Great!
It's not clear to me that we agree about the central point of the post- I think Egan's examples are generally worthless or wrong. In the Murder Lesion, shooting is the correct decision if she doesn't have the lesion, and the incorrect decision if she does. Whether or not she should shoot depends on how likely it is that she has the lesion. He assumes that her desire to kill Alfred is enough to make the probability she has the lesion high enough to recommend not shooting- and if you stick that information into the problem, then CDT says "don't shoot." Note that choosing to shoot or not won't add or remove the lesion- and so if Mary suspects she has the lesion, she probably does so on the basis that she wouldn't be contemplating murdering Alfred without the lesion.*
In the Psychopath button, Paul can encode the statement "only a psychopath would push the button" as the statement "if I push the button, I will be a psychopath," and then CDT advises against pushing the button. (If psychopathy causes button-pushing, but the reverse is not true, then Paul should not be confident that only psychopaths would push the button!) This is similar to his 'ratifiability' idea, except instead of bolting a clunky condition onto the sleek apparatus of CDT, it just requires making a causal graph that accurately reflects the problem- and thus odd problems will have odd graphs.
In Egan's Smoking Lesion, he doesn't fully elaborate the problem, and makes a mistake: in his Smoking Lesion, smoking does cause cancer, and so CDT cautions against smoking (unless you're confident enough that you don't have the lesion that the benefits of smoking outweigh the costs, which won't be the case for those who think they have the lesion). It amazes me that he blithely states CDT's endorsement without running through the math to show that it's the endorsement!
* Edited to add: I agree that if the original Smoking Lesion problem has a "desire to smoke" variable that is a perfect indicator of the presence of the lesion, then EDT can get the problem right. The trouble should be that if the "desire to smoke" variable is only partially caused by the lesion (to the point that it's not informative enough), EDT can get lost whereas CDT will still recognize the lack of a causal arrow. I suspect, but this is a wild conjecture because I haven't run through the math yet, that EDT will set a stricter bound on "belief that I have the murder lesion" than CDT will in the version of the Murder Lesion where there's a "desire to kill" node which is partially caused by the lesion.
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.