Where Cross-Question Structure in LLM Errors Comes From: Shared Seeds, Shared Prompts, and Answer-Letter Preference

Language models now answer questions alongside other claims: a note in the system prompt, a message from another agent, their own earlier answer. We ask what it takes to talk a model out of an answer it gets right on its own, and separate three factors that earlier studies vary together: where the advice sits in the prompt, who is said to have written it, and what the model has already written. On Qwen3.5-27B and four-option MMLU-Pro items, with the rest of the advice held fixed in each comparison, we find three things. First, position matters far more than the API channel, in opposite directions for a bare claim and an argument: a bare "the answer is X" does most harm just before the model answers, while the same claim with a false rationale does most harm before the question, where it raises error on items the model otherwise almost never misses from 1% to 67%; moving the claim between the system message and the user message at the same position changes error by a few points. Second, attributing the note to an authority rather than to another participant, and phrasing it assertively, each raise error by 10-27 points, while the two authorities we tested differ by under two. Third, replaying a correct worked answer before the advice protects it whether the text is shown as the model's own or as someone else's, and the same replay keeps wrong answers from being corrected by a bare correct note. The position result replicates under an independently written prompt. Code, items and all result tables are released at https://github.com/coolkillercat/safety.

Large language models (LLMs) are powerful black-box systems, making it difficult to discern whether their answers reflect stable internal beliefs or superficial pattern matching. We identify cross-contextual consistency as an underutilized behavioral property of LLMs: a credible answer should remain stable when the same task is placed under topic-aligned, content-neutral contextual variation. Building on this intuition, we operationalize Cross-Contextual Consistency (C3) by comparing model generations under original and perturbed prompts. Across 26 models and six benchmarks spanning reasoning, factuality, and code generation, we find that answers with smaller cross-contextual shifts are more likely to be correct or factual. We demonstrate that C3 provides a complementary axis of evaluation and can serve as a benchmark usefulness diagnostic, identifying which portions of a benchmark remain informative even when aggregated scores are widely considered "saturate".

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model's score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.