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

We thank the reviewer for the constructive feedback and for acknowledging the novelty of our theoretical framework, and also complimenting the clarity of our manuscript.

Below, we address your key concerns.

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A1 Clarification on empirical finding

Thank you for this constructive feedback, and we appreciate the opportunity to better clarify the positioning of our work in relation to prior works.

We agree that recent empirical studies—including Smit et al. [1] and Kaesberg et al. [2]—have made valuable contributions by revealing important limitations of multi-agent debate (MAD). These works raise fundamental questions about the robustness and efficacy of MAD, and we believe our paper offers a complementary and timely response to precisely address those concerns.

Specifically, the goal of our empirical analysis is not to claim novelty in observing MAD's limitations, but rather to motivate the need for a theoretical framework that can explain and predict when and why such limitations arise. This is the central contribution and novelty of our work, as you also recognized. We develop a formal model of belief dynamics under debate and derive analytical results (e.g., Theorem 1 and 2) that shed light on how agent responses evolve and aggregate over time. This framework offers the first principled explanation for this observation -- something not accounted for in prior works. The value and novelty of our work are also recognized by peer reviewers:

"I believe that the formulation introduced in the paper could have a moderate-to-high impact on the MAD community – a field which has suffered from imprecise and ad-hoc approaches in the past." ---- Reviewer 6aic

Lastly, we recognize that we should have cited and discussed these earlier works more directly in our motivation. We will revise the manuscript to better acknowledge their contributions, clarify how our work builds upon them, and make more explicit that our goal is to provide theoretical foundations for previously observed empirical patterns—thereby moving toward a deeper and more principled understanding of multi-agent systems.

[1] Andries Smit, et al. "Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs." Proceedings of the 41st International Conference on Machine Learning (2024)

[2] Lars Benedikt Kaesberg, et al. "Voting or Consensus? Decision-Making in Multi-Agent Debate." arXiv preprint arXiv:2502.19130 (2025)

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A2 Clarification on modeling assumptions

Thank you for this thoughtful critique. We agree that modeling the rich and nuanced dynamics of LLM interactions is inherently challenging, and any abstraction—including ours—comes with limitations. Our goal is not to fully replicate the full semantic depth of LLM debates, but rather to identify and formalize core statistical properties that govern belief evolution and aggregation in multi-agent settings at a reasonable level of abstraction, and at the same time providing tractable and interpretable analysis.

The Dirichlet-Compound-Multinomial (DCM) framework is an ideal choice, as we justified in our manuscript (L150-L162):

"...DCM closely mirrors how practical LLM systems produce different outputs due to uncertainty and sampling variability. In particular, the Dirichlet prior captures the agent’s internal belief over possible answers, while the Multinomial models the stochastic generation process (e.g., via temperature or nucleus sampling). This distribution is thus a natural choice because it encapsulates both internal uncertainty and output randomness, while also providing a principled Bayesian framework for belief updates across debate rounds—enabling analytical study of dynamics during the debate process...."

This proper abstraction enables us to derive formal insights about the role of belief dynamics, which empirically align with key behavioral trends observed in real-world LLM-based MAD systems (more evidence discussed in A3 below, where we directly verified $p_t$).

We acknowledge that prompt tuning strategies----such as rephrasing or refinement----can influence how responses are generated and interpreted. And the sampling variation induced by prompting is precisely what DCM can capture mathematically. To account for such variation, our framework is flexible enough to accommodate this by allowing a variable weight $w$ in the belief equation from Theorem 2:

$$p_t := \frac{\alpha_{i,t-1}^{(1)} + w^{(1)} \cdot c_{i,t}^{(1)}}{\sum_{j=1}^K ( \alpha_{i,t-1}^{(j)} + w^{(j)} \cdot c_{i,t}^{(j)})}.$$

This weight can be adjusted via prompt design, fine-tuning, or human-guided signals, providing flexibility to model more realistic agent behaviors.

We believe our heterogeneous-agent setup in Table 4 partially reflects this idea—for instance, a Programmer agent might be more influenced by the reasoning of a Mathematician than that of a Lawyer. Yet even in this more nuanced setting, performance trends remain largely stagnant, reinforcing the core idea of our theory.

Overall, we view our theoretical framework as a sufficiently general foundation that can incorporate richer dynamics and guide future improvements to debate protocols.

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A3 Empirical evidence for DCM. Did you check signals such as $p_t$ directly?

