The Smoking Lesion is a problem for testing decision theories, stated as follows:
Smoking is strongly correlated with lung cancer, but in the world of the Smoker’s Lesion this correlation is understood to be the result 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”, since 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.