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anon85 comments on A Proposal for Defeating Moloch in the Prison Industrial Complex - Less Wrong Discussion
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Suppose you're Bayesian, and you're calculating
P(lead causes crime | data) = P(data | lead causes crime) * P(lead causes crime) / P(data).
What Pinker is saying is that P(data | lead causes crime) is not as high as you'd think, because if lead really does cause crime, we should not expect the crime curve to be a time-shifted version of the lead curve. It's probably still true that P(data | lead causes crime) > P(data), so that you should update in the direction of lead causes crime, but this update should probably be smaller than you thought before reading that paragraph.
Has anyone figured out what crime curve you would expect based on the lead curve (presumably a version that is shifted & smeared out based on the age distribution of criminals), and checked how well it fits the actual crime data? It's not obvious to me, from looking at the pictures that I've seen with the shifted curves, that adding the smearing would make the fit worse. For instance, the graph I linked earlier shows that the recent drop in crime is more gradual than the drop in lead that happened 20-30 years ago, which seems to fit the more rigorous "time-shifted and smeared out" prediction better than it fits the simplistic time-shifted curve approach that Nevin used.