This is actually a really tough problem, because it's even unclear which rate to talk about. If you look at "trial by peers" as a test, what error rates are we worried about/trying to make unreasonably rare? Sensitivity? Specificity? FDR? Posterior probability under what prior? One of the many many others used in stats?

I might argue that FDR [0] is the right number, given that you want to look at the set of convicted people and say it's unreasonable to doubt that a randomly picked one of them is guilty.

[0] https://en.wikipedia.org/wiki/False_discovery_rate