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Demystifying Multi-Agent Debate: The Role of Confidence and Diversity

Xiaochen Zhu, Caiqi Zhang, Yizhou Chi, Tom Stafford, Nigel Collier, Andreas Vlachos

arXiv:2601.19921v3cs.CLcs.AI

TL;DR

Vanilla MAD can underperform majority vote, and its homogeneous-agent, unweighted-update dynamics preserve expected correctness. The paper adds diversity-aware initialization and confidence-modulated updates; across six reasoning-oriented QA benchmarks, these methods consistently outperform vanilla MAD and majority vote.

  • Problem

    Vanilla MAD can underperform majority vote, while standard protocols lack diverse initial viewpoints and explicit, calibrated confidence communication.

    Source: §1 · pp. 1–2

  • Method

    The paper selects a more diverse initial answer pool and trains agents to express calibrated confidence and condition debate updates on others’ confidence.

    Source: §1 · p. 2, §4.2 · p. 5

  • Results

    Across six reasoning-oriented QA benchmarks, the methods consistently outperform vanilla MAD and majority vote.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The work connects human deliberation theory with LLM-based debate and offers guidance for designing more effective multi-agent systems.

    Source: §1 · p. 2, §8 · p. 8

    The theoretical analysis relies on the Dirichlet–categorical debate model and homogeneity assumptions, which do not fully capture real LLM behavior.

    Source: Limitations · p. 9

Abstract

from arXiv · show

Multi-agent debate (MAD) is widely used to improve large language model (LLM) performance through test-time scaling, yet recent work shows that vanilla MAD often underperforms simple majority vote despite higher computational cost. Studies show that, under homogeneous agents and uniform belief updates, debate preserves expected correctness and therefore cannot reliably improve outcomes. Drawing on findings from human deliberation and collective decision-making, we identify two key mechanisms missing from vanilla MAD: (i) diversity of initial viewpoints and (ii) explicit, calibrated confidence communication. We propose two lightweight interventions. First, a diversity-aware initialisation that selects a more diverse pool of candidate answers, increasing the likelihood that a correct hypothesis is present at the start of debate. Second, a confidence-modulated debate protocol in which agents express calibrated confidence and condition their updates on others' confidence. We show theoretically that diversity-aware initialisation improves the prior probability of MAD success without changing the underlying update dynamics, while confidence-modulated updates enable debate to systematically drift to the correct hypothesis. Empirically, across six reasoning-oriented QA benchmarks, our methods consistently outperform vanilla MAD and majority vote. Our results connect human deliberation with LLM-based debate and demonstrate that simple, principled modifications can substantially enhance debate effectiveness.

1 Introduction

Vanilla MAD can underperform majority vote despite higher computational cost, while homogeneous agents and unweighted updates preserve expected correctness. This paper addresses missing initial diversity and confidence use with interventions that improve debate outcomes across six reasoning-oriented QA benchmarks.

1 Introduction

  • Under homogeneous agents and unweighted updates, vanilla MAD preserves expected correctness and can underperform majority vote despite higher computational cost.Debate therefore does not systematically increase the probability of reaching the correct answer under these conditions.Source: §1 · pp. 1–2
  • Standard MAD often lacks diverse initial answers and explicit confidence use, while LLMs can be overconfident even when wrong.Similar models and post-training alignment can induce diversity collapse; current protocols rarely request or use confidence signals.Source: §1 · p. 2
  • The paper introduces diversity-aware initialization and confidence-modulated updates, with theoretical guarantees and consistent gains over vanilla MAD and majority vote across six reasoning-oriented QA benchmarks.The interventions target different stages: initial hypotheses and how agents weight others’ contributions.Source: §1 · p. 2

2 Related Work

Prior work identifies shortcomings in MAD and links diversity and confidence to effective deliberation. The paper highlights gaps in simple ways to increase initial-answer diversity and in how agents interpret and use confidence.

Multi-Agent Debate

  • Homogeneous LLM agents can exhibit martingale-like debate dynamics, and MAD may fail to outperform majority vote, especially over multiple rounds.Prior work also reports that low-quality contributions can propagate as noise rather than dissipate.Source: §2 · p. 3

Diversity in Collective Problem Solving

  • Prior work associates diverse reasoning with improved performance, but leaves unclear how to increase initial-answer diversity simply and without training.Existing approaches alter prompts, prune responses during debate, or rely on model and prompt heterogeneity rather than directly targeting the initial pool.Source: §2 · p. 3

Confidence, Calibration, and Uncertainty Communication

  • Numerical-confidence approaches use post-hoc calibration but may not ensure calibrated expression or teach agents to interpret and appropriately weight others’ confidence.LLMs can be systematically overconfident in verbalized confidence judgments.Source: §2 · p. 3

3 Formulation

The formulation isolates debate dynamics using homogeneous LLM agents answering questions. It contrasts independent majority voting with iterative revision based on prior-round responses.