Yes, we did! In fact, Figure 4 presents the mean $p_t$ values across debate rounds (with raw values provided in Appendix E). Importantly, $p_t$ reflects the single-agent belief in the correct answer at debate round $t$, and the mean $p_t$ is the average among agents ($y$-axis in the figure). This measure differs from the overall task accuracy, which the reviewer may have misinterpreted. This trajectory captures the agent's evolving belief and directly aligns with the DCM update model used in our theoretical analysis. As shown in Figure 4, the mean $p_t$ values remain largely stationary over rounds, providing direct empirical support for the martingale behavior----consistent with the theoretical result in Theorem 2.

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A4 Practical impact of theoretical insights

We appreciate the reviewer’s concern and would like to clarify on the practical impact of our theoretical analysis. One of the key insights of our analysis is that debate has the potential to substantially outperform simple voting when appropriately guided. This is clearly demonstrated through the MAD-Oracle. These gains indicate that there is considerable headroom in the design space of MAD, and that our theory helps uncover this significant potential.

The purpose of our proposed interventions—MAD-Conformist and MAD-Follower—is not to fully bridge this gap, but to empirically validate concrete predictions derived from our theory. These methods are intended to show promise, demonstrating that even minimal, theory-driven modifications can improve upon vanilla MAD. Our aim is not to claim state-of-the-art performance or argue against the utility of alternative approaches (including [1]), but rather to establish a foundation for designing more effective strategies grounded in a deeper understanding of belief dynamics.

We see these methods as initial, illustrative steps—proofs of concept that MAD performance can be steered by principled design. Far from limiting the practical value of our theory, these findings highlight its role in enabling targeted improvements. As we objectively and transparently note in the manuscript (L256–258):

"While they do not reach the oracle’s upper bound performance, they demonstrate that simple, theory-informed modifications can yield meaningful improvements—pointing to a promising direction for future work to close the gap."

[1] Andries Smit, et al. "Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs." Proceedings of the 41st International Conference on Machine Learning (2024)

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A5 When will the interventions beat majority voting?

This is a very insightful question. The bottleneck in our current interventions is that they lack reliable estimation of which answer is correct, and thus cannot consistently introduce the directional bias needed to steer belief evolution productively. As a result, their gains are often modest. This stands in contrast to MAD-Oracle, which demonstrates the full potential of such a strategy when the correct signal is known/correctly estimated—achieving substantial improvements over majority voting.

We expect that future work incorporating better estimators of correctness (e.g., via confidence scoring, calibrated self-reflection, or external signal integration) can realize significantly larger gains. In short, our framework suggests a clear direction for improving MAD: design agents that can more effectively estimate and amplify correctness early in the debate. We will incorporate such a discussion in our revised manuscript. Thanks again for your comment!

I thank the authors for providing the individual agent trajectories. However, their response appears to be a misunderstanding of my request.

I intended to ask for an empirical validation of the martingale property. This requires estimating the conditional expected value, $\\mathbb{E}[p\_{i,t} | \\mathcal{F}\_{t-1}]$, for each agent i and time step t. Here, $\\mathcal{F}\_{t-1}$ denotes the filtration, representing all information available up to step t-1, including the agent's belief $p\_{i,t-1}$.

To estimate this expectation, one must:

1. Fix a state at an intermediate debate round (t-1).
2. Rerun the subsequent step (t) multiple times to average over the stochasticity of the process.

Presenting a single, random trajectory is insufficient to validate a claim about expected values, a point I have noted previously.

To be perfectly clear, my request is to see direct evidence of whether the core martingale property, $\\mathbb{E}[p\_{i,t} | \\mathcal{F}\_{t-1}] \\approx p\_{i,t-1}$, holds empirically. I strongly believe that, without this validation, the central theoretical claim of the paper lacks the necessary empirical support.

We thank the reviewer for the constructive and thoughtful feedback! We are deeply encouraged by and grateful for your words:

"I believe that the formulation introduced in the paper could have a moderate-to-high impact on the MAD community – a field which has suffered from imprecise and ad-hoc approaches in the past."

which is exactly what prompted us to write this paper :)

Below, we address your key concerns.

