The problem statement does not include the proviso that choosing not to smoke does not improve the payoff. It just says that if you have the lesion, you get cancer, and if you don’t, you don’t. And it says that people who choose to smoke, turn out to have the lesion, and people who choose not to smoke, turn out not to have the lesion. No proviso about not smoking not improving the payoff.
You might be right. But then TDT chooses not to smoke precisely when CDT does, because there is nothing that’s logically-but-not-physically/causally connected with the exogenous decision whether or not to smoke. Which arguably makes this version of the problem quite uninteresting.
The problem statement does not include the proviso that choosing not to smoke does not improve the payoff. It just says that if you have the lesion, you get cancer, and if you don’t, you don’t. And it says that people who choose to smoke, turn out to have the lesion, and people who choose not to smoke, turn out not to have the lesion. No proviso about not smoking not improving the payoff.
You might be right. But then TDT chooses not to smoke precisely when CDT does, because there is nothing that’s logically-but-not-physically/causally connected with the exogenous decision whether or not to smoke. Which arguably makes this version of the problem quite uninteresting.