What if the referee itself is noisy?

research/noisy-referee

Scoring verifiers against a noisy judge: raw proper scores elicit e0+γp and shrink Brier incentives by γ², can reverse rankings (η*=0.25), the unbiased surrogate score is exactly proper at a 1/γ payment spread and 1/γ² sample cost, and misestimated rates give a closed-form bias.

12 tests

What it found

When verifiers are paid against a judge whose label flips with rates e₀, e₁, any proper score elicits the noisy probability e₀+γp (γ=1−e₀−e₁), the Brier incentive shrinks by γ², and rankings of truthful verifiers reverse at η*=0.25. The backward-corrected surrogate score is exactly unbiased for the true loss, at a 1/γ payment spread and (balanced case) 1/γ² more evidence; misestimated rates produce a closed-form affine bias whose cost falls as 1/m in gold checks. Stylised.

A figure from its own output

Figure produced by research/noisy-referee: gold_budget — noisy-referee/experiments/gold_budget.svg, written by the project's own experiment code.

Paper, code and results

More in Proper scoring & elicitation

Can audits be predictable without corrupting scores?Scoring when truth exists only on audited tasks: report-dependent audit rates make naive scoring improper (shift −bp(1−p)/(2(a+bp)), full hiding for steep rates), inverse-propensity weighting is exactly proper for any audit rule, and Neyman allocation gains only 3–11% variance.
Can a calibration test certify a verifier?Calibration tests are gameable: an information-free Foster–Vohra/Blackwell hedger keeps expected ECE ≤ √(K+1)(1/(2K)+1/√T) against any outcome sequence (measured 0.016, Brier 0.254 vs 0 informed), so slashing must use a resolution-sensitive score; a Brier-gap test detects it in 100/100 runs.
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Other research topics

Proper scoring & elicitation28 Effort & peer prediction9 Verification games & slashing19 Detection & tolerances14 Markets as routers13 Prediction-market design9 Paying contributors8 Decentralised training systems23 Digital twins & sim-to-real164 LLM chip design loops40 Robot manufacturing loops53 Ambient AI assistant46 Self-replicating manufacturing34 Simulation-first design64 Engineered clothing45 Task-specific AI accelerators40 Algorithmic chip-design loops42 Open-source purpose-built robots44 The software-engineering loop43 Adversarial human imitation41 Open-source residential construction41 Autonomous multi-angle capture34 Sensing, imaging and 3D31 Energy supply and dense energy storage39 Robot societies among people31 Agentic co-design of low-cost robots27 Laundry-hanging robots25 Machine learning on qualitative data23 Robots on the building site27 Civilizations & group psychology1 History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.