Wisdom of Crowds & Diversity

Hong-Page theorem: diversity beats ability in collective estimation

Hong-Page Theorem: A diverse group of problem-solvers can outperform a group of high-ability solvers. Key insight: individual error = bias² + variance; crowd mean cancels variance when estimates are independent. Left: individual estimates (dots) vs aggregates. Right: accuracy vs diversity scatter — adding a worse-but-different estimator often improves the ensemble. Correlation ρ reduces diversity benefit — crowds work best when estimators are independent.