Breaking the Martingale Curse: Multi-Agent Debate via Asymmetric Cognitive Potential Energy

Summary

Names and formalizes the Martingale Curse - standard multi-agent debate cannot improve belief correctness beyond majority voting because correlated errors drive convergence to erroneous consensus - and proves that only nonlinear aggregation can convert an informational asymmetry into submartingale drift toward truth. The mechanism is a peer-prediction step in which agents forecast peers' belief distributions, scored with strictly proper scoring rules, so truth-holders are identifiable because they anticipate the crowd's misconceptions. This supplies a rigorous impossibility-style baseline for the aggregation dimension: it tells the paper which aggregation rules cannot in principle beat voting, which sharpens the contrast between voting, debate and synthesis.

Contribution

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Method

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Relevance to RISE

Surfaced by the 2026-09-07 literature sweep as a high-priority candidate for the Architecture as Epistemology (ISR) paper (angle: aggregating LLM judgments; correlated errors / homogeneity across LLM agents). Verified against: Opened https://arxiv.org/abs/2603.06801 (arXiv abstract page; confirmed title, 7 authors, cs.AI, v1 6 Mar 2026, full abstract read)

Critique / open questions

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Key quotes

Multi-Agent Debate (MAD) has emerged as a promising paradigm for enhancing large language model reasoning. (abstract)

However, recent work reveals a limitation:standard MAD cannot improve belief correctness beyond majority voting; we refer to this as the Martingale Curse. (abstract)