Can a verifier be paid for a tolerance interval, not a point?

What it found

The Winkler interval score is strictly proper for the pair of quantiles, with closed-form regret and an optimal expected score of exactly 4sφ(z)/α. Misreporting the width by the same factor costs more when narrow at 95% coverage but more when wide at 80%, so there is no universal rule that overconfidence is worse. Under Cauchy drift the scores have no mean, yet paired differences are bounded, so evaluate verifiers against a benchmark report.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Proper scoring & elicitation

• How should a tolerance interval be paid for?Paying for a drift tolerance interval: Winkler interval score is proper for the equal-tailed pair with exact regret (finite for Cauchy) but unbounded payment; the bounded width-plus-miss loss elicits the shortest interval (22–31% narrower on lognormal drift) at a 3–48× larger detection sample for α≥0.1.
• How should a verifier's vector report be scored?Scoring a verifier's vector report: the precision score Σ⁻¹ is uniformly most detectable among quadratic Bregman scores (Cauchy–Schwarz), an isotropic score can need (1+κ)²/(4κ) times more tasks (25× at κ=100, power 0.29 vs 0.80), diagonal normalisation barely helps, estimated precision reaches 0.61 efficiency at m=2d draws.
• What does a verifier's score gap cost in decisions?From a verifier's excess proper score to a certified cap on accept/audit/slash decision regret: exact calibration functions (Brier ε², log KL), linear transfer only for non-proper hinge, audit action tightens the guarantee.
• Which surrogate should train a verifier that can escalate?Polyhedral surrogates for accept/reject/escalate verifiers: minimiser embeds the Bayes action, linear regret transfer with constant exactly 2d, logistic transfer ratio 2d(1-d)/δ, and a negative SGD result.
• How do you pay a verifier whose report decides the job?Scoring verifiers whose report decides acceptance and whose outcome is seen only on acceptance: a truthful reserve exists iff the score centre τ_s ≥ τ_d (unique c0 = 1+τ_d²−2τ_dτ_s), plain Brier fails above τ_d = ½, recentring fixes it at rent τ³/3, exploration costs 1/ε payment variance.
• What if the referee itself is noisy?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.

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Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & 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.