Diagnosing LLM Judge Reliability: Conformal Prediction Sets and Transitivity Violations

LLM-as-a-judge has become the dominant approach to scalable evaluation in NLP pipelines, yet judges themselves carry systematic biases that raw accuracy hides: they favor responses placed in slot A (position bias), they prefer longer responses regardless of quality (verbosity bias), and their reliability degrades sharply in lower-resource languages. We introduce BabelJudge, an open-source benchmark and reliability audit framework that measures all four failure modes -- position bias, verbosity bias, order inconsistency, and cross-lingual degradation -- on any judge model, without requiring human preference labels. The key insight is gold-labelling by degradation: starting from a high-quality reference response and applying a controlled perturbation yields a pairwise item whose gold label is known by construction, eliminating annotation cost. We evaluate Qwen2.5-7B-Instruct-4bit across English, Hindi, Arabic, and Swahili and find that our composite bias-penalised reliability score drops from 0.714 in Hindi to 0.550 in Swahili, a gap that raw accuracy (0.835 vs. 0.660) understates. Swahili order consistency collapses to 0.480, meaning judge verdicts are near-random under slot-order swaps -- a failure mode invisible to accuracy alone. We further extend the framework to agentic evaluation via nine trajectory-level perturbations (argument corruption, tool swaps, hallucinated calls, missing steps) and three new metrics: tool accuracy, hallucination detection rate, and trajectory-length bias. BabelJudge is released as a Python package supporting 11 judge backends. Code: https://github.com/Shreyaskc/BabelJudge

LLM-as-a-Judge has become the dominant evaluation paradigm for language models, but judge validation in practice relies on exact-match agreement, a metric that does not correct for chance and systematically overstates discriminative ability. We present the largest systematic evaluation of LLM-as-a-Judge to date: 21 judges from nine providers across MT-Bench, JudgeBench, and RewardBench, evaluated under three protocols (agreement, consistency, bias audit) over 118 runs and approximately 541,000 individual judgments. Four findings emerge, consistent across the full cohort, including the April 2026 frontier: kappa deflation between exact match and Cohen's kappa is universal (33--41 pp on MT-Bench), judge rankings shift by up to 14 positions across benchmarks, high test--retest reliability (>0.95) coexists with severe position bias (>0.10) in two production-deployed judges (instantiating a consistency--bias paradox), and verbosity bias is small (<0.011) across our cohort under a single pairwise rubric. We distill these into a Minimum Viable Validation Protocol.

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.