Mass_Driver comments on Hearsay, Double Hearsay, and Bayesian Updates - Less Wrong
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I think the intended question is whether the legal system adds anything beyond a pure chance element. Somehow we'd need a gold standard of actually guilty and innocent suspects, then we'd need to measure whether p(guilty|convicted) > 80%. You could also ask if p(innocent|acquitted) > 20%, but that's the same question.
Thank you! Intended or not, it's a fantastic question, and I don't know where to look up the answer. I'm not even sure that anyone has seriously tried to answer that question. If they haven't, then I want to. I'll look into it.