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Nine judges, how many votes?

Critics that share a model, a prompt, or a training distribution share their mistakes. From two measured numbers — per-critic error and pairwise co-error — this tool recovers the shared error component, the accuracy ceiling no amount of same-substrate sampling crosses, and the panel's effective size. It then says whether your next unit of budget should buy more samples or a decorrelated channel.

Background: Measured self-critique correlation and the ε correction.

Panel · how much is your judge panel actually worth?

Examples
error correlation ρ0.286
shared error s0.109
majority ceiling 1−s0.891
n_eff of 52.33
your panelif critics were independent
0.5000.6000.7000.8000.9001.00010203040criticsmajority accuracyceiling 1−s = 0.891N = 5
Exact majority vote under the common-cause model; ties count as half right, which is why even panel sizes dip. Same-substrate critics flatten toward the ceiling; independent ones keep climbing.
No number of same-substrate critics pushes majority accuracy past 0.891. Your 5 critics are worth 2.33 independent votes.
Target 0.900 is above the ceiling. More same-substrate critics cannot reach it — spend the next unit of budget on a decorrelated channel (a different model or training distribution, execution, a solver, a source check), which attacks s directly.

s = (P_both − e²)/(1 + P_both − 2e), ρ = (P_both − e²)/(e(1−e)), n_eff = N/(1 + (N−1)ρ). Classical mathematics — Ladha 1992, Clemen–Winkler 1985, Breiman 2001 — made actionable. At small N a better-but-correlated critic can still beat worse-but-independent ones.

From data · measure e and P_both from a miss matrix

Run your critics over items where the answer under review is wrong, then record one row per item and one column per critic: 1 if the critic missed the error (endorsed the wrong answer), 0 if it caught it, blank or NA if it abstained. A header row is optional. Error bars are a 1,000-draw bootstrap over items, as in the research code. Nothing leaves your browser.

Check-tail · can you trust a Φ-based ε?

The Gaussian ε law ε = Φ(−gap/(σ√2)) is Thurstone's 1927 Case V identity — exact for Gaussian scores and uniformly optimistic under heavy tails (measured 11× at gap/σ = 4 and 723× at gap/σ = 6). Paste verifier scores to test the precondition; excess kurtosis separates the regimes. Nothing leaves your browser.

Φ-based ε2.34e-3

Run it locally (Python, standard library only)

python verifier_panel.py panel --e 0.30 --pboth 0.15 --n 5 --target-acc 0.9
  python verifier_panel.py check-tail scores.txt
  python verifier_panel.py check-tail --gap 1.0 --sigma 0.25

Leadership

A word from the founder — on why the brain is the blueprint, and why the next decade of intelligence will be built here.

"The brain is the universe's only proof that general intelligence is possible. We treat it as the blueprint."

From cortical interfaces to photonic silicon, every program at NeuroGenesys exists to answer one question: how does intelligence arise — and how do we build it safely.

Will Schulz

Will Schulz

Founder, NeuroGenesys • AW3 Technology