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Can you trust your LLM judge?

An LLM judge that agrees with humans 90% of the time can still be close to useless if 90% of the answers pass anyway. Paste judge and human labels, or enter a 2×2 table, to see agreement corrected for chance, where the judge errs, and how many human labels it can stand in for.

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1 · Your labels

Examples

2 · Agreement

items300
raw agreement92.3%
Cohen's kappa0.739
95% interval0.638 – 0.840

Kappa 0.739 is “substantial” on the Landis & Koch scale. Chance alone would give 70.7% raw agreement here, which is why 92.3% agreement can still be weak when one label dominates.

human ↓ · judge →positivenegative
positive428
negative15235
sensitivity84.0%
specificity94.0%
human positive rate16.7%
judge positive rate19.0%

3 · What the judge is worth

judge-assisted rate16.0%
95% interval13.0% – 18.9%
human labels it's worth2.1×
Combining your 300 human labels with 5,000 judge verdicts (prediction-powered inference, PPI++) gives an interval as tight as about 619 human labels alone. Human labels only: 16.7% (12.9% – 21.3%). The method weights the judge by how well it tracks humans (λ = 0.69), so a poor judge can't make the estimate wrong, only less useful.

Questions

What is a good Cohen's kappa for an LLM judge?

By the common Landis & Koch convention, 0.61–0.80 is substantial and above 0.80 almost perfect. These bands are conventions, not tests. What matters more is the interval (a kappa of 0.7 from 50 items could easily be 0.5) and whether the judge's errors are the ones you care about, which sensitivity and specificity show.

Why use kappa instead of percent agreement?

Percent agreement counts matches that would happen by chance. If 90% of answers pass and the judge always says pass, it agrees 90% of the time with kappa 0. Kappa subtracts the agreement expected from each rater's label frequencies.

How many human labels do I need to validate an LLM judge?

Enough to make the kappa interval narrow and to see the rare class. For a failure rate near 10%, a few hundred labels give only a few dozen failures, so sensitivity stays uncertain. Label more of the cases the judge is unsure about, or enrich for failures, and keep a random sample for the overall rate.

How can a judge replace human labels without biasing the result?

Prediction-powered inference (PPI++, Angelopoulos et al.) combines a small human-labelled set with many judge verdicts. It uses the human set to correct the judge's bias and weights the judge by how well it tracks humans, so the estimate stays valid even when the judge is poor; a good judge makes the interval as tight as several times more human labels.

Which label should be 'positive'?

The outcome you want the judge to catch, usually fail, wrong or unsafe. Sensitivity is then the share of real failures the judge flags, and specificity the share of good answers it lets through.

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Will Schulz

Will Schulz

Founder, NeuroGenesys • AW3 Technology