Will the Judge Flip? Predicting Position-Sensitive LLM Judgments from Residual Stream Activations

LLM-as-a-Judge is now widely used to rank model outputs, train reward models, and populate public leaderboards, but its run-to-run reliability remains under-characterized. We study repeated identical evaluations on 29 tasks spanning 10 categories using two OpenAI judge models (GPT-4o-mini and GPT-4.1-mini), with 50 pairwise trials and 50 pointwise trials per question, supplemented by temperature and prompt-sensitivity ablations. Across judges, pairwise preferences flip on average 13.6% of the time, with 28% of questions exceeding a 20% flip rate and one question reaching 56%. GPT-4o-mini also exhibits a significant first-position bias (72% A-majority, p = 0.024). At the same time, mean pointwise score gaps are small (0.19--0.36 on a 10-point scale) and not statistically significant in aggregate, producing a pairwise--pointwise gap: judges frequently choose a winner even when their own scalar scores provide little evidence of a meaningful quality difference. Beyond within-judge instability, cross-judge agreement is only 76% ($κ= 0.51$), semantically equivalent prompt templates change majority outcomes in 25% of tested cases, and deterministic decoding reduces but does not eliminate inconsistency. A reliability curve analysis shows that, in our dataset, 11 repeated trials are needed for a majority vote to recover the 50-trial reference verdict with 95% probability on average, rising to 15 for high-variance questions. These findings suggest that single-trial LLM judging is often too noisy for high-stakes evaluation, and that multi-trial aggregation, position randomization, and explicit uncertainty reporting should be standard practice. Because both judges are from a single provider, cross-provider replication remains an important next step.

LLM judges are often asked to extract criteria and evidence before choosing between candidate answers. This workflow assumes that the intermediate record preserves the information needed for a later verdict. For reasoning-capable models, visible field order does not reveal internal decision order, so we test an observable alternative: persist the evidence in one call and make it the exclusive input to the next. Across 24,000 judgments over HelpSteer3, FeedbackQA, and CoVal, we compare standard pairwise judging, structured one-call judging, two-call evidence locking, and three-call pointwise locking with Claude Sonnet 4.5 and GPT-5. Evidence locking reduces agreement with released human preferences by 4 to 6 percentage points and increases answer-order inconsistency by 8 to 10 points relative to structured one-call judging. Pointwise locking is also harmful, while structured evidence elicitation remains close to standard judging. The result holds for both judges and all three datasets. Persisted evidence can support auditability, but it should not replace the source answers at decision time.

Modern LLM evaluation assumes that pinning a judge to a fixed model version and decoding at temperature zero yields reproducible verdicts. We show this assumption fails as a property of how LLM-as-Judge is operationalized on cloud serving infrastructure, not of any particular model family. Across four frontier judges served via a single major enterprise cloud platform and three standard benchmarks (Arena-Hard, AlpacaEval 2, MT-Bench), identical inputs to the same temperature-zero judge, at a constant serving-reported model version, produce different verdicts across re-runs: per-item flip rates of roughly 5% on average and about 40% on the close-call items that decide leaderboard margins, with a per-judge magnitude spanning a 40x range (0.13% to nearly 10%). We introduce metrics tailored to this instability: per-item flip rate, a two-part stability profile (waver fraction and conditional intensity), and adjacency separability. For the principal judge the aggregate ranking is stable (0% top-K instability, 0% pooled winner flip); what degrades is precision: under a paired hierarchical bootstrap, roughly one-fifth to three-quarters of adjacent leaderboard positions are statistically indistinguishable, a noise floor driven mainly by finite prompt sampling rather than the judge. Across judges, leaderboards agree on the coarse ordering but diverge in the middle (Kendall's tau of 0.42-0.64 between Gemini and Sonnet judges on Arena-Hard, values sensitive to answers truncated at the generation cap). Of 15 expected head-to-head orderings we re-judge, 12 survive every re-run of the principal judge but only 8 survive every judge. Leaderboards thus report unhedged point estimates that overstate their precision. We propose a minimal, low-cost reporting protocol: several judge re-runs, published stability profiles and adjacency intervals, and results under at least two judges from different families.