How would you rule out that taxes cause lesions, or that taxes cause cancer? How would you show that taxes reduce smoking, given only that higher taxes are a leading indicator of reduced smoking?
At some point, you have to bring in domain knowledge of causation. How do you know that pushing on the accelerator will make the car go faster?
One can think up scenarios in which taxes do indirectly cause cancer (or lesions): higher tax on tobacco --> people continue to use tobacco but switch to some cheaper, less preferred foodstuffs --> among which is one that unknown to anyone yet causes cancer (or lesions). But the first of those links is observable. If they don't change their diet but do reduce their tobacco consumption, this chain is refuted.
For taxes causing reduced smoking, you could look at temporal relations, or ask people why they've cut down. If you find yourself inventing reasons why no-one can detect the dragon in your garage, at some point you have to accept that there is no dragon.
Evenly divide all people into two groups, and apply higher taxes to one group.
Changing taxes for everyone fails to test for a common cause of tax changes and smoking.
I can track a solid determimistic relationship from the accelerator pedal to the drivetrain. Deterministic cause and effect is easy to test. Stochastic cause and effect, much less so, especially with unknown confounding factors.
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.