Suppose I'm a one-boxer, Omega looks at me, and is sure that I'm a one-boxer. But then, after Omega fills the boxes, Mentok comes by, takes control of me, and forces me to two-box. Is there a million dollars in the second box?
Er… yes? Assuming Omega could not foresee Mentok coming in and changing the situation? No, if he could foresee this, but then the relevant original state includes both me and Mentok. I'm not sure I see the point.
Let's take a step back, what are we discussing? I claimed that my version of the smoking problem in which the gene is correlated with your decision to smoke (not just with your preference for it) is like the Newcomb problem, and that if you are a one-bower in the latter you should not smoke in the former. My argument for this was that both cases are isomorphic in that there is an earlier causal node causing, through separate channels, both your decision and the payoff. What is the problem with this viewpoint?
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.