Can the log score be made payable?

What it found

Log score is ideal for rare faults but a confident wrong report costs unbounded stake. Extending the log generator past [ε,1−ε] by its second-order Taylor polynomial gives a strictly proper score, identical to log up to a constant inside, with worst-case payment exactly ln((1−ε)/ε)+1/(1−ε). Per unit of payment range it has 63× Brier’s curvature at p=10⁻³ but loses to Brier above a closed-form crossover (≈0.07), and ε=p is the best cutoff for truth p.

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

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• Can we elicit the mode of a mixture of honest and cheating drift?Eliciting the modal drift with the window loss 1[|y−r|>α]: exact window-mass regret, best width α=σ (normal) / γ/√3 (Cauchy), closed-form critical width α* above which bimodal drift has one α-mode, and 0 bias against contamination where the mean moves 5ε.

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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.