Label Agreement Does Not Measure Authorization

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.

Reliable evaluation of inter-annotator agreement (IAA) is important for assessing the consistency of annotation processes. While established IAA metrics such as Cohen's kappa, Fleiss' kappa, and Krippendorff's alpha are commonly applied in single-label settings, multi-label tasks require additional decisions about how full label sets, joint selections, and joint omissions should be compared. In this work, we present Multi-Label Agreement (MLA), a flexible framework for evaluating agreement in multi-label annotation tasks. MLA preserves the full binary label vectors assigned to each item and uses average pairwise Hamming agreement, thereby accounting for both joint selections and joint omissions. Its pooled-marginal form is not a mathematically independent coefficient: it is a chance-disagreement-weighted average of label-wise Fleiss/Scott-type coefficients and is closely related to Krippendorff's alpha with normalized Hamming distance. The framework supports pooled-marginal, Gwet AC1, and fixed-baseline normalizations, yields item-level, label-level, and corpus-level results, and includes a conditional minimum-agreement diagnostic. Through a worked example and Monte Carlo simulations, we show how the resulting values depend on label prevalence, the declared label inventory, and the selected model of expected agreement. We also provide a Python implementation. MLA thus offers a transparent and interpretable framework for multi-label agreement analysis without claiming that one normalization is universally preferable.

LLM judges are increasingly deployed as panels, and disagreement among panel members is often read as a symptom of an unclear rubric. We test a label-free procedure that turns this disagreement into rubric repairs. The procedure decomposes each rubric into sub-criteria, ranks them by cross-judge disagreement on a development split, and has an editor model rewrite only the most contested ones. An additional stage that moves text-checkable sub-criteria to deterministic checkers transferred none in our evaluation. Human labels are never used to select or edit clauses; they are used only to evaluate the outcome. We pre-specified four hypotheses in a version-controlled protocol and evaluated six rubric conditions with a panel of five judges from three providers on SummEval, the HealthBench meta-evaluation, and USR Topical-Chat, for a total of 129,770 judge requests, excluding retries. On SummEval, the procedure raised inter-judge Krippendorff's $α$ by 0.069 (95% CI 0.046 to 0.092) over the original rubric and by 0.074 over a control that applied the same edits to an equal number of randomly chosen clauses that were not selected. Agreement with expert ratings showed no detectable change (Kendall $τ$ difference -0.007, 95% CI -0.037 to 0.021). On HealthBench and USR, neither inter-judge agreement nor human agreement met the preregistered effect criteria. In a preregistered secondary comparison, human agreement after editing the contested clauses was lower than after editing the control clauses on all three datasets in point estimate, although no interval excluded zero. Selecting clauses by disagreement makes judges agree with each other more than editing arbitrary clauses does, but in our setting the added consensus did not bring the judges closer to human annotators. We will release code, frozen rubrics, item identifiers, and judge scores.