# Minority Sentinel: When to Overturn Majority Voting in Multi-Agent LLM Debates

arXiv: https://arxiv.org/abs/2606.29270 · HTML: https://mlsanity.com/paper/2606.29270/

## Key facts

- Cited by 5 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 8 of its 23 references that are in the map.
- First posted on arXiv 28 Jun 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, 8 of 8)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [MAIN-RAG: Multi-Agent Filtering Retrieval-Augmented Generation](https://mlsanity.com/paper/2501.00332/) (2024)
- [Can LLM Agents Really Debate? A Controlled Study of Multi-Agent Debate in Logical Reasoning](https://mlsanity.com/paper/2511.07784/) (2025)
- [Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information](https://mlsanity.com/paper/2510.01499/) (2025)

## Built on by (most cited first, 5 of 5)

- [Candidate supply and answer selection shape the value of LLM judging in multi-agent systems](https://mlsanity.com/paper/2608.25937/) (2026)
- [Self-Cleaning and Captured Anyway: One Measured Primitive for Error in a Store an Agent Writes to Itself, and What a Falling Score Actually Measures](https://mlsanity.com/paper/2609.25052/) (2026)
- [Unanimity Without Persuasion: A Single Round of Debate Erases the Disagreement That Verification Needs](https://mlsanity.com/paper/2609.26145/) (2026)
- [Social Circuits behind Multi-agent Echo Chambers](https://mlsanity.com/paper/2609.34444/) (2026)
- [Beyond Final Accuracy: Auditing Communication in LLM Multi-Agent Systems](https://mlsanity.com/paper/2610.01042/) (2026)

## Abstract (arXiv)

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.