Crowd Wisdom — Signal vs Noise Aggregation
Diversity, independence, and the wisdom-of-crowds effect in collective estimation
Setup
True value:
500
N estimators:
100
Individual noise σ:
150
Shared bias b:
50
Correlation ρ:
0.0
New Sample
Theory
xᵢ = μ + b + σεᵢ (εᵢ~N(0,1))
Var(x̄) = σ²(ρ+(1-ρ)/N)/1
Diversity = Var(xᵢ) - Var(x̄)
Crowd error² = Bias² + Var(x̄)
Results