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A1 Assumption that the correct answer has the largest initial belief $\alpha^{(1)}$

You are raising an excellent question here. We would like to emphasize that this assumption reflects only a weak prior preference, not a strong or certain belief. For example, suppose a single agent assigns a belief of 0.01 to the correct answer and 0.009 to the next-best option. While the agent’s accuracy is only 1%, Theorem 1 shows that with enough agents, majority voting can boost correctness to nearly 100%, which is the core benefit of majority voting. Importantly, this works even if the correct option is only slightly favored, no matter how small that margin is.

Moreover, we provide an alternative version of the theorem in Appendix D, which does not assume that the correct option has the largest initial belief. Theorem 1.A establishes a lower bound on the probability that the correct answer is selected by majority vote, without assuming any belief constraints. This highlights that the benefit of voting is not solely due to prior confidence, but also emerges from the statistical structure of ensembling.

Lastly, we want to emphasize that this assumption is not required for the general formulation of our belief dynamics or for understanding the behavior of multi-agent debate more broadly. Theorem 2 does not rely on this assumption. The martingale property holds regardless of whether the correct option initially has the highest belief or not. It tells us that in expectation, beliefs do not drift toward the correct answer over time unless external structure or directional bias is introduced. This explains why naive multi-agent debate may not consistently outperform majority voting—debate alone, without guidance, cannot correct a misaligned initial prior.

Indeed, the most important and challenging setting is where the agents do not initially favor the correct answer. Our theoretical framework helps us understand what structural mechanisms are needed to shift beliefs in such settings. It also highlights the limitations of relying solely on peer interactions and motivates our design of guided interventions.

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A2 Extending the Bayesian update rule beyond count vectors and defining "consensus" for open-ended tasks

This is an insightful and important question! We agree that multi-agent debate becomes more nuanced in open-ended or long-form NLP tasks. That said, we believe the core intuition of our belief update framework remains applicable, with a few key adaptations. Below, we address both (i) extending the update rule and (ii) defining consensus in open-ended tasks:

(i) Extending the update rule

Although open-ended responses are not easily countable in a strict categorical sense, they can still be modeled in distributional or similarity-based forms. Specifically, the core mechanism of our Bayesian update rule,

$$p_t := \frac{\alpha_{i,t-1}^{(1)} + c_{i,t}^{(1)}}{\sum_{j=1}^K ( \alpha_{i,t-1}^{(j)} + c_{i,t}^{(j)})},$$

does not inherently require hard categorical responses. In open-ended settings, the count vector $c_{i,t}$ can be interpreted more generally—for example, as

• a soft histogram over clustered response types,
• an embedding-based semantic agreement metric,
• or a weighted similarity score between textual outputs.

Thus, the Bayesian belief update process can be extended by letting $c_{i,t}$ reflect aggregated semantic signals rather than strict response counts.

(ii) Defining consensus in open-ended tasks

Similar to the extended update rule for open-ended tasks, consensus is better defined semantically, not symbolically. For example, if agents independently generate similar explanations or rationales, we may consider this as semantic consensus, even if the surface forms differ. This can be operationalized via thresholds on embedding similarity, Levenshtein distance, or overlap in reasoning chains etc.

Our current experiments use discrete agreement on multiple-choice question tasks, but we believe the above adaptations can extend naturally to open-ended contexts. We view this direction as an exciting next step for generalizing the MAD framework beyond classification.

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A3 Limiting counts to $K$ possible responses is restrictive ... one would want an agent to be persuaded by the additional context from other agents, biasing its belief towards the correct response. Do you consider this setting?

Absolutely! We agree that persuasion via explanation is a desirable property of debate. However, we respectfully clarify that the limitation to $K$ discrete responses is not inherently at odds with such persuasive dynamics.

The use of $K$ responses in our framework is simply a modeling abstraction to make the belief update process tractable and interpretable. This $K$-way formulation can be readily generalized to larger or even infinite response spaces (e.g., open-ended generation tasks discussed in Q1), without invalidating the core martingale result. What matters is how agents map peer responses—whether discrete or continuous—into belief adjustments.

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A4 What are “optimal persona sets” and how is this implemented in practice?

As noted in Lines 272–276, the "optimal persona sets" refer to a collection of agent roles selected via the "agent selection algorithm" introduced in [1]. This method identifies a combination of personas that are empirically effective when collaborating in multi-agent tasks.

In practice, we implement this by assigning each agent a system prompt that encodes a specific role or persona—e.g., Mathematician, Programmer, Lawyer—using the same prompt templates provided in [1]. We agree that our manuscript would benefit from more explicit implementation details, and we will include a full description of the relevant details in the revised version.

