Metric Match: A Subset Selection Approach to Evaluating LLM Judge Reliability

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.

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-judge frameworks are increasingly used for automatic NLG evaluation, yet their per-instance reliability remains poorly understood. We present a two-pronged diagnostic toolkit applied to SummEval: $\textbf{(1)}$ a transitivity analysis that reveals widespread per-input inconsistency masked by low aggregate violation rates ($\barρ = 0.8$-$4.1\%$), with $33$-$67\%$ of documents exhibiting at least one directed 3-cycle; and $\textbf{(2)}$ split conformal prediction sets over 1-5 Likert scores providing theoretically-guaranteed $\geq(1{-}α)$ coverage, with set width serving as a per-instance reliability indicator ($r_s = {+}0.576$, $N{=}1{,}918$, $p < 10^{-100}$, pooled across all judges). Critically, prediction set width shows consistent cross-judge agreement ($\bar{r} = 0.32$-$0.38$), demonstrating it captures document-level difficulty rather than judge-specific noise. Across four judges and four criteria, both diagnostics converge: criterion matters more than judge, with relevance judged most reliably (avg. set size $\approx 3.0$) and coherence moderately so (avg. set size $\approx 3.9$), while fluency and consistency remain unreliable (avg. set size $\approx 4.9$). We release all code, prompts, and cached results.