Jury theorem

A jury theorem is a mathematical result in social choice theory establishing that the probability of a group making the correct decision increases as the group grows, provided each individual has an independent probability greater than 0.5 of being correct. The original Condorcet's jury theorem, formulated by the Marquis de Condorcet in 1785, states that if each voter is more likely than not to choose the correct option, then the majority vote of a large group is almost certain to be correct.

Jury theorems formalize the intuition behind ensemble methods in machine learning: that diverse, independent estimators produce better collective judgments than any single expert. The independence assumption is crucial — if voters' errors are correlated, the theorem's guarantees collapse. This makes jury theorems as much a theory of when collective intelligence fails as when it succeeds. The conditions under which independence breaks down — social proof, information cascades, and homophily — are the central concerns of modern collective epistemology.