Haochen Xie

Mengdie Flora Wang, Haochen Xie, Guanghui Wang et al.

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 ${\geq}\,1{-}α$, 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 $α{=}0.05$. 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 $α$.

Mengdie Flora Wang, Haochen Xie, Guanghui Wang et al.

Multi-agent deliberation among LLMs can improve reasoning, but deployment requires deciding when the current answer is reliable enough to act on and when it should be escalated to human review. We formulate this as budgeted act-or-defer decision making. At each round, the system maps the debate prefix to a low-dimensional state, computes a $k$-nearest-neighbor lower confidence bound on state-conditional correctness using calibration data, and acts only when the bound exceeds a user-specified reliability threshold. The certificate controls wrong actions through the decomposition $β= δ+ α+ \varepsilon_{\mathrm{act}}$, separating calibration failure, residual action risk, and representation gap. The guarantee is conditional, not distribution-free: it relies on a valid local bias envelope and an action-region representation-gap bound, and each assumption is paired with falsification-style diagnostics. Because the same absolute wrong-action budget has different meanings across tasks of different difficulty, we set budgets relative to each task's final-round error using training data only, and evaluate safety by normalized budget usage $\mathrm{WA}/β$. On six benchmarks against nine baselines, the method uses 9--12% of the pre-declared budget on activated datasets, reaching up to 84% automation and 96% acted-on accuracy; on stress-test datasets, it defers rather than forcing unreliable automation. Rather than relying on per-task post-hoc threshold search, the method prospectively converts a user-declared wrong-action budget into an auditable act-or-defer operating point before deployment, under explicitly stated assumptions.