Title: Multi-Agent Debate for LLM Judges with Adaptive Stability Detection
Venue: NeurIPS 2025
Accepted: yes
Keywords: LLM-as-Judge

Multi-Agent Debate

Adaptive Stopping
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.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present a framework using collections of LLMs in an interactive turn based debate procedure to address problems of accuracy in evaluation tasks. The procedure is claimed to be better than majority voting schemes and is supported by a strong theoretical model with proofs. While this procedure comes at high cost, the authors have proposed a stability detection framework to recognize when continued processing is unnecessary. Experiments using four different models show the debate algorithm performing better than majority voting on a majority of tasks for two different benchmarks, and they conclude with an analysis of their early stopping criteria.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n+ Paper is well written, and presents a straightforward algorithm, although one that comes at considerable cost.\n+ The early stopping work alone probably suffices to make this worth publication, and this may be useful in other contexts.\n+ Complete details, likely allowing others to reproduce this work.\n\nWeaknesses:\n+ Comparing against just simple majority voting seems like a bit of a straw man, if querying multiple models in parallel or sequentially there's a lot that can be done to increase the yield of a single round, versus the multiple rounds which is extremely expensive.\n+ This paper is quite theoretical yet also uses benchmark results for its claims - this is okay but I'd like the the claims to be clearer between theory and practical.\n\nQUESTIONS:\nI honestly struggled with some of the theoretical parts, and I apologize if my own unfamiliarity gets some of this wrong, but...\n\nL120 - the conditional independence with respect to both Z^(t) and x - this is seems like a very strong assumption and I don't think there's enough support here to justify why this is okay to do, and where it might night be true. Especially marginalizing with respect to x...\n\nL140 - the theta-star \"true\" concept, while it's clear that there is a probability maximizing concept, calling it true seems to demand a bit of luck. My confusion is compounded by the statement in L143 about \"simplifying the space of possible misinterpretations\" - which sounds almost like word salad to me. Can you clarify what you are saying here?\n\nL152 - assuming any independence of agents seems almost certainly to be untrue, as all LLMs invariably are trained upon the same crawled web.\n\nWhile these assumptions enable the proofs, and the establishment of an E-M procedure - it's not clear to me that convergence won't be to some local maximum, so I'm not certain how valuable the theoretical guarantees are, practically speaking.\n\nLIMITATIONS:\nYes. The authors are talking about an incremental improvement over existing uses of LLMs in evaluation tasks, and the risks are generally the same as the prior published works.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe multi-agent ensemble is a common solution to accumulate multiple LLM judgements. However, the multi-agent ensemble can be unreliable in complex or ambiguous cases. Thus, this paper proposes a multi-agent debate judge framework via the debating process. The drawbacks of iterative debating are the expensive computation. As a result, this work proposes a stability detection mechanism based on a time-varying mixture of Beta-Binomial distributions. Comprehensive experiments were conducted across diverse benchmarks, LLM frameworks, and modalities (visual and non-visual tasks), where competitive results were obtained.\n\nSTRENGTHS AND WEAKNESSES:\nStrength\n\n* The paper is generally well written and easy to follow. The examples for the assumptions or concepts benefit the understanding of the paper. \n* The proposed EM algorithm is novel.\n* The experiments are comprehensive.\n\n\nWeakness\n\nSome assumptions are overly strong, and some terms are unclear. \n\n* The assumption in L122 might be too strong, as the agent system can, in fact, access the debate history—unless the previous chat history is not provided for this turn.\n* The assumption in L179 assumes there is at least one initial response generated via the correct concept. What if this response does not exist?\n* Defining the likelihood of one response as a consistency in L159 is somewhat strange. A better explanation is expected.\n\nQUESTIONS:\n* What is the difference between the proposed framework and the related works in the Subsection of \"Multi-agent debate\" between L63 and L76? Could you please discuss the difference from this paper, \"Faithful, Unfaithful or Ambiguous? Multi-Agent Debate with Initial Stance for Summary Evaluation. NAACL 2025\", in terms of method? \n* Have the LLM achieve the maximum token limitation in the experiments?\n* Based on the example in L107, could we understand the latent concepts as the knowledge base?\n* How can we know a true concept?\n* How to understand responsibilities in L213? Are they the confidence score? \n* The performance does not significantly improve in Table 1. How could we know whether the proposed model performs better than SOM?\n* [Suggestion] You may replace the yellow color with another color for better visualization.  \n\nI will improve my score if my concerns are addressed.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a new multi-agent debate framework that iteratively refines\njudgment and has an adaptive stability detection mechanism. This stop mechanism employs a time-varying mixture of Beta-Binomial distributions combined with the Kolmogorov-Smirnov (KS) statistic to identify convergence points for early stopping. Experiments on benchmarks like BIG-Bench, TruthfulQA, and LLMBar show that the approach outperforms majority voting in both accuracy and robustness across various model backbones, including 2.0-Flash, LLaMA-3.1-8B-Instruct, Qwen-2.5-7B-Instruct for language tasks, and Gemma-3-4B-Instruct, LLaMA-3.2-11B-Vision-Instruct, and Qwen-2.5-VL-7B-Instruct for visual tasks.