This has helped me understand much better what you were coming at in the other subthread. I disagree that CDT ought to one-box in Newcomb, at least in the "Least Convenient World" version of Newcomb that I will describe now (which I think captures the most essential features of the problem).
In this LCW version of Newcomb, quantum mechanics is false, the universe consists in atoms moving in perfectly deterministic ways, and Omega is a Laplacian superintelligence who has registered the state of each atom a million years ago and ran forward a simulation leading to a prediction on your decision. In this case none of your diagrams seem like a good causal formalization: not only does Omega not see the future magically (so your first two don't work), in addition the causal antecedent to his prediction is not your decision algorithm per se; it is a bunch of atoms a million years ago, which leads separately to his prediction on one side, and to your decision algorithm and your decision on the other side. The conflation you make in your last two diagrams between these three things, ("your decision", "your decision algorithm" and "what causally influences Omega's prediction") does not work in this case (unless you stretch your definition of "yourself" backwards to identify yourself, i.e. your decision algorithm, with some features of the distribution of atoms a million years ago!). I don't think CDT can endorse one-boxing in this case.
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 ju...
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.