Multi-Agent Debate for LLM Judges with Adaptive Stability Detection

TL;DR

The paper introduces a multi-agent debate framework for LLM-based judgments, enabling collaborative reasoning and iterative refinement to surpass static majority voting. A stability-detection mechanism based on a time-varying Beta-Binomial mixture and Kolmogorov-Smirnov testing adaptively terminates debates to save computation. The authors provide theoretical results showing that debate improves accuracy under mild assumptions and empirically validate gains across diverse benchmarks and models, including multi-modal tasks. The approach offers a principled path to robust, scalable LLM judging with quantified consensus dynamics and efficiency gains.

Abstract

With advancements in reasoning capabilities, Large Language Models (LLMs) are increasingly employed for automated judgment tasks. While LLMs-as-Judges offer promise in automating evaluations, current approaches often rely on simplistic aggregation methods (e.g., majority voting), which can fail even when individual agents provide correct answers. To address this, we propose a multi-agent debate judge framework where agents collaboratively reason and iteratively refine their responses. We formalize the debate process mathematically, analyzing agent interactions and proving that debate amplifies correctness compared to static ensembles. To enhance efficiency, we introduce a stability detection mechanism that models judge consensus dynamics via a time-varying Beta-Binomial mixture, with adaptive stopping based on distributional similarity (Kolmogorov-Smirnov test). This mechanism models the judges' collective correct rate dynamics using a time-varying mixture of Beta-Binomial distributions and employs an adaptive stopping criterion based on distributional similarity (Kolmogorov-Smirnov statistic). Experiments across multiple benchmarks and models demonstrate that our framework improves judgment accuracy over majority voting while maintaining computational efficiency.

Figures (5)

• Figure 1: Multi-Agent Debate Framework.
• Figure 2: Judge consensus dynamics during debate. Top: Correct agent distributions across three rounds on JudgeBench, showing convergence to unanimous agreement. Bottom: Fitted Beta-Binomial mixture model closely matches empirical distributions for Llama-3.1-8B.
• Figure 3: KS statistics across ten debate rounds for six datasets. The x-axis shows steps between rounds, the y-axis shows KS values, and the red dotted line marks the stability threshold ($\epsilon = 0.05$).
• Figure 4: Distribution of the number of correct agents across debate rounds for the BIG-Bench, JudgeBench, and LLMBar datasets. Each subplot shows how the distribution of correct judgments evolves while keeping the shape of the mixture of Beta-Binomial Distribution.
• Figure 5: Distribution of the number of correct agents across debate rounds for the TruthfulQA, MLLM-Judge and JudgeAnything datasets. Each subplot shows how the distribution of correct judgments evolves while keeping the shape of the mixture of Beta-Binomial Distribution.

Theorems & Definitions (6)

• Lemma 3.1: Response Generation Model
• Theorem 4.1: Consistent Response Amplification
• Lemma 4.1: Accuracy Increases with Posterior Belief
• Theorem 4.2: Debate Improvement over Majority Vote
• proof
• proof