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.