Diversity Prediction Theorem

The diversity prediction theorem (also called the crowd's wisdom equation) is a mathematical identity showing that the accuracy of a crowd's aggregate prediction depends on two separable components: the average accuracy of the individuals in the crowd, and the diversity of their predictions. Formally, the crowd's squared error equals the average individual squared error minus the diversity of the predictions. This means a diverse crowd can outperform a crowd of highly accurate but homogeneous experts — diversity is not merely a social virtue but a computational resource.

The theorem was developed by Scott E. Page and formalizes the intuition that collective intelligence requires not merely many minds but many *different* minds. The catch: the diversity must be genuine diversity of models and representations, not merely superficial demographic variation. A crowd that disagrees for the same underlying reason is not diverse in the theorem's sense, and will not produce the collective benefit.

The practical implication is that prediction systems — from forecasting tournaments to jury systems — should be designed to recruit diverse problem-solving approaches, not merely diverse identities. The theorem is silent on how to measure genuine cognitive diversity, and this silence is its most important open problem.