A Jury, Not an Electorate: Label-Free Reliability Estimation for Ensembles of Language Models

An LLM judge evaluates outputs at scale. Experts should label only where it is least sure. Its natural escalation signal conflates two uncertainties: aleatoric, real disagreement in the expert pool, which labels cannot reduce, and epistemic, the judge's ignorance, which labels do reduce. A small Bayesian model separates them: a regression on labels already collected learns how far to trust a black-box judge's prediction. Both components follow as simple formulas, with no sampling or further judge calls. The components isolate on a real LLM judge against exactly known truth, and stated confidence is no guide to its actual error. On real human disagreement (ChaosNLI) the epistemic ranking removes 83% more error than total uncertainty for the same expert labels, though simply escalating the least-labelled items does as well there. We demonstrate we can estimate where a judge is ignorant rather than where experts genuinely disagree, and propose using this to direct expert labelling. Code and data are available at https://github.com/composo-ai/judge-uncertainty-decomposition.

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model's score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.

Language models are often asked to make judgments: whether a proposed answer is correct, whether one statement follows logically from another, or whether a response is safe. Yet changing the instructions that specify how the judgment should be expressed can make the final answer less reliable, even for the same input. We ask whether this reflects a change in internal judgment or a failure to express it. Comparing hidden-state vectors for the same input under different instructions, we find that their differences concentrate in a low-dimensional expression subspace. We identify this subspace without benchmark labels and remove its contribution from a linear predictor to obtain an isolated judgment. Across correctness, entailment, and safety, the isolated judgment remains reliable under instructions not used to identify the subspace, even when the model's final answer and the original predictor degrade. When the judgment question is negated, isolation raises the predictor's AUROC from 0.504 to 0.825 for entailment and from 0.480 to 0.891 for safety. We also find that judgment is readable in earlier layers, before the expression subspace begins to disrupt the predictor. Together, these results provide a way to separate judgment from expression and recover internal judgments even when the model's final answers are unreliable.