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Tordmor comments on Rationality & Criminal Law: Some Questions - Less Wrong
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"1) Punishments get scaled by the judged likelihood of guilt, i.e. judge says there's a 65% chance Bill is the killer, Bill gets 65% of the punishment."
Almost. There is a level of probability below which there is "reasonable doubt". Let's say that would be 70%. So if the probability of me being guilty is below that I go free. If the probability is above that I get the punishment in relation to the level that the probability is above it. So if my probability of being guilty is 80% I'd get 1/3 of the punishment.
It's extremely important that the conditional probability of being punished, given innocence, is very low. Most people's decision-making process "overweights"(*) the importance of small probabilities. For example, they prefer a sure $100 over a 0.95 chance of $110 and a 0.05 chance of -$10, even when by most measures their utility of money is essentially linear in this range.
The deterrent effect of the law, therefore, drops substantially if people start thinking "even if I commit no crime, I could very well be convicted anyway." The psychological distance between expectations of punishment conditional on crime vs innocence can diminish by a lot, if the chance of punishment of the innocent rises just a little.
(*) Why the scare-quotes? By standard theories of utility, which I regard with some suspicion, it is wrong to weight possible outcomes non-linearly with their probability.
Rather tangential, but it seems to me that this could be highly relevant to a nasty spiral in certain marginalized groups that (probably correctly) perceive themselves as being unusually likely to be falsely convicted.