No single forecaster is very good — but average enough independent guesses and the errors cancel. That’s the wisdom of crowds, and psychohistory’s whole bet: individuals are noise, the aggregate is a curve. Add forecasters (or tap) and watch the error shrink as 1/√N.
The variance-reduction law behind ensemble forecasting. Each of N forecasters reports the truth plus independent noise of spread σ=1; the ensemble estimate is their mean, whose expected error falls as σ/√N. N is set by the slider (1…50); the running mean and its error are computed live from a fixed seeded pool, and the theoretical σ/√N curve is drawn beside it. Independence is the whole trick — correlated errors don't cancel. A fail-loud self-check throws unless the error at large N is well below the error at N=1 and tracks σ/√N.
Independent Gaussian noise stands in for real (correlated, biased) forecasters — where the √N gain saturates; σ=1 is a fixed scale. The ensemble mean and its error are computed exactly from the seeded pool.