To amplify Paul's point: The legal standard in all criminal trials is "Beyond a reasonable doubt": > The standard that must be met by the prosecution's evidence in a criminal prosecution: that no other logical explanation can be derived from the facts except that the defendant committed the crime, thereby overcoming the presumption that a person is innocent until proven guilty. And yet, DNA testing has exonerated man…
What does “beyond a reasonable doubt” mean in probability terms? Most people say 90-95%, which suggests even Graham’s 4% number (which is on the high end of such estimates, see: https://dc.law.utah.edu/cgi/viewcontent.cgi?article=1130&con... ) is actually consistent with the system working as designed. Also, while you’re thinking about that, what’s your estimate of the probability that Derek Chauvin’s negligence was…
> Most people say 90-95%
Most people believe that the 538's 2016 presidential forecast was incompetent because it said trump only had a 1/3 chance of winning and he won. Other papers put it at 10%. People said this was a huge failure because people generally are terrible at intuitively reasoning about probabilities, which is well established.
I'd put reasonable doubt at closer to 1 in a few hundred, maybe even rarer.
Is the link you included talking about the probability of convicting a person, given that they're innocent, or the probability that a convicted person is innocent? It brings too mind the classic stats issues of testing positive for a disease via a highly accurate test, with it still being probable that you don't have the disease. Even a highly accurate test can be entirely unreasonable as evidence of the rare case. We should probably care about making the false discovery rate the unreasonable one. Of the convicted people, is it unreasonable to doubt that a random one is guilty.