Social Learning from Experts with Uncertain Precision

Abstract: We study social learning from multiple experts whose precision is unknown and who care about reputation. The observer both learns a persistent state and ranks experts. In a binary baseline we characterize per-period equilibria: high types are truthful; low types distort one-sidedly with closed-form mixing around the prior. Aggregation is additive in log-likelihood ratios. Light-touch design -- evaluation windows scored by strictly proper rules or small convex deviation costs -- restores strict informativeness and delivers asymptotic efficiency under design (consistent state learning and reputation identification). A Gaussian extension yields a mimicry coefficient and linear filtering. With common shocks, GLS weights are optimal and correlation slows learning. The framework fits advisory panels, policy committees, and forecasting platforms, and yields transparent comparative statics and testable implications.