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Dmytry comments on Decision Theories: A Less Wrong Primer - Less Wrong
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You would still have priors for all of these things.
Even if you do, how is knowing that the lesion causes cancer going to change anything about P(smokes|gets cancer) ? The issue is that you need to do two equations, one for case when you do have lesion, and other for when you don't have lesion. The EDT just confuses those together.