Understanding Prejudice and Fidelity of Diverge-to-Converge Multi-Agent Systems

W1: This paper mainly proposes a benchmark to test and validate these challenges rather than further addressing them.

Comment:
While the APF benchmark is a significant contribution of this paper, we would like to emphasize the actionable strategies proposed and linked with experiments to address prejudice and fidelity challenges. For example:

• Mitigating Confirmation Bias:
  We introduce problem reframing with controlled initialization (right or wrong solutions) for both model-label and society-label frameworks [Lines: 419–442]. Table 1 showcases three settings: open (vanilla D2C framework), controlled (right), and controlled (wrong) initialization. Notably, for a complex task like Chess Move Validity on GPT-4o, we achieve a 9.7% performance improvement over the open-ended framework [Table 1]. Similarly, Table 2 (Appendix) provides performance data across four models and three settings, reinforcing the superiority of the problem reframing strategy.

• Judge Bias Ratio:
  Our analysis explores how initial agent roles affect "judge bias ratio" in frameworks like Debate. By quantifying bias ratios [Lines: 444–457, Figure 3], we show that controlled debate settings significantly decrease affirmative bias influence, particularly for PIQA and StrategyQA, while increasing negative bias. This shift highlights the impact of control mechanisms during debates on judgment formation [Lines: 444–457]. In the revised version, we also propose a potential solution to address social biases in D2C frameworks.

• Exploring Fidelity:
  We analyzed scaling behavior in agent interactions and resource usage [Section 6.2]. Key findings include:

  1. Improved Scaling: Complex tasks like Chess Move Validity benefit significantly from scaling resources. [Figure 5(a), Lines: 496–510]
  2. Saturation Effects: Simpler tasks like PIQA show performance plateaus after four agents, indicating diminishing returns. [Lines: 504–510]
  3. Trade-offs in Agent Interactions: Excessive scaling of interaction rounds leads to degraded performance due to coordination complexity, especially in society-level frameworks. [Lines: 510–517, Figure 6]

These insights and solutions enhance fairness and robustness in multi-agent interactions, offering practical guidance for real-world applications and valuable tools for refining such systems beyond benchmarking.

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W2: In more complex scenarios, problem reframing is difficult.

Comment: Replied in the general response.

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Q1: In Figure 1, should the question be "A ship travels 80 miles east/west and 150 miles north. How far is the ship from its starting point?"

Comment:
Thank you for bringing this to our attention. The question has been updated in the revised version.

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Q2: D2C instead of C2D, e.g., Section 5 Debatepedia, Dataset Problem Reframing, etc.

Comment:
Thank you for pointing this out. We have corrected the references to "D2C" in the revised version. Please refer to lines 287 and 295.

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Q3: Inconsistent symbol representation. In Section 3, C stands for the total number of calls, whereas in Section 4, C stands for Agent Count.

Comment:
Thank you for highlighting this inconsistency. The symbols have been unified in the revised version.

Dear Reviewer xVhp,

We deeply appreciate your recognition of our work and your insightful feedback, which has been essential in enhancing both the robustness and quality of our study.

Thank you once again for your valuable support! We are truly thankful for your time and thoughtful consideration.

Best regards,

The Authors

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Figures 5 and 6 of the paper illustrate the averaged performance versus resource usage of various LLMs in multi-label and society-level frameworks across four datasets. These figures evaluate different parameters, including (1) the number of agents, (2) the number of debate rounds, (3) the number of tokens, and (4) LLM API calls. In the revised manuscript, we will provide quantitative measures for all the subplots in these two figures, similar to the sample table shown for Figure 5 (b).

Table R1 for Figure 5 (b)

The averaged accuracy (Acc) of GPT-4o in multi-agent frameworks on four datasets, with ratios of samples where the number of rounds happend ($n$) equals and exceeds 1.

For brevity:

• Open: Open-ended.
• CR: Controlled (right).
• CW: Controlled (wrong).

Q1: Page 18, Case 2, GSM8k: Could the authors provide complete inputs to the models and their outputs for each iteration?

Comment:
Thank you for highlighting this. We will include complete inputs and outputs for each iteration in the GSM8k case study in the appendix of a revised version of the paper. This will ensure that readers can fully understand the iterative process and its impact on the results.

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Q2: Is there a hypothesis around why the results hold and such biases occur in language models? Are there reasonable tests that can be conducted around this?

Comment:
We hypothesize that the observed biases stem from the inherent structure of pretraining data and the optimization objectives used in training language models. These factors can lead to over-representation or under-representation of certain patterns. To validate this hypothesis, we plan to conduct controlled experiments that isolate specific biases and evaluate their persistence across diverse datasets and tasks. For instance, ablation studies and interventions in pretraining data distribution could provide insights into the underlying causes of such biases.

