 Assume that each individual accesses independent private information, on which alone their judgment is based, without any information sharing or dependence on common influences (assumed in Dietrich &amp; List 2004). For instance, doctors perform independent tests on one and the same patient to judge whether some virus is present, or chemists perform independent experiments to judge whether a liquid contains a given molecule. This private information is truth-conducive: given any true state, the information supports the true state with probability above \(\frac{1}{2}\)—the same probability for each information (each individual). More problematically, private evidence is independent given the true state. This rules out, implausibly, that any common causes (except the state itself) affect different private information: for instance, the patient’s physiology cannot affect virus tests (possibly rendering all tests unreliable), and the liquid’s acidity level cannot affect tests for the molecule (possibly rendering all tests unreliable). Under these questionable assumptions, majority judgments are asymptotically infallible, as the (State-)Conditional Jury Theorem applies.