Multi-Agent Debate (MAD) with Majority Voting is a dominant paradigm for improving LLM reasoning, yet its effectiveness rests on the Condorcet Jury Theorem's assumption of independent errors. Because contemporary LLMs share similar pretraining corpora, their errors are strongly correlated, causing the majority to systematically suppress correct minority opinions, a phenomenon we term Minority Truth. Through debates among three heterogeneous LLM agents on six benchmarks, we find that roughly one in four divergent cases has the minority holding the correct answer, yielding a 10-percentage-point theoretical recovery margin. We propose Minority Sentinel, a lightweight meta-classifier that extracts a multi-dimensional debate fingerprint from debate logs and trains a LightGBM model to decide when to overturn majority voting. Minority Sentinel achieves a stable Flip Precision of 81.2% with positive Net Gain across all six datasets and all 20 random seed trials, demonstrating that debate logs contain sufficient behavioral signals for a non-LLM classifier to reliably recover suppressed minorities without degrading system accuracy. The LLM-as-Judge baseline yields negative Net Gain despite higher recall, confirming that flip safety, not recovery volume, determines intervention value.
Majority voting is the default unsupervised aggregator for multi-sample LLM inference, but it discards two signals: within-group answer entropy and between-group reasoning geometry. We aggregate by delegation instead (Propagational Proxy Voting, PPV): each group of samples keeps weight on its own answer in proportion to its entropy-based confidence (When) and routes the rest to peers by reasoning-embedding similarity (Whom); the stationary distribution of the resulting delegation matrix picks the consensus answer. This requires neither gold labels nor training. On MMLU-Pro with 128 samples per question, delegation beats majority by +1.5 pp overall and +2.24 pp on non-trivial questions (McNemar p ~ 1.0e-14, n = 8,099), overturning wrong majorities whose answer cluster is geometrically incoherent while the correct minority is tight. We then characterize exactly when delegation overturns majority: a two-option model gives a closed-form flip condition on each option's confidence and the weight it routes to the other, with a do-no-harm corollary for near-unanimous questions. The condition calls the realized winner on 96.5% of non-trivial questions, and its predicted mass gap tracks the realized gap at r = 0.97. We did not find any other unsupervised ensemble methods that close the oracle gap.
Multi-agent systems (MAS) can substantially extend the reasoning capacity of large language models (LLMs). Most MAS frameworks aggregate agent outputs via simple majority voting, discarding the evidential structure of reasoning traces. Majority voting is brittle under confabulation consensus, where agents share correlated biases and converge on the same incorrect rationale. We introduce AgentAuditor, which moves beyond frequency-based aggregation by organizing agent traces into a Reasoning Tree that explicitly represents agreements and divergences in their reasoning. AgentAuditor resolves conflicts by comparing branch-level evidence at critical divergence points, turning global adjudication into efficient, localized verification. We further propose Anti-Consensus Preference Optimization (ACPO), which trains the adjudicator with evidence-verified preference supervision to reduce conformity to misleading majority cues. Across four MAS frameworks and multiple reasoning benchmarks, AgentAuditor consistently improves aggregation performance over majority voting, with gains of up to 5% absolute accuracy while remaining token-efficient.
When should a language model answer directly, sample and vote, or engage in multi-agent debate? Recent work shows voting often explains much of the gain attributed to debate, while selective-debate systems activate deliberation only on uncertain examples. We ask: under a matched ceiling on generated tokens (960 per example), how much per-example routing headroom exists, and how much is recoverable from cheap pre-deliberation signals? We evaluate greedy decoding, three-sample voting, and a two-agent critique-revise debate on MuSiQue and GSM8K using Llama 3.1 8B Instruct and Ministral 3 8B Instruct. On MuSiQue, an oracle selecting the correct protocol per example gains +14.0 and +13.7 pp over the best fixed one. The best fixed protocol is model- and dataset-dependent: each (model, dataset) cell has a different winner. This headroom is hard to recover from cheap ex-ante signals. A vote-entropy threshold is the only controller that directionally beats the best fixed protocol on both models (+1.3 and +1.7 pp), though individual paired-bootstrap CIs include zero. A joint analysis (meta-analysis +1.6 pp, p=0.125; Bayesian P(both>0)=0.59) is directionally consistent but not significant. Learned controllers (LR, GBT) do not outperform the threshold. The key finding is structural: vote entropy predicts where debate is safe, not where debate is needed. High entropy sharply reduces debate backfire, but 66% of debate-helpful examples (31/47) occur when voting is unanimous but wrong. A single-prompt self-critique probe on Llama flips the answer in 127/127 unanimous cases, yielding zero mutual information with the debate-helpful label; we cannot rule out a prompt-compliance artifact, but either interpretation disqualifies the probe as a router. Recovering the remaining headroom requires behavioral probes that avoid format-compliance confounds at the 8B scale.