Breaking the Martingale Curse: Multi-Agent Debate via Epistemic Asymmetry

Multi-Agent Debate (MAD) is a widely used approach to improving the reasoning of large language models (LLMs), but it can fail when agents make correlated errors and converge on the same wrong answer. Under symmetric, linear belief aggregation, the aggregate belief in the correct answer is a martingale: its expectation does not change across rounds, so debate cannot recover from an incorrect initial majority. We refer to this limitation as the Martingale Curse. We propose AceMAD, a protocol that exploits an epistemic asymmetry between two kinds of agents. Anchored Agents follow the base model's dominant reasoning path and tend to assume that their peers share their view; Exploratory Agents are perturbed away from that path and, when they recognize the majority's error, can anticipate it. AceMAD elicits this second-order information through peer prediction: every agent also predicts the average belief of its peers, the prediction is scored with a Brier-type proper score (the ACE Score), and agents with better-calibrated predictions receive multiplicatively larger influence (ACE Reweighting). We prove that, when Exploratory Agents maintain a persistent score advantage (an ACE Gap), the aggregate belief becomes a submartingale with positive drift toward the correct answer. On challenging subsets of six benchmarks, AceMAD recovers correct minority answers under correlated errors and outperforms majority voting and existing MAD protocols.