Abstract
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 (\bar{\rho} = 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{-}\alpha) 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.