3 Formulation

  • The formulation assumes homogeneous LLM agents performing question answering to isolate debate dynamics from model heterogeneity and role specialization.All agents share identical parameters, with stochasticity arising solely from sampling.Source: §3 · p. 4
  • Majority vote is test-time ensembling without interaction and serves as an empirical baseline for vanilla MAD.The ensemble-level MAD output is also obtained by majority vote over terminal responses.Source: §3 · p. 4
  • MAD iterates for T rounds: agents sample initial answers, then observe the previous round’s responses and revise using a prompting-based answer-update operator.The revision operator is executed by the LLM.Source: §3 · p. 4

4 Methodology

The methodology adds diversity-aware initialization and confidence-modulated debate to vanilla MAD. The interventions alter the initial answer pool and how confidence shapes aggregation, respectively.

4.1 Diversity-aware Initialization

  • Diversity-aware initialization samples at least N candidate answers and greedily selects N with the largest marginal contributions to answer diversity.It requires extra test-time sampling, but no training or architectural modification, and preserves the standard MAD protocol.Source: §4.1 · p. 4

4.2 Confidence-Modulated Debate

  • Confidence is framed as an explicit signal for text-based debate, where human paralinguistic cues such as tone and facial expressions are unavailable.The method focuses on verbalized numerical confidence as a signal agents can exchange and calibrate.Source: §4.2 · pp. 4–5
  • Confidence-modulated debate extends each agent’s output with a self-assessed confidence score from 0 to 10 and uses confidence to scale its influence during aggregation.The confidence score does not change answer content; it changes the answer’s influence on aggregation.Source: §4.2 · p. 5
  • The method trains agents with reinforcement learning to express calibrated confidence and to perceive and use confidence signals during debate.The training addresses both miscalibrated verbal scores and the possibility that agents ignore or misuse others’ confidence.Source: §4.2 · p. 5

5 Theoretical Analysis

The analysis separates two ways to improve debate: broaden the initial hypothesis pool while keeping later updates unchanged, or weight updates by confidence so expected belief in the correct answer rises.

5 Theoretical Analysis

  • Under homogeneous, fully connected agents with shared priors, the Dirichlet–categorical model updates beliefs by adding counts for prior-round answers.The analysis builds on Choi et al. (2025).Source: §5 · pp. 5–6
  • With unweighted updates in this setting, belief in the correct answer is a martingale, so vanilla debate neither helps nor hurts expected performance.This result is stated for the homogeneous, fully connected setting.Source: §5 · pp. 5–6

5.1 Diversity Improves What Is Debated

  • Diversity-aware initialization raises prior success probability when conditional success is nondecreasing in distinct hypotheses and the initializer stochastically increases their number.The intervention changes the initial pool, not the subsequent unweighted dynamics.Source: §5.1 · p. 6

5.2 Confidence Improves How Debate Aggregates

  • When confidence is positively correlated with correctness, confidence-weighted updates make correct-answer belief a strict submartingale, with expected belief increasing over rounds.The theorem assumes homogeneous, fully connected agents and confidence-weighted counts.Source: §5.2 · p. 6

6 Experiment Setup

Experiments examine five-turn debates with five homogeneous agents, then evaluate the methods on in-domain and out-of-domain QA benchmarks using two instruction-tuned models.

6 Experiment Setup

  • Vanilla dynamics are tested with five homogeneous same-model agents over five turns; sampling uses temperature 1.0 and nucleus p = 0.9, with ten diversity candidates.Confidence calibration and perception use GRPO with LoRA; comparisons include single-model, majority-vote, and post-debate majority-vote baselines.Source: §6 · pp. 6–7
  • Evaluation covers GSM8K, CommonsenseQA, HellaSwag, and MMLU in-domain, plus GPQA-Main and ARC-Challenge as out-of-domain benchmarks.MMLU includes 57 subtasks across diverse knowledge domains.Source: §6 · pp. 6–7
  • Table 1 covers benchmark performance by model and dataset, with green cells marking gains over majority vote; Table 2 reports diversity–gain correlations, and Figure 2 shows round 1-to-5 correctness transitions.Figure 2's caption identifies improved answer revision under confidence-modulated debate.Source: Table 1 · p. 7, Table 2 · p. 7, Figure 2 · p. 7
  • Vanilla and trained debate variants use Llama-3.1-8B-Instruct and Qwen-2.5-7B-Instruct, prompted for chain-of-thought and, for confidence, a numerical score.Source: §6 · p. 7

