When Models Disagree: Rethinking LLM Evaluation for Public Comment Analysis

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.

Imagine two users interact with the same LLM. One has been told it is the cutting-edge flagship model; the other, an older, weaker model. They walk away with markedly different ratings of its usefulness and intelligence, yet they used the same model. In a controlled study, 162 participants each used one of six LLMs from two families across three collaborative tasks, after first viewing a landing page that matched, overstated, or understated their model's true capability. This pre-interaction framing shifted user opinions and interaction behavior while task performance did not. Oversold users rated the model more favorably and used more directive prompting, while Undersold users wrote longer, more collaborative prompts. The quality of what users and the model produced together depended only on the model's true capability, not on what users were told. Participants' change in model impressions after use, measured across two impression measures, was not predicted by task performance ($β= -0.01$ and $0.11$, both n.s.), but by whether the model met users' expectations ($β= 0.47$ and $0.50$, both $p < .001$) and how confident they felt working with it ($β= 0.47$ and $0.36$, both $p < .001$). After interaction, users are still rating the pitch, not the product: user-elicited LLM evaluations, including the preference data driving public leaderboards, measure expectation management at least as much as the model itself.

LLM-as-a-judge panels aggregate votes from multiple models, with the expectation that diverse models yield more reliable evaluations. We develop a framework to measure the true informational value of such panels and quantify how far their reliability falls short of the independent-voting ideal. Testing a panel of 9 frontier LLMs from 7 model families on three natural language inference datasets (each with 100 human annotations per item), we find that the 9 judges effectively provide only about 2 independent votes' worth of information. Roughly three-quarters of the panel's nominal independence is lost because the models make the same mistakes on the same items. The consequences are stark: the panel's actual accuracy falls 8-22 percentage points short of what independent voting would achieve, and the best single judge matches or outperforms the full panel across all conditions. Neither adding more judges nor using smarter aggregation algorithms helps -- established methods close at most 11% of this gap, even with access to the correct answers. We quantify these findings using the Kish effective sample size (n_eff) and a Condorcet null model, and show the deficit is robust across prompt variants, temperatures, chain-of-thought reasoning, and a pairwise preference task (RewardBench). The bottleneck is correlated judges, not the aggregation algorithm, implying that scaling up panels cannot substitute for genuinely independent evaluation.