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wedrifid comments on The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom - Less Wrong
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No! In this context confidence intervals around the probability have no meaning!
I do agree that adding extra information about confidence is important for things like this. It's just that this isn't a case for which confidence intervals (approximately) work. It would make more sense if the probability was a property of the universe itself, then you could establish bounds on where the 'true probability' lies (as discussed with komponisto).
Why can't they be confidence intervals around the probability after doing [some amount] more research?
Relevant post: Readiness Heuristics
That you can do.