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Notes -
Thanks for the background on reasonable doubt.
You are correct, in the absence of numerical odds given by the jury and given that updates after the verdict are very costly, we should have some hysteresis built in for the verdict. Say we don't want to execute some man who is innocent with a probability p_k (perhaps 10%, or 5%, or 1%). What we should do is require a higher standard for conviction verdicts, perhaps p<p_k/x (Where x might be 5, perhaps). Then after the verdict, we have some slack to not revert the verdict even in the case of evidence with an odds ratio 1:x in favor of innocence.
Of course, an extremist view would be that we should never overturn verdicts and just accept the deaths of innocents as already priced in, statistically, in our p_k threshold (as long as the juries are well calibrated). However, not using all the available info (with exception of the exclusionary rule in court) seems indefensible (and I see neither you nor anyone here arguing for it). The reasonable doubt standard on judgement day likely applies on a case-by-case base, the governor who signed an execution order for a man who is likely innocent and just tells God 'well, I found that jury verdicts generally achieve your ordained threshold, and found it to bothersome to update, but look, the other 19 men I hanged were all murderers, so statistically speaking, we are good' would likely be hellbound in most theologies.
Of course, Scott Alexander advocates explicit probabilities:
I'm confused as to what you're saying here, so I don't want to argue about it too hard until you explain it.
I think you're ignoring the systemic value of finality in verdicts. If we constantly allow convictions and sentences to be paused and altered while we sit and consider whether some new piece of evidence alters the probability of guilt to a degree too great to countenance, we'll never get anything done.
Made up probabilities are all well and good for those of us in the peanut gallery, but for decision makers final decisions must be made, and they must be respected with some degree of certainty.
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