Language Models Agree With Each Other, Not With Readers

A benchmark score means nothing without knowing what a trivial method achieves and what the best possible method could achieve. We construct both bounds for a task with a rare kind of ground truth: predicting which sentences a crowd of readers -- highlighting for their own purposes, unpaid, uninstructed, and blind to each other -- marked in 120 web documents. The floor is naive truncation (lead); the ceiling is a split-half oracle: half the crowd predicting the other half. The gap between them is +0.2028 AP [+0.1698, +0.2342, domain-clustered], and three findings structure it. First, the gap is semantic: position and length features recover 5% of it. Second, frontier language models reach 35-53% of it zero-shot -- far above classical baselines, far below the crowd; a state-of-the-art prompt compressor (LLMLingua-2) lands below the floor, indistinguishable from random selection. Third, an unweighted cross-vendor fusion of five frontier rankings plus a position prior reaches 60%, beating the best single model by +0.0159 [+0.0044, +0.0269; Holm p=0.019] -- a gain that survives ablation of its best member, split-half arm selection, prompt paraphrase, and label, gate, and seed perturbations, and was CONFIRMED by a pre-registered replication on 217 independent documents (+0.0179, Holm p=0.042). Finally, the bracket compresses: distilling the fusion into one open-weight 8B student that reads the whole document retains 90% of the fusion's edge and reaches statistical parity with the strongest single frontier model (+0.0070 [-0.0068, +0.0200]), where a local-context student retains only 63% -- the crowd's signal lives in document-level structure, and the cheapest known improvement is to ask several different models and average.

Context compression discards most of a document before a language model reads it, and is normally evaluated by downstream task accuracy - which makes another model the judge of what mattered. Naturalistic social highlighting offers a non-circular reference: many people independently marking passages on the same page. But the obvious metric, the fraction of crowd-marked sentences a compressor keeps, is confounded twice: crowd marks are front-loaded and crowd-marked sentences are longer, so any method favouring early or long sentences scores well regardless of readers. We remove both by matching each marked sentence against unmarked sentences of the same document at equal relative depth and equal within-document length rank, and we calibrate every estimator on synthetic nulls built from position and length alone - a step that matters, since depth-only stratification returns a false positive on 20-36% of nulls containing no effect. On 120 web documents (at least 12 independent readers each), a language-model importance ranking keeps 38.4% of crowd-marked sentences against 19.9% of their matched neighbours: an enrichment of +0.196 [+0.148, +0.239], at p = 0.0005 under an exact randomization test that assumes nothing about clustering, and replicated cross-vendor. Naive truncation, whose keep rule is position, correctly falls to +0.003. To give the number a scale: scored identically, on the same budget, against a crowd label recomputed to exclude them, a single human reader reaches +0.182 - indistinguishable from GPT-5.4 (+0.002 [-0.081, +0.088]) and below Claude Opus 5. Classical methods are not null - Luhn's 1958 heuristic reaches +0.088 - so reader selection is partly recoverable by counting words; conditioning additionally on lexical centrality removes only 0.010, so the agreement is not centrality. We also report that a claim in our own prior work does not reproduce on this corpus.

Agreement among repeated samples of a language model is routinely read as evidence about answer reliability, yet wrong answers can agree just as strongly as right ones. This paper asks what information wrong-consensus agreement actually contains, and answers with a quantitative decomposition. A pluralistic agreement index Gamma, normalized by the reference scale d=(1-p)/(C-1), is split into a mechanical component (agreement delivered by a per-case answer preference alone) and a preference-unexplained residual. The mechanical reference is leak-free: each case's preference and accuracy are estimated from its other runs only. On public GPT-4.1 per-run data, coverage phi (the mechanical/empirical ratio) shows a benchmark-associated direction: 0.81-0.93 on multiple-choice GPQA-Diamond against 0.59-0.78 on open-domain AIME, where a residual of 1.54-2.80 Gamma units survives, more than absorbed by a calibrated run-level preference-heterogeneity reference. A controlled replication under one fixed protocol (four runs per question, K=32 votes) on five open-weights checkpoints (Qwen3.5-9B/122B, Qwen3.8-27B, Gemma4-26B/31B) finds near-complete mechanical coverage in all ten cells (phi approximately 1, with a small overshoot consistent with a quantified finite-donor plug-in bias), robust to a two-run design; the largest cell (qwen3.5-122b, p=0.222) sits inside the GPT-4.1 AIME accuracy range and still saturates (phi=1.041). A cross-system contrast at comparable aggregate accuracy contrasts near-complete mechanical agreement in the open-weights models against a larger preference-unexplained residual in the frontier family. This contrast is confounded with sampling protocol by design. Agreement is graded evidence, not certification. No new voting method is proposed; code and evidence are committed.