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Q3: Could there exist better reframing techniques? Why was the binary reframing technique selected? Will it work for all tasks?

Comment:
Our controlled (right or wrong) initialization through problem reframing was chosen for its simplicity and ease of implementation, making it a suitable starting point for exploring problem reframing. However, we acknowledge that more nuanced reframing techniques could yield better results, especially for complex tasks. Future work will investigate alternative reframing strategies, such as multi-dimensional reframing or task-specific dynamic reframing. We will also evaluate the generalizability of these techniques across different tasks to determine their broader applicability.

W1: The paper explores only problem reframing as a bias mitigation strategy. However, not every problem can be converted into a binary problem, and other strategies are not explored at all.

Comment: Replied in the general response.

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W2: The paper does not perform evaluations on any open-source models.

Comment: Thank you for your valuable feedback. We acknowledge the importance of evaluating open-source models to increase the reproducibility and accessibility of our findings. While the current study primarily utilizes proprietary models like GPT-4o and Gemini due to their advanced capabilities and relevance to state-of-the-art D2C systems, we recognize the potential benefits of including open-source models in future work. In subsequent iterations of this research, we plan to incorporate evaluations of open-source models such as LLaMA and Falcon, particularly to ensure broader applicability and transparency of our approach.

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W3: The refinement strategy for datasets could introduce selection bias and skew results. I would be interested in seeing results across a random subset of the test set on the benchmarks used.

Comment: We appreciate this insightful observation. Following [1], the refinement strategy was designed to improve the focus and relevance of the dataset by prioritizing samples that were incorrectly answered in our specific tasks, as detailed in Algorithm 1 of the paper. Notably, for the Chess Move Validity dataset, we considered all 1,000 problems (or samples) for all the experiments conducted in the paper. The reason for downsizing the GSM8K and PIQA datasets is that their performance is largely saturated for the considered LLMs. To demonstrate the efficacy of our approach, we downsampled these datasets using Algorithm 1. As for the StrategyQA dataset, it contains 2290 questions, making it prohibitively expensive to conduct experiments on all samples [1]. However, we believe that testing on the full dataset would help assess the robustness of our approach and verify whether the observed results consistently hold across diverse data splits. Moreover, we have conducted additional experiments on the GSM8K dataset, using all samples within the Multi-Agent Debate framework, as noted below:

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W4: The paper spends its first 5.5 pages providing a background on the problem and multi-agent LLM settings. This takes away from its key contributions, which are limited to the problem reframing strategy and very introductory work on scaling laws around fidelity. Section 6.2 is extremely limited and does not back up its claims with linked experiments.

Comment: We appreciate the reviewer's concerns regarding the balance between background content and key contributions. The detailed background section was included to contextualize our work for a broader audience, but we recognize that it may detract from the primary contributions. In a revised version, we will streamline the background content to focus on essential context and allocate more space to elaborate on our contributions.

Regarding Section 6.2, we confirm that all our claims are derived from Figures 5 and 6 of the paper. We acknowledge this and sincerely apologize for not including the corresponding figure references to support the observations and claims related to scaling laws and fidelity. In the revised manuscript, we will address this by adding the appropriate figure references and providing quantitative evidence in the appendix, like https://openreview.net/forum?id=EP6n8LCEK6&noteId=etZ2jBIeZX.

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W5: The appendix presents examples of model outputs; however, it does not provide examples of inputs to the models (especially in the problem reframing setting). I’ve posed questions around these examples in the Questions section of my review.

Comment:
We understand that providing inputs alongside outputs is crucial for a comprehensive understanding of the examples, particularly in the problem reframing setting. In future iterations, we will ensure that the appendix includes complete input-output pairs for all presented examples. This will provide greater clarity and transparency, addressing the questions raised and allowing for a more thorough evaluation of the methods proposed.

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Ref:
[1] Yilun Du, Shuang Li, Antonio Torralba, Joshua B Tenenbaum, and Igor Mordatch. Improving factuality and reasoning in language models through multiagent debate. arXiv preprint arXiv:2305.14325,

W1: Limited Real-World Testing.

Comment: Replied in the general response.

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W2: Potential Oversimplification

Comment: Replied in the general response.

W3: Scalability Constraints

Observation: The performance degradation observed in saturated systems indicates a limitation in scaling D2C frameworks effectively.

Comment:
Our experimental observations reveal that scaling improves model performance in more complex tasks, such as Chess Move validity. Adding more agents significantly enhances strategic diversity in these scenarios. However, saturation occurs in simpler tasks; for instance, with the PIQA dataset, performance saturates when adding more than four agents.

