Multi-agent debate improves LLM reasoning, yet agreement is not evidence of correctness. When agents converge on a wrong answer through social reinforcement, consensus stopping commits that error to automated action with no recourse. We introduce Conformal Social Choice, a post-hoc layer that converts debate outputs into calibrated act-versus-escalate decisions. Verbalized probability distributions from heterogeneous agents are aggregated via a linear opinion pool and calibrated with split conformal prediction, yielding fixed-round marginal coverage: at any pre-specified round, the correct answer is included with probability ≥1-𝛼, without assumptions on individual model calibration. A hierarchical action policy maps singletons to autonomous action and larger sets to human escalation. Across eight MMLU-Pro domains and two additional benchmarks, fixed-round coverage stays close to target. The key finding is not that debate becomes more accurate, but that the conformal layer makes its failures actionable: at the final round, 81.9% of wrong-consensus cases are flagged by non-singleton sets at 𝛼=0.05. Separately, among cases that reach a singleton before the final round, accuracy reaches 90.0–96.8% on MMLU-Pro (up to 22.1pp above consensus stopping): a selection effect, not a reasoning improvement. Simple probability- and entropy-threshold rules attain comparable interception; conformal’s distinct value is a finite-sample fixed-round coverage guarantee together with explicit candidate sets for escalation. Adaptive first-singleton stopping is evaluated empirically and not covered by this guarantee.

The extraction of lung lesion information from clinical and medical imaging reports is crucial for research on and clinical care of lung-related diseases. Large language models (LLMs) can be effective at interpreting unstructured text in reports, but they often hallucinate due to a lack of domain-specific knowledge, leading to reduced accuracy and posing challenges for use in clinical settings. To address this, we propose a novel framework that aligns generated internal knowledge with external knowledge through in-context learning (ICL). Our framework employs a retriever to identify relevant units of internal or external knowledge and a grader to evaluate the truthfulness and helpfulness of the retrieved internal-knowledge rules, to align and update the knowledge bases. Experiments with expert-curated test datasets demonstrate that this ICL approach can increase the F1 score for key fields (lesion size, margin and solidity) by an average of 12.9% over existing ICL methods.