Diagnosing LLM Judge Reliability: Conformal Prediction Sets and Transitivity Violations

TL;DR

This paper introduces diagnostic tools for assessing the reliability of LLM-based judges in NLG evaluation, revealing inconsistencies and proposing conformal prediction sets for per-instance reliability measurement.

Contribution

It presents a transitivity analysis and conformal prediction methodology to evaluate and improve the reliability of LLM judges, with theoretical guarantees and cross-judge agreement evidence.

Findings

Widespread per-input inconsistency masked by low aggregate violation rates

Prediction set width correlates with document difficulty and shows cross-judge agreement

Relevance is judged most reliably, while fluency and consistency are less reliable.

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.