All justice systems (informal to formal, small to large) ought to acknowledge that they are not perfect: they lack the resources to make a perfect decision.
Encode this imperfection by having verdicts expressed as probabilities rather than binary yes or no. Then pass on the verdict to a trusted random number generator to render the final decision.
Such a system seems radical by modern standards, but not too unusual when compared to ancient ones which explicitly incorporated an element of chance into judicial decisions: trial be combat or decisions rendered by divination.
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