[1] Z. Liu, et al. "Dynamic llm-agent network: An llm-agent collaboration framework with agent team optimization" (COLM 2024).

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A5 How do the empirical and theoretical findings presented in the paper align with paragraph “Pros of Multi-Agent Debate”?

Thank you for this observation. First, we would like to clarify that the paragraph titled "Pros of Multi-Agent Debate" appears in the Related Works section and is intended as a summary of claims made in prior literature—not the central claim of our own work.

In contrast, our paper critically examines those assumptions and challenges the notion that multi-agent debate in its current form consistently improves factual accuracy or reasoning quality. Our theoretical and empirical results show that, without carefully designed mechanisms or external interventions, MAD can stagnate or even degrade performance over time due to its martingale dynamics.

We appreciate the opportunity to clarify this and will revise the manuscript to clearly distinguish the claims of prior work from our contributions.

We thank the reviewer for the constructive feedback and for acknowledging the value of our experiments and theoretical analyses.

Below, we address the key concerns.

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A1 Instability of LLaMA3.1-8B-Instruct results

Thank you for the question! We would like to emphasize that this behavior is entirely consistent with our theoretical framework, which models MAD as a martingale process—meaning that the expected correctness of agents does not improve with additional debate rounds unless directional signals are injected.

As shown in Table 1 in the manuscript, LLaMA occasionally shows gains from MAD, but those gains are modest and non-monotonic, aligning with our martingale-based explanation (Theorem 2). This demonstrates that instability is not a flaw of the experiment, but a key empirical support for our theoretical claim: MAD, in its vanilla form, does not consistently lead to correctness improvements. We will clarify this interpretation more explicitly in the revised manuscript.

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A2 Further experiments on larger-scale models

Thank you for this suggestion. In response, we have conducted additional experiments using the larger-scale Qwen2.5-32B-Instruct model across four representative benchmarks. As shown in the table below, the effect of Decentralized MAD varies. For Arithmetics, GSM8K, and HellaSwag, we observe slight performance degradation or oscillation across rounds, while for Professional Medicine (MMLU), MAD improves over majority voting. These results further support the generality of our martingale-based analysis: even with highly capable agents.

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A3 Further experiments on closed-source models

In response to your request for experiments on closed-source models, we conducted additional evaluations using three GPT-4 agents across four benchmarks. The overall trends remain consistent with those observed in our open-source model experiments, supporting the generality of our findings.

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A4 Application to open-ended tasks

Great point! We agree that multi-agent debate becomes more nuanced in open-ended or long-form NLP tasks. That said, we believe the core intuition of our belief update framework remains applicable, with a few key adaptations. In particular, we discuss below: (i) extending the update rule and (ii) defining consensus in open-ended tasks:

(i) Extending the update rule

Although open-ended responses are not easily countable in a strict categorical sense, they can still be modeled in distributional or similarity-based forms. Specifically, the core mechanism of our Bayesian update rule,

$$p_t := \frac{\alpha_{i,t-1}^{(1)} + c_{i,t}^{(1)}}{\sum_{j=1}^K ( \alpha_{i,t-1}^{(j)} + c_{i,t}^{(j)})},$$

does not inherently require hard categorical responses. In open-ended settings, the count vector $c_{i,t}$ can be interpreted more general—for example, as

• a soft histogram over clustered response types,
• an embedding-based semantic agreement metric,
• or a weighted similarity score between textual outputs.

Thus, the Bayesian belief update process can be extended by letting $c_{i,t}$ reflect aggregated semantic signals rather than strict response counts.

(ii) Defining consensus in open-ended tasks

Similar to the extended update rule for open-ended tasks, consensus is better defined semantically, not symbolically. For example, if agents independently generate similar explanations or rationales, we may consider this as semantic consensus, even if the surface forms differ. This can be operationalized via thresholds on embedding similarity, Levenshtein distance, or overlap in reasoning chains etc.

Our current experiments use discrete agreement on multiple-choice question tasks, but we believe the above adaptations can extend naturally to open-ended contexts. We view this direction as an exciting next step for generalizing the MAD framework beyond classification.

