MISP-Bench: Decomposing User-Provided False Priors into Answer, Rationale, and Guard Effects

Large language models in clinical and educational settings routinely receive user-provided context containing incorrect prior beliefs. Existing benchmarks measure aggregate susceptibility to such priors but do not disentangle which structural component (the asserted answer, the supporting rationale, or their combination) drives the damage, nor test whether safety meta-prompts such as "verify the reasoning firs" consistently mitigate it. We introduce MISP-Bench, a factorial benchmark of 1,724 audited multiple-choice items (1,430 MedMCQA medical + 294 GSM8K quantitative) evaluated under 13 prompt conditions across 10 open-weight instruction-tuned models (1B-27B) in chain-of-thought and direct modes, with approximately 1.33M audited response records across three runs per condition. Distractors were generated by GPT-5.4 and the model was excluded from the evaluated set to prevent circular evaluation. Targeted and arbitrary distractor subsets yield similar aggregate Misinformation Damage Index (MDI; accuracy drop relative to a distractor-free baseline) at +19.7 vs +20.4 pp but diverge by 39.1 pp in sycophancy rate (78.4% vs 39.3%). The subsets differ in baseline difficulty, so this is a between-subset composition gap rather than a within-item causal effect. The combined answer-plus-rationale attack exhibits sub-additive saturation (+20.3 pp observed vs +24.5 pp expected under independence; 7/10 models sub-additive, 2 additive, 1 super-additive). Verification-style safety guards split models into three groups by sign at =0.05 (4 reversal, 3 recovery, 3 null), while source-independence and explicit-override guards yield positive recovery in 8/10 and 9/10 models. A six-category audit excludes 770 items, including 732 multi-correct items structurally incompatible with single-best-answer evaluation. The audit list is reusable beyond MISP-Bench. The corpus, response records, notebooks, and audit are released on Hugging Face Datasets (https://huggingface.co/datasets/yh0502/misp-bench) under CC-BY-4.0 (with original-source license inheritance for MedMCQA Apache-2.0 and GSM8K MIT content) with Croissant RAI metadata, with companion code at https://github.com/anon-misp-2026/misp-bench.