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n-  The use of a debate framework to refine LLM judgments is interesting. The approach leverages their collaborative reasoning potential, offering a new perspective on multi-agent systems.\n\n-  The paper provides a formal mathematical model to establish the debate process's advantage over majority voting under mild assumptions. \n\n- The framework is tested across a wide range of tasks and LLM architectures, highlighting its practical applicability.\n\n### Weaknesses\n**1. Sensitivity to Stability Threshold?** How sensitive is the adaptive stopping mechanism to the chosen stability threshold? For a new model or task, how should this value be set?\n\n**2. Dependence on Assumptions:** The theoretical guarantees rely on assumptions like the existence of a true latent concept and agents' ability to update beliefs based on observed responses. Can the authors discuss a bit more on why this assumption should hold in practical?\n\n**3. Stop mechanism is not really effective?** While adding more complexity, it's not clear how Stop mechanism helps. Table 2 compares adaptive stopping to a full 10-round debate, but previous work shows diminishing returns with more rounds [1, 2]. It would be clear to compared with fixed Stop (e.g., only debate with fewer rounds, such as 3 rounds).\n\n[1] Improving Factuality and Reasoning in Language Models through Multiagent Debate, Du et al., ICML'24\n\n[2] Exploring Collaboration Mechanisms for LLM Agents: A Social Psychology View, Zhang et al., ACL'24\n\n**4. Limited baselines**: While the framework outperforms majority voting, comparisons with other advanced ensemble methods or judgment aggregation techniques are not extensively explored. Did the authors compare the proposed method against some other debate methods, e.g., [1,2,3,4,5,6] ? \n\n[1] CAMEL Camel: Communicative agents for\" mind\" exploration of large language model society\n\n[2] Llm-blender: Ensembling large language models with pairwise ranking and generative fusion\n\n[3] Let models speak ciphers: Multiagent debate through embeddings\n\n[4] Rethinking the bounds of LLM reasoning: Are multi-agent discussions the key?\n\n[5] Encouraging divergent thinking in large language models through multi-agent debate\n\n[6] Socialized learning: making each other better through multi-agent collaboration\n\nQUESTIONS:\n**1. Stop mechanism**: How does adaptive stopping compare to a fixed small number of rounds (e.g., 3)? This would offer a more fair comparison as both method would assume the same number of tokens (on average) across datasets.\n\n**2. Majority vote**: How is majority voting implemented? How many responses are generated per question? For a fair comparison, the token budget should match that of the debate setup (e.g., 7 debaters × 11 rounds = 77 generations for the Majority Vote). Notably, Table 1 shows that majority voting outperforms debate on BIG-Bench and JudgeAnything. Why does it do better on simpler tasks? Does this contradict the paper's main claim?\n\n**Typo**\n- There are 2 \"Response A\"s in the top left box of Fig. 1\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a multi-agent debate framework where multiple LLMs collaboratively refine their judgments through iterative discussion, replacing static aggregation methods like majority voting. The authors provide mathematical formalization using latent concepts and prove theoretical advantages over static ensembles. They introduce an adaptive stability detection mechanism using Beta-Binomial mixture models with Kolmogorov-Smirnov testing to efficiently halt debates when consensus emerges. Experiments across six benchmarks and multiple models show consistent improvements over majority voting while maintaining computational efficiency.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Theoretical Foundation: The paper provides a solid mathematical framework grounded in latent concept theory and Bayesian inference. The formalization of the debate process through latent concepts is well-motivated, and the theoretical proofs (Theorems 4.1 and 4.2) establish clear advantages over static aggregation methods under reasonable assumptions.\n- Comprehensive Experimental Validation: The evaluation spans multiple domains (hallucination detection, alignment evaluation, reasoning, multi-modal tasks), various model architectures (both proprietary and open-source), and includes thorough ablation studies examining ensemble size, temperature effects, and intervention strategies.\n- Practical Relevance: The framework addresses a real need in LLM evaluation systems where single judges can be unreliable and simple aggregation methods fail in complex scenarios.\n\nWeaknesses: \n- There are no baseline comparisons with other multi-agent debate frameworks from the past, despite the authors claiming that their method shows significant improvements in judgment accuracy over those that use majority voting.\n- The accuracy improvements are often modest (1-3 percentage points). For some datasets like BIG-Bench and JudgeAnything, majority voting sometimes matches or slightly exceeds debate performance, questioning the universal applicability.\n- Despite adaptive stopping, the framework still requires multiple model calls and iterative processing, making it computationally expensive compared to single-judge approaches. The scalability to very large ensembles or real-time applications remains unclear.\n- There are limited experimental analysis on the experiment results. The paper is essentially just reporting final accuracy numbers and what is shown in the figures without going beyond and providing meaningful interpretations.\n\nQUESTIONS:\n- Given the modest accuracy improvements and computational overhead, under what specific conditions would practitioners prefer this framework over simpler approaches? Could the authors provide clearer guidelines for when the computational cost is justified?\n- How does the framework perform with larger ensemble sizes (more agents) or longer debate sequences? More analysis of this scalability limitation would strengthen the contribution.\n- In cases where the debate framework performs worse than majority voting, what are the common failure modes?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}