Smoking lesion

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The Smoking Lesion is a problem for testing decision theories, stated as follows:

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".

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