Exploring Collaboration Mechanisms for LLM Agents: A Social Psychology View (2024)

Abstract: As Natural Language Processing (NLP) systems are increasingly employed in intricate social environments, a pressing query emerges: Can these NLP systems mirror human-esque collaborative intelligence, in a multi-agent society consisting of multiple large language models (LLMs)? This paper probes the collaboration mechanisms among contemporary NLP systems by melding practical experiments with theoretical insights. We fabricate four unique ‘societies’ comprised of LLM agents, where each agent is characterized by a specific ‘trait’ (easy-going or overconfident) and engages in collaboration with a distinct ‘thinking pattern’ (debate or reflection). Through evaluating these multi-agent societies on three benchmark datasets, we discern that certain collaborative strategies not only outshine previous top-tier approaches but also optimize efficiency (using fewer API tokens). Moreover, our results further illustrate that LLM agents manifest human-like social behaviors, such as conformity and consensus reaching, mirroring foundational social psychology theories. In conclusion, we integrate insights from social psychology to contextualize the collaboration of LLM agents, inspiring further investigations into the collaboration mechanism for LLMs. We have shared our code and datasets1, hoping to catalyze further research in this promising avenue.

text: Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 14544–14607 August 11-16, 2024 ©2024 Association for Computational Linguistics
As Natural Language Processing (NLP) systems are increasingly employed in intricate social environments, a pressing query emerges: Can these NLP systems mirror human-esque collaborative intelligence, in a multi-agent society consisting of multiple large language models (LLMs)? This paper probes the collaboration mechanisms among contemporary NLP systems by melding practical experiments with theoretical insights. We fabricate four unique ‘societies’ comprised of LLM agents, where each agent is characterized by a specific ‘trait’ (easy-going or overconfident) and engages in collaboration with a distinct ‘thinking pattern’ (debate or reflection). Through evaluating these multi-agent societies on three benchmark datasets, we discern that certain collaborative strategies not only outshine previous top-tier approaches but also optimize efficiency (using fewer API tokens). Moreover, our results further illustrate that LLM agents manifest human-like social behaviors, such as conformity and consensus reaching, mirroring foundational social psychology theories. In conclusion, we integrate insights from social psychology to contextualize the collaboration of LLM agents, inspiring further investigations into the collaboration mechanism for LLMs. We have shared our code and datasets1, hoping to catalyze further research in this promising avenue.
1 Introduction
With the prevalence of LLMs (Zhao et al., 2023; Yin et al., 2023; Zhu et al., 2023) integral to daily social collaboration, there is a growing imperative to cultivate AI systems embodied with social intelligence. This also resonates with the Society of Mind (SoM) concept (Li et al., 2023a; Zhuge et al.,
∗ Equal Contribution. † Corresponding Author.
1https://github.com/zjunlp/MachineSoM.
2023; Wang et al., 2023), which suggests that intelligence emerges when computational modules interact with each other, achieving collective objectives that surpass the capabilities of individual modules (Minsky, 1988; Singh, 2003). Previous studies (Park et al., 2023; Du et al., 2023b; Liang et al., 2023; Shinn et al., 2023; Madaan et al., 2023; Hao et al., 2023; Liu et al., 2024; Akata et al., 2023) have delved into strategies where LLM instances, termed agents (Wang et al., 2024c; Xi et al., 2023; Gao et al., 2023a; Cheng et al., 2024; Ma et al., 2024b), cooperate synergistically (e.g., debate and reflect) to accomplish tasks (Du et al., 2023a; Pezeshkpour et al., 2024; Guo et al., 2024; Du et al., 2024; Han et al., 2024). As illustrated in Figure 1, such collaboration fosters divergent thinking processes in LLMs, making them particularly effective for tasks demanding profound reflection.
Intuitively, reflecting on human societies (Siegal and Varley, 2002; Leslie et al., 2004; Sap et al., 2022; Shapira et al., 2024), where a myriad of individuals with distinct goals and roles coexist, the SoM framework champions harmonious interactions (Singh, 2003). Intriguingly, despite the fusion of social psychology (Tajfel, 1982; Tajfel and Turner, 2004; Johnson and Johnson, 2009) in SoM with human group dynamics (Woolley et al., 2010; Alderfer, 1987), which illuminates psychological patterns within social groups, its interpretation in the realm of LLMs is relatively uncharted (Ke et al., 2024). Besides, our grasp of how social behaviors influence LLMs is still in its nascent stages.
