"That would save a lot of time and money on court cases and – on average – would be just as fair as the traditional system" It would convict the same number of people on average. But its only "as fair" if it is true that chance of conviction is completely uncorrelated to actual guilt. I'd hope that there is at least a little correlation. For elections, I think you can do even better by choosing the representative for each constituency by random sortition. This means you parliament is (on average) representative of your population.