From Debate to Decision: Conformal Social Choice for Safe Multi-Agent Deliberation

Abstract

Multi-agent debate improves LLM reasoning, yet agreement among agents is not evidence of correctness. When agents converge on a wrong answer through social reinforcement, consensus-based stopping commits that error to an automated action with no recourse. We introduce Conformal Social Choice, a post-hoc decision 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 prediction sets with a marginal coverage guarantee: the correct answer is included with probability ${\geq}\,1{-}\alpha$, without assumptions on individual model calibration. A hierarchical action policy maps singleton sets to autonomous action and larger sets to human escalation. On eight MMLU-Pro domains with three agents (Claude Haiku, DeepSeek-R1, Qwen-3 32B), coverage stays within 1--2 points of the target. The key finding is not that debate becomes more accurate, but that the conformal layer makes its failures actionable: 81.9% of wrong-consensus cases are intercepted at $\alpha{=}0.05$. Because the layer refuses to act on cases where debate is confidently wrong, the remaining conformal singletons reach 90.0--96.8% accuracy (up to 22.1pp above consensus stopping) -- a selection effect, not a reasoning improvement. This safety comes at the cost of automation, but the operating point is user-adjustable via $\alpha$.