1. Capture beliefs about others
Each forecaster submits p (their probability) and m (their estimate of the group average). The second number is the meta-belief.
Why standard extremizing fails
Aggregate probabilistic forecasts on binary events are often conservative. The classic response is an extremizing transform: take the mean forecast and push it farther from 0.5. That works when the group’s prior is uninformed.
It fails when forecasters share a biased prior. Optimism, recency, groupthink, fund-cycle memory, or a manager’s pet category all shift the group’s default. Extremizing from 0.5 then amplifies the shared error.
The two-step algorithm
2. Estimate the shared prior
Meta-beliefs expose anchors people will not report directly. From the distribution of m and personal belief gaps, PRIOR estimates the shared prior q̂.
3. Transform away from q̂
Recalibrate the aggregate mean using an extremizing transform centered on q̂, not 0.5. Parameters α and β are tuned on historical outcomes.
pᵢ = probability estimate from forecaster i
mᵢ = belief about the average of others
q̂ = estimated shared prior from {mᵢ, pᵢ}
p̄ = mean(pᵢ)
p* = q̂ + α · (p̄ − q̂) · |p̄ − q̂|^β
clip p* to [0.01, 0.99]
// defaults before client tuning
α = 0.7
β = 0.4What you deploy
- Meta-belief capture in the form or channel your team already uses (Slack, form, CRM, forecast sheet)
- Recalibration service that returns raw mean, estimated prior, PRIOR-calibrated forecast, and diagnostics
- Backtest pack: Brier/log score vs naive average and naive extremization
- Drift monitor: alerts when the estimated prior shifts or calibration degrades
Where it wins
Decision problems where forecasters are competent but correlated: investment committees, revenue forecasts, risk panels, intelligence cells, medical consensus, commodities desks, prediction-market superforecaster pods.