Thus, while scalability constraints may appear in simpler tasks, they are less prominent for complex, real-world problems, where scaling continues to contribute to performance gains.

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W4: Bias Mitigation Trade-offs

Observation: While the approach reduces biases, it may inadvertently introduce new limitations or biases in certain contexts.

Comment:
We appreciate the opportunity to address the potential trade-offs involved in bias mitigation. While our framework demonstrates efficacy in reducing biases, we acknowledge the possibility of introducing new limitations or biases, particularly in under-represented domains or tasks.

In the revised manuscript, we will:

• Discuss how task-specific characteristics may influence the redistribution or amplification of biases.
• Highlight potential limitations in monitoring and mitigating emerging biases during scaling or deployment.

These additions will provide a more balanced perspective on the advantages and trade-offs of our approach.

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Q1: Why do you study D2C frameworks rather than other MAS frameworks? Is D2C a typical and widely adopted MAS framework? What are the incentives behind this choice?

Comment:
Thank you for your question regarding our selection of the Diverge-to-Converge (D2C) framework for our study.

1. Adoption and Typicality of D2C: D2C is indeed a typical and widely adopted MAS framework. We conceptualize this adoption as part of a broader trend where more MAS frameworks are embracing the D2C paradigm. This trend is exemplified by the frameworks we have explored in our paper, including self-consistency, consultancy, debate, and LLM agents society, which all follow the D2C approach. Some later follow-up works include [1-4].

2. Benefits and Observations of D2C: Based on these D2C frameworks, we have been able to identify inherent characteristics such as prejudice and fidelity, which arise from the framework’s encouragement of agent divergence. This divergence allows for a broad exploration of solutions, which is crucial for potential improvement.

[1] Wang, Junlin, et al. "Mixture-of-Agents Enhances Large Language Model Capabilities." arXiv preprint arXiv:2406.04692 (2024).

[2] Li, Dawei, et al. "SMoA: Improving Multi-agent Large Language Models with Sparse Mixture-of-Agents." arXiv preprint arXiv:2411.03284 (2024).

[3] Li, Yunxuan, et al. "Improving Multi-Agent Debate with Sparse Communication Topology." arXiv preprint arXiv:2406.11776 (2024).

[4] Zhang, Guibin, et al. "Cut the crap: An economical communication pipeline for llm-based multi-agent systems." arXiv preprint arXiv:2410.02506 (2024).

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W1: Could have discussed a greater variety of biases other than confirmation bias

Comment:
In Section 2 (lines 115–123), we discuss various biases examined in prior works, along with our findings regarding different biases in D2C frameworks. Specifically, we uncover an inherent confirmation bias in D2C systems and propose a problem reframing strategy to mitigate it.

Additionally, in Section 6.1.2 (lines 444–469), we highlight:

1. Affirmative vs. negative agent bias: Explored in both open and controlled debate scenarios (refer to Figure 3).
2. Social biases: Including gender (or sex) bias, such as male or female bias (refer to Figure 4, right bars), and political bias, such as left- or right-wing bias (refer to Figure 4, middle bars).
   We believe these discussions provide a broader perspective on biases beyond confirmation bias and will clarify them further in the revised manuscript.

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W2: It isn't clear how questions of real-world importance that are open-ended can always be brought into binary form.

Comment: Replied in the general response.

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W3: Conceptual advances are limited—scaling laws and reframing techniques themselves feel rather incremental

Comment:
We acknowledge the reviewer’s concern about the perceived incremental nature of the scaling laws and reframing techniques. While these methods build upon existing frameworks, our contribution lies in their novel application to D2C systems. Specifically, we demonstrate:

• Scalability: The potential and limitations of collaborative agent frameworks for real-world tasks versus simpler tasks. [Section 6.2]
• Reframing strategies: The ability to mitigate confirmation bias while maintaining performance. [Section 6.1.1, Lines: 419-442]

These findings provide actionable insights for improving agent collaboration and addressing biases, advancing the understanding of D2C frameworks in significant ways. We will clarify this contribution in the revised manuscript.

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W4: Line 216 "menifest"

Comment:
Thank you for pointing out the typographical error. The spelling of "menifest" has been corrected to "manifest" in the revised manuscript. [Line 216]

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Q1: How do you prevent bias in the debate judgments?

Comment:
We appreciate the reviewer’s interest in preventing bias in debate judgments. Our current work focuses on uncovering and addressing confirmation bias through a problem reframing strategy. While this strategy effectively mitigates confirmation bias in D2C systems, we acknowledge the need for broader investigations into bias prevention in debate judgments.

Future studies will explore additional mechanisms for detecting and addressing subtle biases, and we plan to address these challenges in subsequent work.