When LLM Judge Scores Look Good but Best-of-N Decisions Fail

When an LLM judge filters instruction-tuning data, its scoring format (binary verdict, 1--5 rating, 0--100 score, or comparison) is rarely justified or ablated. Holding the candidate pool, judge prompt, decoding and selection budget fixed, we score 15,406 UltraFeedback candidates under five formats with three judges, curate, fine-tune 66 models, and evaluate them with four judges. A 0--100 scale is worth only 7--12 equally used levels, two to three times a 1--5 scale rather than twenty, and a binary verdict leaves the top score tied in 77--78% of prompts, so most selections are made at random. These properties are set by the format almost independently of the judge. Kendall's $τ_b$ hides them: it ranks binary best while $τ_a$ and top-1 agreement rank it last, because it discounts the ties a selector must break at random. Both comparative formats inherit a slot bias whose sign differs across judges. Downstream, curated data beat random selection under every evaluation judge, robust to length and markdown adjustment, but no ordering among formats is detectable. We propose four quantities that judge-based curation pipelines should report.

Using a language model to score or rank candidate responses has become a scalable alternative to human evaluation in reinforcement learning from human feedback (RLHF) pipelines, benchmarking, and application layer evaluations. However, output reliability depends heavily on prompting and aggregation strategy. We present an empirical investigation of four drop-in techniques -- ensemble scoring, task-specific criteria injection, calibration context, and adaptive model escalation -- for improving LLM judge accuracy on RewardBench 2, with a unifying lens of noise control on the stochastic judge: ensembling as Monte Carlo averaging over per-call noise, criteria injection as between-response discrimination sharpening, and per-response score variance as an uncertainty signal. Ensemble scoring and task-specific criteria injection (the latter virtually cost free) together reach up to 85.8% accuracy, +13.5pp over baseline. Calibration context and adaptive model escalation also improve over baseline but are dominated by criteria + ensembling on the cost-accuracy Pareto frontier. Small models benefit disproportionately from ensembling, making high-accuracy LLM judges accessible at low cost. We show that these techniques generalise across model providers, evaluating on both OpenAI GPT and Anthropic Claude families.

Validating an LLM judge against human annotations usually means reporting several agreement statistics: accuracy, precision, recall, $F_1$, Cohen's $κ$, and one or more rank correlations. A survey of 24 recent LLM-as-judge papers finds metric choice entangled with the judgment scale, tie handling, invalid outputs, and abstention handling, and those choices rarely stated. For binary criteria -- the common case in rubric-based evaluation, where each criterion is graded MET or UNMET -- most of the reported numbers are redundant: Pearson's $r$, Spearman's $ρ$, Kendall's $τ_b$, the phi coefficient $φ$, and the Matthews Correlation Coefficient all reduce to a single number on non-degenerate binary data, so reporting several of them only creates an illusion of corroborating evidence. Cohen's $κ$ is the one agreement coefficient that adds information: it shares $φ$'s numerator but normalizes differently, and the gap between them measures how far the judge's positive-label rate has drifted from the human's. We then trace what changes when a judge may abstain with a CANNOT_ASSESS verdict: the three common ways of handling abstentions are not interchangeable preprocessing choices but answer different questions, and they break the binary equivalences. The same equivalences reappear, up to a negligible finite-sample correction, for multi-judge ensembles scored with Fleiss' $κ$ or Krippendorff's $α$. We close with a reporting checklist that names the judgment scale, the abstention and tie handling mode, coverage, the confusion matrix, and the aggregation level alongside any scalar agreement coefficient.