Same Output, Different Gold: Measuring How Reference Choice Moves a Multilingual Benchmark Score

Preference benchmarks are built by hiring annotators, and the identity of those annotators is treated as an implementation detail. We measure what that detail buys. On the 2,885 MultiPref items where both pools are internally unanimous, so no tie-breaking convention is consulted at all, expert and crowd annotators assign a different majority label to 23.6% and name the opposite winner on 9.2%; on the 246 comparably unanimous MT-Bench cells, benchmark authors and recruited experts differ on 30.5% and reverse on 8.5%. Yet on both corpora the resulting model leaderboards are bit-identical: Kendall tau = 1.00 with zero of six models displaced. That invariance is far weaker evidence than it looks, and we quantify how weak. Switching pools moves a model's win rate by 1.9pp (SD), one adjacent pair in our own leaderboard sits 0.8pp apart and had a 38% chance of swapping, and an item-level bootstrap displaces at least one model in 28% of resamples. The observed zero is the common outcome, not a property of aggregation: on the same measured perturbation, a ten-model leaderboard is displaced with probability 0.86 and a twenty-model leaderboard with probability 0.9997. Reporting a six-model leaderboard is safe; the safety does not generalise, and everything that consumes labels per item is not safe at any size. We make the distinction precise, show that a widely used dataset's stated assumption of no intra-group annotator variability is false, and show that an LLM judge tracks the crowd pool over the expert pool on all three models we test, including one from a different vendor. All code, per-call outputs, and pre-registered decision rules will be released upon acceptance.

Benchmarks scored by an LLM judge routinely adjudicate differences of a tenth of a point, but the resolution of those benchmarks has never been measured. Existing sample-complexity work covers accuracy benchmarks and leaves the judged case open. Treating the system as the object of measurement, we decompose 373,019 judgments into system, item, judge and interaction components using generalizability theory. The central result is structural: under a single judge, generalizability asymptotes to sigma2_s/(sigma2_s+sigma2_sj) regardless of item count, because the system-by-judge term carries no n_i. Items saturate; judges do not. The item cost of a target diverges as the target nears that ceiling. The ceiling is a property of pointwise rubric scoring, not of LLM judging. Run as a pairwise preference in both presentation orders, sigma2_sj falls two orders of magnitude below sigma2_s and the ceiling rises to 0.986 (bootstrap [0.934, 1.000] on 11 systems), so one judge suffices. Pairwise buys a different problem: a system presented first wins 8.6 percentage points more often than the same system presented second, a bias 1.23x the median improvement claimed in the 53 published win-rate comparisons we recovered. Protocol design dominates panel size. Measured floors are 0.41-1.24 points on a 0-5 scale at native item counts, against a median reported improvement of 0.28 points; on the one benchmark recurring often enough for an exactly matched comparison, all 17 recovered MT-Bench improvements fall below MT-Bench's own floor, and 70% of the win-rate claims fall below the pairwise floor. An audit of 628 arXiv papers, double-coded by two independent models and validated against blind human coding (kappa=0.73), finds fewer than one paper in four states whether its evaluation was run more than once, and only 46-67% report uncertainty of any kind.

Multilingual LLM judges produce different evaluator-backbone rankings depending on the prompt language: on an eight-language Agent-as-a-Judge benchmark, the top-ranked backbone alternates across English, Arabic, Chinese, Hindi, Japanese, Spanish, Turkish, and Swahili, and 7 of 15 backbone pairs show statistically significant pairwise rank reversal. We treat this as a measurement problem. The multilingual judge score decomposes additively into task difficulty, backbone skill, and a language-backbone interaction term, the last of which is recoverable without human labels by double-centering the cell-mean score matrix. We make this estimator (Consensus-Based Calibration, CBC) explicit, give an $O(1/\sqrt{n})$ finite-sample concentration bound with variance constant $(1-\tfrac{1}{m})(1-\tfrac{1}{k})$, and show that it is unbiased even when task-language interactions are present. Across 7{,}920 judge runs (6 backbones, 8 languages, 55 tasks, 3 frameworks), CBC raises held-out cross-task rank consistency $τ$ from 0.650 to 0.902 and agrees with the held-out additive-model oracle in 100% of per-language decisions versus 68.5% raw; these are consistency diagnostics, not human-grounded correctness measures. On a separately collected M-RewardBench panel (7 languages, 1{,}500 items per language, 10{,}500 language-item instances, 5 evaluators), panel agreement with the public human gold preferences rises from 68.7% to 76.6% (gain 7.9 percentage points, 95% CI $[6.0, 9.9]$), our strongest external evidence of downstream usefulness. The estimator is the standard two-way ANOVA interaction-recovery operation under sum-to-zero contrasts; our contribution is its application as a label-free post-hoc calibrator for multilingual LLM judges, an explicit finite-sample concentration bound, and an unbiasedness result that holds even under task-language misspecification.