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Multi-Agent Debate for LLM Judges with Adaptive Stability Detection

🕒 Published (v1): 2025-01-01 · Source: NeurIPS · Venue: NeurIPS 2025 · link

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TL;DR

Proposes a multi-agent debate framework where LLMs iteratively refine evaluation judgments, paired with a statistically-grounded adaptive stopping mechanism that halts debate when judge consensus stabilizes. The framework is formally proven to outperform majority voting under mild assumptions, and experiments across six benchmarks confirm accuracy gains with reduced compute.

Problem

Static aggregation methods (majority voting, averaging) for LLM-as-a-Judge ensembles fail in ambiguous or complex cases where agents share biases or the correct answer is a minority opinion. Fixed-round debates waste compute when consensus is reached early or terminate prematurely. No prior work provides a theoretically grounded, computationally efficient multi-agent debate mechanism for evaluation tasks specifically.

Method

Debate process: n agents each generate an initial judgment; in each subsequent round, all agents observe the full debate history and update their response. Debate terminates on unanimous consensus or after T rounds (majority vote fallback). The framework is formalized via a latent concept space Θ: agent responses are modeled as Bayesian posteriors over latent concepts, enabling belief propagation across agents.

Stability detection: Judge collective accuracy per round is modeled as a time-varying mixture of two Beta-Binomial distributions (capturing bimodal high/low-competence regimes). Parameters are estimated via EM (E-step: responsibility weights; M-step: L-BFGS-B on Beta-Binomial parameters). Stability is detected by computing the Kolmogorov–Smirnov statistic D^t between the CDFs of consecutive rounds; debate halts when D^t < 0.05 for two consecutive rounds.

Theory: Under four Bayesian assumptions (true concept predictiveness, task-concept alignment, positive priors, independent agent responses) plus an initial-seed assumption, two theorems are proven: (1) a single strongly-consistent response in round t raises expected correctness in round t+1 (Consistent Response Amplification); (2) the final debated outcome strictly exceeds initial majority vote accuracy.

Key Contributions

  • Formal latent-concept probabilistic framework for multi-agent LLM debate with correctness proofs over static ensembles
  • Time-varying Beta-Binomial mixture model for tracking judge accuracy dynamics, estimated via EM
  • KS-statistic adaptive stopping criterion that reduces debate rounds without significant accuracy loss
  • Empirical validation across 6 benchmarks (TruthfulQA, JudgeBench, LLMBar, BIG-Bench, MLLM-Judge, JudgeAnything) with both visual and non-visual tasks

Results

  • LLMBar: Gemini-2.0-Flash improves from 77.75% (majority vote) → 81.83% (debate); Qwen-2.5-7B from 66.22% → 69.81%
  • TruthfulQA: Gemini-2.0-Flash 72.01% → 74.30%; Llama-3.1-8B 53.94% → 55.34%
  • JudgeBench: Gemini-2.0-Flash 66.13% → 68.06%
  • BIG-Bench / JudgeAnything: Debate offers no improvement or slight regression vs. majority vote (e.g., Llama-3.1-8B BIG-Bench: 81.80% → 74.00%), consistent with the theory that debate adds value only in high-variance, complex tasks
  • Adaptive stopping (Table 2): Terminates in 2–8 rounds (vs. 10 max) with accuracy drops of ≤0.67 percentage points across all models/benchmarks; ensemble size 7 identified as optimal

Limitations

  • Accuracy gains are inconsistent and sometimes negative on simpler tasks (BIG-Bench, JudgeAnything), limiting universal applicability
  • Assumes at least one agent generates a correct initial response (Assumption 4.5); framework degrades when this fails
  • Independent agent response assumption (Assumption 4.4) is violated when agents share training data or exhibit shared biases, which is common in practice with same-family models
  • Stability detection threshold (ε = 0.05, 2 consecutive rounds) is empirically chosen rather than theoretically derived
  • All experiments use homogeneous ensembles of the same model; cross-model heterogeneous debate is not evaluated

Relevance to Agentic AI / LLM Agents

Multi-agent debate is a core coordination primitive for agentic systems that require reliable judgment—fact verification, self-critique, reward modeling, and tool-use evaluation. This work directly addresses the failure mode of majority-vote aggregation in LLM judge ensembles, which underlies many agentic evaluation and RLHF pipelines. The adaptive stopping mechanism is practically important for inference-time compute budgeting in multi-agent loops. The theoretical grounding via latent concept Bayesian updating offers a principled account of why iterative agent interaction improves over independent sampling, relevant to understanding emergent correctness in collaborative agent networks.