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.
The closest thing I know of is the “actually innocent, but convicted” sample that gradually came to light under DNA testing of inmates. Unreported crime rates get estimated somehow, so I’d be surprised if nobody had combined those numbers to do a study in this vein. Haven’t found one with a cursory googling, though.
I don’t see how those are “the same question”. If out of 8 accused 4 are guilty and two of them are convicted, the rest acquitted. Than p(guilty|convicted) = 1 and p(innocent|acquitted) = 2⁄3.
The assumption was that 80% of defendants are guilty, which is more than 4 of 8. Under this assumption, asking whether p(guilty|convicted) > 80% is just asking whether conviction positively correlates with guilt. Asking if p(innocent|acquitted) > 20% is just asking if acquittal positively correlates with innocence. These are really the same question, because P correlates with Q iff ¬P correlates with ¬Q.
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.
The closest thing I know of is the “actually innocent, but convicted” sample that gradually came to light under DNA testing of inmates. Unreported crime rates get estimated somehow, so I’d be surprised if nobody had combined those numbers to do a study in this vein. Haven’t found one with a cursory googling, though.
I don’t see how those are “the same question”. If out of 8 accused 4 are guilty and two of them are convicted, the rest acquitted. Than p(guilty|convicted) = 1 and p(innocent|acquitted) = 2⁄3.
The assumption was that 80% of defendants are guilty, which is more than 4 of 8. Under this assumption, asking whether p(guilty|convicted) > 80% is just asking whether conviction positively correlates with guilt. Asking if p(innocent|acquitted) > 20% is just asking if acquittal positively correlates with innocence. These are really the same question, because P correlates with Q iff ¬P correlates with ¬Q.
Perfect. Thanks.