexample to CDT, as follows:
Here EDT correctly tells her not to smoke. CDT refuses to use her possible decision as evidence that she has the gene and tells her to smoke. But this makes her very likely to get cancer, as she is very likely to have the gene given that she smokes.
The idea behind this new example is that EDT runs into paradoxes whenever there is a common cause (G) of both some action (S) and some undesirable consequence (C). We then take that problem and modify it so that there is a common cause G of both some action (S) and of a causal relationship between that action and the undesirable consequence (S→C). This is then often a paradox of CDT.
It isn't perfect match - for instance if the gene G were common, then CDT would say not to smoke in the modified smoker's lesion. But it still seems that most EDT paradoxes can be adapted to become paradoxes of CDT.