Does agreement pay reward shared laziness?

research/focal-laziness

Peer prediction when lazy verifiers share a default answer: agreement pay is 2G·Cov, effort is a coordination game with threshold a*=(k/2G+s)/(pq+s), the all-lazy equilibrium always exists and pays as much as honesty when the default matches the prior, and gold checks needing more mass than the honest pay close it.

9 tests

What it found

Multi-task peer prediction pays 2G·Cov of two reports. If lazy verifiers copy a shared per-task default (the same public model’s guess) pay becomes 2G[a_ia_jpq + (1−a_i)(1−a_j)d(1−d)], effort is a coordination game with threshold a* = (k/2G + s)/(pq + s), and the all-lazy profile is always an equilibrium paying 2G·d(1−d): equal to honest pay when the default matches the prior, 1.19× it at p=0.3, d=0.5. Closing it with gold checks needs payment mass (2Gs+k)/(1−acc_D), larger than the honest pay itself. Stylised.

A figure from its own output

Figure produced by research/focal-laziness: lazy_vs_honest — focal-laziness/experiments/lazy_vs_honest.svg, written by the project's own experiment code.

Paper, code and results

More in Effort & peer prediction

How noisy is peer-prediction pay with finitely many tasks?Finite-sample noise in multi-task peer prediction: the plug-in payment is 2× the sample covariance with an exact variance (matches enumeration), √2 less noisy than fresh penalty tasks, pays a constant reporter 0, and a lazy coin still earns ≈σ/√(2π) under limited liability; deductibles and detection/ranking sample sizes in closed form.
When most verifiers miss a fault, who should be believed?Surprisingly-popular verdicts for rare-but-diagnostic signals: majority errs 0.84 on faulty jobs at n=101 when detection is 0.45, SP is an exact fraction threshold v/(1−u+v) (2.1×10⁻⁵ error, 47 votes for 10⁻³ vs Bayes 36), a wrong believed prior wrecks finite-n accuracy, a wrong believed detector breaks the limit, Byzantine breakdown at exactly 13.6%.
Why should the first verifiers be sealed?Sequential verifiers who see earlier verdicts herd: wrong-cascade probability exactly (1−a)²/(a²+(1−a)²), cascade after 2/(a²+(1−a)²) signals, accuracy capped at 0.845 (a=0.7) versus ≈1 for an independent majority, and a sealed first batch of ≥3 lifts the cap (0.875 at m=3, 0.949 at m=11); checked against Bayesian agents.
When should a paid verifier stop checking?Verifiers who choose when to stop checking under a proper score: optimal policy is a symmetric threshold (matches dynamic programming), closed-form accuracy 1/(1+((1−a)/a)^k) and cost k(2p_k−1)/(2a−1), participation κ ≥ 4c/(2a−1)², and adaptive stopping matches fixed-sample accuracy with 2–3× fewer checks.
Peer-prediction markets for decentralized ML training verificationPeer-prediction and prediction-market mechanisms for verifying decentralized ML training, with adversarial evaluation.
What does it cost to pay a verifier to check?Paying verifiers for costly checking effort with proper scoring rules: implementable efforts = concave envelope of the value curve, exact Brier rent (n−1)/(a+b), log score needs half Brier's payout spread on rare-fault priors.

All 9 Effort & peer prediction projects →

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.