not only does Omega not see the future magically
In the case where the universe is deterministic and Omega is a Laplacian superintelligence, it sees the world as a four-dimensional space and has access to all of it simultaneously. It doesn't take magic- it takes the process you've explicitly given Omega!
To Omega, time is just another direction, as reversible as the others thanks to its omniscience. Saying that there could not be a causal arrow from events that occur at later times to events that occur at earlier times in the presence of Omega would be just as silly as saying that there cannot be causal arrows from events that are further to the East to events that are further to the West.
So in the LCW version of Newcomb, the first diagram perfectly describes the situation, and reduces to the second diagram. If I choose to one-box when at the button, Omega could learn that at any time it pleases by looking at the time-cube of reality. Thus, I should choose to one-box.
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. I am quite sure that with the standard meaning of "cause", here the causal diagram is:
[Initial state of atoms] ==> [Omega's computer] ==> [Prediction] ==> Money
while at the same time there is parallel chain of causation:
[Initial state of atoms] ==> [Your mental processes] ==> [Your ...
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.