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A5 Rationale for choosing the Dirichlet-Compound-Multinomial model for LLM response generation

This is an insightful question. We adopt the Dirichlet-Compound-Multinomial (DCM) formulation as the backbone of our belief-update model, grounded in both theoretical rigor and empirical observations:

• Principled Bayesian foundation: The Dirichlet distribution is the conjugate prior of the Multinomial distribution, making it a straightforward and well-established choice for modeling the nature of LLM text generation dynamics. In our setup, an agent’s belief over $K$ possible responses is updated as it receives signals from other agents, and the DCM provides a closed-form way to model this update: an agent starts with a Dirichlet prior $\alpha$, observes peer responses, and updates beliefs based on the posterior. This mirrors classical Bayesian updating and lends a principled probabilistic structure to belief evolution in a multi-agent setting.

• Empirical alignment with LLM dynamics: As shown in Figure 4 of our manuscript, the evolution of $p_t$ over rounds of decentralized debate aligns well with the expectation-neutral behavior predicted by DCM. That is, belief trajectories exhibit symmetric drift under majority influence, without systemic bias toward any particular answer choice. This symmetry and neutrality are core predictions of DCM and match what we observe across multiple rounds of real LLM-agent interactions.

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A6 What is the base model used for Figure 3?

The base model for Figure 3 is Qwen2.5-7B-Instruct. We will make sure to include this in our revised version. Thank you for pointing this out.

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A7 Can an average result column be added to Tables 1 and 2?

Of course! We will add the average columns in our revised version. We appreciate your suggestion.

We thank the reviewer for the constructive feedback and for complimenting the strong and extensive empirical results.

Below, we address the key concerns.

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A1 Clarification on agent setting

We understand the reviewer’s concern and fully agree that diversity is valuable in multi-agent debate settings. We would like to clarify the key considerations of out setup:

• Homogeneous agents allow us to isolate the core mechanisms, rigorously dissecting the contribution of inter-agent debate vs. simple majority voting, without introducing confounding factors such as varied model capabilities or role-specific behaviors. This clean setup enables both a rigorous theoretical analysis and a principled understanding of where performance gains originate.
• The homogeneous agent setting is the most commonly studied setup in prior MAD work (e.g., [1,2,3,4,5]), making our theoretical framework broadly relevant and well-grounded in the established research landscape. For a theoretical foundation paper, it's important to first fully understand the essential ground, which can later inform and extend to more advanced/specialized cases.

That said, we want to emphasize that our framework does not preclude diversity:

1. Stochastic response diversity does arise in our setting: As Estornell et al. rightly emphasize, response diversity is important for productive debate. Crucially, such diversity can still emerge in homogeneous agent setups. Even when agents share the same base prompt and belief prior, stochastic sampling (e.g., temperature tuning or top-p sampling) induces variability in responses—allowing agents to explore different reasoning paths and generate disagreement.
2. Our theory does allow capturing different beliefs: As defined in Definition 1 of our paper, each agent samples its belief $\boldsymbol{\theta}\_{i,t}$ from a Dirichlet distribution. Even if all agents share the same prior concentration parameter $\boldsymbol{\alpha}$, the sampled beliefs $\boldsymbol{\theta}\_{i,0}$ differ across agents due to the inherent randomness in the Dirichlet process. This means that agents can hold distinct initial beliefs and produce diverse responses, enabling non-trivial interactions during debate.
3. Lastly, our theoretical model and empirical results remain applicable and informative, even as richer forms of agent heterogeneity are introduced. As you recognized, we do study heterogeneous agents in Section 6 (Table 4), where we assign different personas (e.g., "Mathematician", "Lawyer") following established practices. Even in these diverse settings, we observe that simple Majority Voting remains highly competitive, further supporting our claim that ensembling is a primary driver of MAD performance. For these reasons, we believe our work lays a strong foundation for future research in this direction.

[1] C. Chan et al., "ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate" (ICLR 2024)

[2] Y. Du et al., "Improving Factuality and Reasoning in Language Models through Multiagent Debate" (ICML 2024)

[3] Y. Li et al., "Improving Multi-Agent Debate with Sparse Communication Topology" (EMNLP-findings 2024)

[4] Q. Wang et al., "Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?" (ACL 2024)

[5] G. Zhang et al., "Cut the Crap: An Economical Communication Pipeline for LLM-based Multi-Agent Systems" (ICLR 2025)

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A2 Do diverse personas result in diverse responses?

