Abstract
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 ${\geq}\,1{-}\alpha$, 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 $\alpha{=}0.05$. 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.
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URL
https://arxiv.org/abs/2604.07667
