Title:Agreement Metrics for LLM-as-Judge Evaluation: What to Report and Why

Abstract:Validating an LLM judge against human annotations usually means reporting several agreement statistics: accuracy, precision, recall, $F_1$, Cohen's $\kappa$, 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 $\rho$, Kendall's $\tau_b$, the phi coefficient $\phi$, 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 $\kappa$ is the one agreement coefficient that adds information: it shares $\phi$'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' $\kappa$ or Krippendorff's $\alpha$. 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.

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