Naive causal decision theory says "yes", and naivesince smoking in this world has no causal effect on whether or not you get cancer. You either get cancer or not; in both cases, smoking is preferred. Naive evidential decision theory says "no"., because smoking is strongly correlated with cancer. Functional Decision Theory says "yes": your decision procedure in this problem doesn't influence whether or not you get cancer - and with or without cancer, smoking is preferred.
Smoking is strongly correlated with lung cancer, but in the world of the Smoker's Lesion,Lesion this correlation is understood to be becausethe result of a common cause—cause: a genetic lesion that tends to cause both smoking and cancer. Once we fix the presence or absence of the lesion, there is no additional correlation between smoking and cancer.
The smoker's lesionSmoking Lesion is a problem infor testing decision theorytheories:, stated as follows:
The smoker's lesion is a problem in decision theory:
Smoking strongly correlated with lung cancer, but in the world of the Smoker's Lesion, this correlation is understood to be because of a common cause—a genetic lesion that tends to cause both smoking and cancer. Once we fix the presence or absence of the lesion, there is no additional correlation between smoking and cancer.
Suppose you prefer smoking without cancer to not smoking without
cancer, and prefer smoking with cancer to not smoking with cancer. Should you smoke?
Naive causal decision theory says "yes", and naive evidential decision theory says "no".
I know this is the classic, but I just came up with a more elegant variation, without another world.
Toxoplasma infection makes you more likely to pet a cat. You like petting cats, but you are very afraid of getting toxoplasmosis. You don't know if you are infected, but you know this particular cat is healthy, so you can't become infected by petting it. Should you pet this cat?