7 Results & Analysis

The analysis finds that confidence-modulated debate improves aggregation across evaluated datasets, while diversity-aware initialization improves accuracy and the likelihood that debate starts with a correct answer. Initial diversity is also associated with final accuracy and with the greater gains MAD tends to achieve on harder datasets.

Diversity alone improves MAD performance

  • Initial answer diversity in vanilla MAD is significantly correlated with final answer accuracy, although the reported correlation is weak.The authors present this pattern, together with diversity collapse in the instruct model, as motivation for explicitly leveraging diversity.Source: §7 · p. 7

The Role of Initial Diversity

  • On harder datasets, vanilla MAD produces more diverse initial answer pools and tends to yield larger debate performance gains.Difficulty is defined as a model’s accuracy on a dataset; Figure 3 covers 62 datasets, including 57 MMLU subtasks.Source: §7 · p. 8, Figure 3 · p. 8

Diversity alone improves MAD performance

  • Diversity-aware initialization improves accuracy on nearly all datasets across both models and increases initial answer diversity and Pass@5 across the board.The authors interpret the increases as raising the prior probability of MAD success by making an initially correct hypothesis more likely to be present.Source: §7 · p. 8, Table 3 · p. 8

Confidence-modulated debate improves aggregation

  • Confidence-modulated debate outperforms simple aggregation across all evaluated datasets, including two OOD benchmarks, and corrects initially wrong answers while stabilizing correct ones.The protocol trains agents to express calibrated confidence and use others’ confidence when revising answers.Source: §7 · p. 8

8 Conclusion

The paper frames MAD through human group deliberation and identifies diversity and calibrated confidence as missing ingredients in standard LLM debates. It introduces interventions for each and reports theoretical and empirical support for their effectiveness.

8 Conclusion

  • The paper identifies initial viewpoint diversity and explicit, calibrated confidence communication as two missing ingredients in standard LLM debates.The interventions are a diversity-aware initialization and a protocol in which agents express and use calibrated confidence.Source: §8 · p. 8
  • Theoretically, diversity-aware initialization raises the prior probability of MAD success without changing martingale dynamics, while confidence-weighted updates yield a submartingale over correctness.Source: §8 · p. 8
  • Across six benchmarks, the methods consistently outperform vanilla MAD and majority vote.The authors conclude that simple, principled changes inspired by human deliberation can improve LLM multi-agent debate.Source: §8 · p. 8

Limitations

The authors qualify their theoretical assumptions, diversity-selection strategy, confidence calibration, experimental debate setting, and benchmark scope. These boundaries limit how broadly the paper’s analysis and findings can be applied.

Limitations

  • The theoretical analysis uses a Dirichlet–categorical debate model and homogeneity assumptions that do not fully capture real LLM behavior.The model reduces updates to counting and omits differing inputs, contextual positions, position bias, and belief refinement through self-reflection or internal reasoning.Source: Limitations · p. 9
  • Diversity-aware initialization selects heuristically from a fixed candidate pool and is not claimed to be optimal.The authors note that more principled or adaptive diversity objectives may further improve outcomes.Source: Limitations · p. 9
  • Confidence-modulated debate assumes expressed confidence is positively correlated with correctness after calibration.Confidence miscalibration remains a challenge, and failed confidence estimation could reduce confidence-weighted aggregation’s effectiveness.Source: Limitations · p. 9
  • Experiments use homogeneous agents and fully connected debate graphs, leaving other model and communication settings outside the tested scope.Heterogeneous models, asymmetric topologies, or larger agent populations may introduce additional dynamics.Source: Limitations · p. 9
  • Evaluation focuses primarily on English-language question-answering benchmarks, so generalization to open-ended, interactive, or real-world multi-agent settings remains to be assessed.Source: Limitations · p. 9

Ethics Statement

The paper reports its ethics practices and provides appendix material on prompts and sampling and training. The supplied passages specify compliance checks, the initial confidence prompt, and key compute and training settings.

