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 decision] ==> {Money]
and no causal arrow goes from your decision to the prediction.
So I find it a weird use of language to say your decision is causally influencing Omega, just because Omega can infer (not see) what your decision will be. Unless you mean by "your decision" not the token, concrete mental process in your head, but the abstract Platonic algorithm that you use, which is duplicated inside Omega's simulation. But this kind of thinking seems alien to the spirit of CDT.
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 ana
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.