To address these issues, we delve into the machine society, probing the extent and ways that LLMs manifest social intelligence and collaboration capabilities (Mei et al., 2024). Utilizing powerful LLMs like GPT-3.5 (OpenAI, 2022), we build a test-bed across three datasets: MATH (Hendrycks et al., 2021b), MMLU (Hendrycks et al., 2021a) and Chess Move Validity (Srivastava et al., 2022). Our approach incorporates four societies character-
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ized by two individual traits (easy-going and overconfident) with three agents: totally/mostly easygoing; totally/mostly overconfident. These traits are employed to emulate nuanced human society dynamics (Soni et al., 2024; Wang et al., 2024b,a; Li et al., 2023b; Kong et al., 2023).
Moreover, we delve into two distinct thinking patterns under multi-round collaboration: debate (Perelman, 1971; Sunstein, 2005; Amgoud and Prade, 2009; Du et al., 2023b; Liang et al., 2023) and reflection (Bogumil, 1985; Mezirow, 2003; Bolton, 2010). With the permutation of thinking patterns, we can constitute various collaborative strategies. To this end, we implement two patterns of collaboration in the collaborative strategies: (i) All agents adopt the same thinking pattern at each round; (ii) One agents adopts the different thinking patterns from others at each round. We then execute these multi-round collaborative strategies within different societies. Through our empirical analysis, we primarily discern the following insights (Further takeaways are in §3, §4 & Appendix A):
(1) Collaborative strategies with various permutations of thinking patterns vary significantly in performance, and engaging in substantive debates enhances collaboration performance. Intriguingly, multi-agent societies composed of agents with different traits do not clearly differ in performance.
(2) Employing uniform thinking patterns across all agents within a round of collaboration enhances efficiency. Besides, merely increasing the number of agents or the number of collaboration rounds does not consistently yield better outcomes. The balance between agent quantity and strategies emerges as a key determinant in collaboration.
(3) LLM agents manifest behaviors reminiscent of human social tendencies, such as conformity
(Allen and Levine, 1969; Cialdini and Goldstein, 2004) or the principle of majority rule in group thinking (Seal et al., 1998), which resonate with several fundamental theories in social psychology (Castro and Liskov, 1999; Tajfel and Turner, 2004).
Concretely, our findings challenge the dominant belief that mere scale is the key. We posit that smallgroup collaboration with rational strategies might present a more efficacious approach to utilizing LLMs. In wrapping up, we encapsulate the core contributions of this research as follows:
• We initiate an elaborate exploration into collaboration mechanisms in multi-agent society. Our goal is to identify how and to what extent LLMs manifest social intelligence through collaboration. To enrich our inquiry, we draw upon theories from social psychology, contextualizing the behaviors and tendencies displayed by LLM agents.
• Our research framework includes a meticulously crafted test-bed, integrating diverse multi-agent societies with agent individual traits, thinking patterns, and collaborative strategies, evaluated over three datasets. Notably, our empirical findings can inspire how to design a better multi-agent system through collaboration, beyond merely scaling up LLMs and Agents.
• Interestingly, our observations underscore a fascinating parallel: LLM agents mirror certain social behaviors typical of human collaboration. It could further emphasize the potential of human-AI interaction. Generally, fostering effective and efficient collaborative strategies for multi-agent systems could be the key to more socially-aware AI.
2 Explore Collaboration Mechanisms with Multiple LLM Agents
In this section, we formulate and simulate the collaboration mechanisms explored within the machine society, drawing upon relevant concepts. We also illustrate the society settings in Figure 2.
2.1 Preliminary Concepts in Collaboration
Individual Trait. Inspired by intelligence emerging from the collective efforts of numerous smaller and relatively simple agents (Minsky, 1988), each characterized by diverse traits, we set two types of agents exhibiting typically contrasting traits: easygoing and overconfident, as shown in Figure 2(a). Easy-going agents keep things in perspective, adapt well to different situations, and are compatible with various types of agents (Friedman and Schustack, 1999), which results in a harmonious societal structure with democracy (Mutz, 2006; Held, 2006). Conversely, overconfident agents tend to overestimate their competence, ignore potential risks, and resist others’ opinions (Moore and Healy, 2008).
Thinking Pattern. Considering the SoM concept (Minsky, 1988) states that intelligence emerges when specialized individuals within a society cooperate through thinking, we aim to study what thinking patterns are most successful
in producing such emerging intelligence. Thus we explore two thinking patterns: debate (Sunstein, 2005; Du et al., 2023b; Liang et al., 2023) and reflection (Bogumil, 1985; Bolton, 2010; Shinn et al., 2023), as illustrated in Figure 2(c). (i) In the debate pattern, several agents propose ideas, exchange responses, engage in collective argumentation, and ultimately reach a consensus. This fosters knowledge sharing, facilitates learning, and promotes adaptation among all agents within the society (Weiß, 1995; Stone and Veloso, 2000; Vidal, 2006; Wooldridge, 2009). (ii) In the reflection pattern, agents review their prior responses, extract lessons from their experiences, and refine their answers accordingly. These two patterns can unfold over several rounds.
