I argue that medieval judicial ordeals accurately assigned accused criminals' guilt and innocence. They did this by leveraging a medieval superstition called iudicium Dei (judgments of God). According to that superstition, God condemned the guilty and exonerated the innocent through clergy-conducted physical tests. Medieval citizens' belief in iudicium Dei created a separating equilibrium in which only innocent defendants were willing to undergo ordeals. Conditional on observing a defendant's willingness to do so, the administering priest knew he or she was innocent and manipulated the ordeal to find this. My theory explains the peculiar puzzle of ordeals: trials of fire and water that should have condemned most persons who underwent them did the reverse. They exonerated these persons instead. Boiling water rarely boiled persons who plunged their arms in it. Burning iron rarely burned persons who carried it. Ordeal outcomes were miraculous, but they were miracles of mechanism design.
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