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

arXiv: https://arxiv.org/abs/2603.06801 · HTML: https://mlsanity.com/paper/2603.06801/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 30 of 34)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [MedAgents: Large Language Models as Collaborators for Zero-shot Medical Reasoning](https://mlsanity.com/paper/2311.10537/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration](https://mlsanity.com/paper/2307.05300/) (2023)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [Cut the Crap: An Economical Communication Pipeline for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2410.02506/) (2024)
- [Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs](https://mlsanity.com/paper/2311.17371/) (2023)
- [Improving Multi-Agent Debate with Sparse Communication Topology](https://mlsanity.com/paper/2406.11776/) (2024)
- [Examining Inter-Consistency of Large Language Models Collaboration: An In-depth Analysis via Debate](https://mlsanity.com/paper/2305.11595/) (2023)
- [Debate or Vote: Which Yields Better Decisions in Multi-Agent Large Language Models?](https://mlsanity.com/paper/2508.17536/) (2025)
- [Beyond Self-Talk: A Communication-Centric Survey of LLM-Based Multi-Agent Systems](https://mlsanity.com/paper/2502.14321/) (2025)
- [Voting or Consensus? Decision-Making in Multi-Agent Debate](https://mlsanity.com/paper/2502.19130/) (2025)
- [From Skepticism to Acceptance: Simulating the Attitude Dynamics Toward Fake News](https://mlsanity.com/paper/2403.09498/) (2024)
- [MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems](https://mlsanity.com/paper/2404.04735/) (2024)
- [CoMM: Collaborative Multi-Agent, Multi-Reasoning-Path Prompting for Complex Problem Solving](https://mlsanity.com/paper/2404.17729/) (2024)
- [The Truth Becomes Clearer Through Debate! Multi-Agent Systems with Large Language Models Unmask Fake News](https://mlsanity.com/paper/2505.08532/) (2025)
- [The Stepwise Deception: Simulating the Evolution from True News to Fake News with LLM Agents](https://mlsanity.com/paper/2410.19064/) (2024)
- [Forest Before Trees: Latent Superposition for Efficient Visual Reasoning](https://mlsanity.com/paper/2601.06803/) (2026)

## Built on by (most cited first, 3 of 3)

- [The Reasoning Trap: An Information-Theoretic Bound on Closed-System Multi-Step LLM Reasoning](https://mlsanity.com/paper/2605.01704/) (2026)
- [The impact of multi-agent debate protocols on debate quality: a controlled case study](https://mlsanity.com/paper/2603.28813/) (2026)
- [Attention Tax, Handoff Tax: A Stylised Model of When Multi-Agent LLM Systems Help](https://mlsanity.com/paper/2610.06069/) (2026)

## Abstract (arXiv)

Multi-Agent Debate (MAD) has emerged as a promising paradigm for enhancing large language model reasoning. However, recent work reveals a limitation:standard MAD cannot improve belief correctness beyond majority voting; we refer to this as the Martingale Curse. This curse arises because correlated errors cause agents to converge toward erroneous consensus, where debate merely reinforces collective mistakes rather than filtering noise. We propose AceMAD, a framework that breaks the Martingale Curse by harnessing asymmetric cognitive potential energy to transform MAD from a random walk into a directed convergence process with positive drift. Through a peer-prediction mechanism, agents predict their peers' belief distributions, revealing asymmetric cognitive potential: truth-holders not only know the correct answer but also anticipate the crowd's misconceptions, while the hallucinating majority remains blind to their collective error. This asymmetry creates a potential energy gap that we quantify via strictly proper scoring rules. We prove this cognitive potential manifests as information-theoretic superiority and, under nonlinear aggregation, converts into submartingale drift toward truth, directly breaking the Martingale Curse. Experiments on challenging subsets across six benchmarks show AceMAD recovers sparse truth signals even when initial majorities are incorrect, substantially outperforming baseline methods.