Ethics Statement

  • The authors report checking software and dataset licenses, identifying no privacy concerns, anticipating no further risks, and using AI assistance only for grammar checking.Source: Ethics Statement · p. 9

A Prompts

  • Table 4 presents the initial-round prompt with confidence.Source: Table 4 · p. 13

B Sampling and Training Schema

  • Experiments use NVIDIA A100 GPUs (80GB) for approximately 1,500 GPU hours, with vLLM inference, float16 precision, and LoRA rank 64 for fine-tuning.Source: B Sampling and Training Schema · p. 13

B.1 Confidence Expression Training

These sections describe confidence training and its use in debate, report experiments that did not induce answer-level diversity, and formalize baseline and modified debate dynamics. The proofs distinguish diversity’s effect on the initial pool from confidence weighting’s effect on later belief updates.

B.1 Confidence Expression Training

  • 5k self-consistency examples provide confidence targets, followed by RL on 10k difficult examples; trained models retain similar accuracy, with no new knowledge attributed to training.The calibration table reports Brier score and ECE as lower-is-better, and AUROC and accuracy as higher-is-better.Source: §B.1 · p. 13, Table 6 · p. 13

B.2 Confidence Perception and Usage Training

  • Because debate rounds are Markovian, GRPO trains on single-turn inputs and outputs with correctness and confidence rewards, while an engagement constraint encourages responses to others’ reasoning and confidence.The constraint rewards discourse cues after training showed agents could ignore peer contributions and output only a final answer.Source: §B.2 · pp. 13–14

C What We Tried but Did Not Work

  • Raising Qwen’s temperature from 1.0 to 1.2 did not increase answer diversity or improve MAD performance, and could harm instruction following and output quality.The authors attribute the result to temperature diversifying reasoning paths rather than final answers; stylistic or language variation could leave the answer unchanged.Source: C What We Tried but Did Not Work · p. 14, Table 9 · p. 14
  • Training confidence on a manually curated harder subset improved convergence and produced more stable calibration after uniform sampling struggled with reward diversity and sampling efficiency.The harder subset brought model accuracy closer to 50%.Source: C What We Tried but Did Not Work · p. 14

D Proofs

  • Diversity injection improves prior success without changing the baseline debate dynamics, while confidence-weighted updates can make belief a submartingale.The confidence result is presented under the paper’s formal assumptions; the baseline dynamics preserve expected correctness.Source: D Proofs · p. 15

D.1 Baseline DCM Debate Model

  • In the baseline DCM model, agents update Dirichlet beliefs using counts of neighbors’ answers; in the homogeneous, fully connected setting, expected belief in correctness is preserved.The passage characterizes this as a martingale: in expectation, debate neither helps nor hurts.Source: §D.1 · p. 15

D.2 Effect of Diversity Injection

The analysis formalizes two distinct routes to improved debate outcomes: increase the useful hypothesis coverage of the initial pool, or weight later updates by confidence. The latter yields an upward expected-belief result under stated assumptions, while the example illustrates an agent revising after considering peer reasoning.

D.2 Effect of Diversity Injection

  • Diversity-aware initialization raises eventual correctness when success is nondecreasing in the number of informative initial hypotheses and the diverse pool stochastically dominates random sampling in coverage.The theorem’s conclusion concerns overall success probability; it does not require changing the debate dynamics.Source: §D.2 · p. 16
  • With s distinct informative hypotheses, each correct with probability p, the probability of at least one correct hypothesis increases with s, illustrating how broader initial coverage raises prior success.The proof relates diversity’s gain to the distribution of the initial debate state, while conditional expected correctness remains unchanged once that state is fixed.Source: §D.2 · pp. 16–17

D.3 Confidence-Weighted Debate

  • Confidence-weighted debate adds neighbors’ answers in proportion to their confidence, using real-valued weighted counts in the Dirichlet update.Each agent emits an answer-confidence pair, and the weighted counts preserve conjugacy.Source: §D.3 · p. 17

D.4 From Martingale to Submartingale

  • With homogeneous agents in a fully connected graph and confidence positively correlated with correctness, confidence-weighted belief is a strict submartingale and its expected value can rise.The paper contrasts this with unweighted debate, whose symmetry preserves expected belief.Source: §D.4 · p. 20

E Example Output

  • After reviewing peers’ reasoning, the example agent revises its answer to (A) and reports confidence 8, favoring an argument that identifies the third-quarter phase.The agent’s initial answer was (D), with confidence 3.Source: E Example Output · pp. 21–22

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