Debate or Vote: Which Yields Better Decisions in Multi-Agent Large Language Models?

TL;DR

This paper investigates whether multi-agent debate or simple majority voting leads to better decision-making in large language models, finding that voting often accounts for most performance gains and debate's theoretical benefits are limited.

Contribution

The study disentangles debate and voting in multi-agent LLMs, providing a theoretical framework and empirical analysis showing voting's dominance and debate's limited effectiveness.

Findings

Majority voting explains most MAD performance gains

Debate modeled as a stochastic process with martingale properties

Simple ensembling often outperforms complex debate strategies

Abstract

Multi-Agent Debate~(MAD) has emerged as a promising paradigm for improving the performance of large language models through collaborative reasoning. Despite recent advances, the key factors driving MAD's effectiveness remain unclear. In this work, we disentangle MAD into two key components--Majority Voting and inter-agent Debate--and assess their respective contributions. Through extensive experiments across seven NLP benchmarks, we find that Majority Voting alone accounts for most of the performance gains typically attributed to MAD. To explain this, we propose a theoretical framework that models debate as a stochastic process. We prove that it induces a martingale over agents' belief trajectories, implying that debate alone does not improve expected correctness. Guided by these insights, we demonstrate that targeted interventions, by biasing the belief update toward correction, can meaningfully enhance debate effectiveness. Overall, our findings suggest that while MAD has potential, simple ensembling methods remain strong and more reliable alternatives in many practical settings. Code is released in https://github.com/deeplearning-wisc/debate-or-vote.