 Ordinary jury theorems assume the classic paradigm of epistemic democracy: collective decisions should be correct, and individuals vote for what they believe to be correct. But collective correctness can emerge even if voters do not pursue it. For instance, decisions can serve the collective interest even if voters vote for what they believe serves their personal interest. This is the message of jury theorems for voters tracking individual facts. They follow a semi-epistemic paradigm of democracy: collective decisions should still be correct, but voters express judgments about individual facts.