We appreciate the reviewer’s interesting suggestion to plot the t-SNE projections. We looked further into this, but since persona is not an explicit attribute that is easily captured in output embeddings, we found that t-SNE projections do not show meaningful differences between single- and multi-persona setups.

As an alternative, we retrieved the frequency table of the mean Levenshtein distance, which is computed as:

$$D = \frac{1}{N^2}\sum_{i=1}^N\sum_{j=1}^N \text{Levenshtein}(y_i, y_j),$$

where $y_i$ is the response from agent $i$ (see table below). 30 samples from GSM-8K were evaluated on the Qwen2.5 agents. The table reveals a clear shift under the multi-persona configuration, indicating greater lexical diversity in the generated responses.

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A3 Structured debate methods

We appreciate the reviewer’s point. Structured debate formats (role-based, judge-mediated systems, etc.) are indeed a powerful line of work. Our focus, however, is to understand the fundamental dynamics of inter-agent communication, which is why we adopt a minimal, decentralized protocol to isolate core mechanisms without added structure.

That said, our theoretical framework is not restricted to simplistic settings. The DCM-based model applies broadly to any debate mechanism where agents update beliefs based on peer responses. Notably, the belief update rule in Theorem 2 can be better generalized as:

$$p_t := \frac{\alpha_{i,t-1}^{(1)} + w^{(1)} \cdot c_{i,t}^{(1)}}{\sum_{j=1}^K ( \alpha_{i,t-1}^{(j)} + w^{(j)} \cdot c_{i,t}^{(j)})},$$

which includes a flexible weight term $w$ that can capture structured signals—such as those from prompt design, fine-tuning, or human-guided adjudication. Structured systems like judge-based debate can be seen as increasing $w^{(1)}$ for more credible or correct responses, introducing a directional bias that helps overcome the stagnation highlighted in our model.

We also want to highlight that other reviewers have explicitly recognized the impact and foundational value of our framework:

“I believe that the formulation introduced in the paper could have a moderate-to-high impact on the MAD community – a field which has suffered from imprecise and ad-hoc approaches in the past.” — Reviewer 6aic

In summary, our framework offers a general foundation for understanding belief dynamics, and can serve as a diagnostic tool even in structured settings. By revealing when and why debate fails to improve accuracy, it provides diagnostic insight that can guide the design of more effective coordination strategies. We see integration with structured protocols as a valuable direction for future work.

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A4 Novelty of MAD-Conformist and MAD‑Follower—needs better context like agreement modulation (Smit et al.).

We thank the reviewer’s suggestion to better contextualize our interventions within related work. We acknowledge that Smit et al.’s work on agreement modulation is closely related and highlights an important connection to our proposed interventions. Our interventions—MAD-Conformist and MAD-Follower—are theoretically motivated by our martingale analysis (Theorem 2), aiming to address the core stagnation issue in MAD dynamics through lightweight, generalizable mechanisms.

To further clarify positioning, we will explicitly compare our designs with related strategies such as Agreement Modulation (Smit et al.), All-Agents Draft (AAD) and confidence-weighted voting (Kaesberg et al.) in the revised paper. We believe this framing will highlight the novelty and complementary nature of our work, both theoretically and practically.

Thank you again for this constructive suggestion, which we believe strengthens the paper.

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A5 Why does accuracy often decrease with more debate rounds?

According to our theoretical framework (Theorem 2), belief updates under a DCM process are expectation-neutral; i.e., in the absence of external directional signals, agents are equally likely to drift toward or away from the correct answer over successive debate rounds. However, when generalizing the belief update rule (see A3), it is possible that the dynamics become skewed: if the update weight $w$ is larger for incorrect responses—e.g., due to persuasive but flawed reasoning, the expected correctness can decline over time.

To capture this phenomenon, we analyze the subversion and correction rates of Qwen2.5 agents across debate rounds (see table below). Here, subversion rate denotes the proportion of responses that were correct in the previous round but became incorrect in the next, while correction rate tracks the opposite. Overall, the subversion rate seems to overwhelm correction rates, suggesting that real-world LLM agents may be slightly more frequently persuaded away from the correct answer—an empirical indicator that the weights $w$ assigned to incorrect responses are higher in practice.

Dear Reviewer HZhH,

Thank you for your follow-up and for recognizing the additional analysis we provided. We sincerely appreciate your openness to reassessing the submission. Your revised evaluation is encouraging, and we’re grateful for your time and effort in reviewing our responses!

Best regards,

The Authors