Collaborative Strategy. Through both critical reflection and active participation in debate, agents are poised to challenge their existing assumptions, acquire fresh perspectives, and ultimately refine their viewpoints. Employing a collaboration mechanism built on these two thinking patterns can foster more insightful decision-making (Wooldridge, 2009; Amgoud and Prade, 2009) and improve reasoning outcomes (Mezirow, 2018). In societal settings, agents typically engage in multiple rounds of collaboration for problem-solving. In this paper, we characterize the collaborative strategy as a per-
mutation of thinking patterns throughout multiround collaboration, as illustrated in Figure 2(d) and further elaborated in §2.2.
We simulate the multi-agent collaborative society, as detailed with symbols shown in Table 1. Specifically, we construct a machine society consisting of n LLM agents, denoted as A = {ai}ni=1. This society contains two distinct agent traits: T = {to, te}, where to and te respectively denotes the overconfident and easy-going trait. For each agent, at any round of collaboration, there are two thinking patterns to choose from, symbolized as P = {p0, p1}, where p0 and p1 corresponds to debate and reflection respectively. By endowing agents A with the traits of T , we can emulate various machine societies. In our primary study (§3), we establish four distinct societies, S = {S1, S2, S3, S4}, each consisting of three agents: {a1, a2, a3}. The societies are constructed based on the combination of three agents with distinct traits, as illustrated in Figure 2(b):
S1 = {(a1 ← to), (a2 ← to), (a3 ← to)} (totally overconfident) S2 = {(a1 ← to), (a2 ← to), (a3 ← te)} (mostly overconfident) S3 = {(a1 ← to), (a2 ← te), (a3 ← te)} (mostly easy-going) S4 = {(a1 ← te), (a2 ← te), (a3 ← te)} (totally easy-going)
where (ai ← tj) denotes that the agent ai possesses the trait tj . If there is an even number of agents, we can also constitute a society with half overconfident and half easy-going agents. In our simulation, all agents consistently employ the same thinking pattern at each round of collaboration, similar to Du et al. (2023b). It gives rise to eight possible 3-round collaborative strategies:
p0p0p0, p0p0p1, p0p1p0, p0p1p1,
p1p0p0, p1p0p1, p1p1p0, p1p1p1
In our subsequent analysis (§3.2), we delve into more intricate scenarios, introducing a larger number of agents, increased collaboration rounds, and a broader range of collaborative strategies.
2.3 Experimental Settings Datasets. We conduct a rigorous evaluation of the reasoning and decision-making capabilities of various machine societies across three distinct tasks, utilizing diverse collaborative strategies:
• High School Multiple-Choice. Leveraging the MMLU (Hendrycks et al., 2021a) dataset, where problems span high school subjects such as statistics, mathematics, computer science, biology, chemistry, and physics, agents are required to identify the correct answer among four multiple-choice options. Our evaluation set consists of 50 randomly selected questions from this dataset.
• Math. Drawing from MATH dataset (Hendrycks et al., 2021b), a repository of math problems sourced from competitive events and expressed in LaTeX, we assess the model proficiency in advanced mathematical and scientific reasoning. The dataset segments these problems into five graded difficulty levels, and for our evaluation, we have randomly chosen 50 cases from Level 3 to 5.
• Chess Move Validity. Utilizing the dataset from the chess state tracking task2 within the comprehensive BIG-Bench Benchmark (Srivastava et al., 2022), a sequence of chess moves denoted in UCI notation3 is provided. Agents are required to predict a legitimate subsequent move for a specified chess piece.
Setups. We craft specific instructions for each task, trait, and strategy, which can be referred to Table 5 at Appendix D.3. To enhance result reliability, we present average accuracy (Acc) and their respective standard deviations across five trials. Notably, our experiments exhibit substantial standard deviations. Hence, we introduce WIN-TIE (W-T) metric, indicating the frequency (over five trials) where the accuracy either matches or surpasses the continuous debate baseline (Du et al., 2023b). Meanwhile, we gauge the average token costs (Cost)
2https://github.com/google/BIG-bench/blob/main/bigbench/ benchmark_tasks/chess_state_tracking/synthetic_short/task.json.
3https://en.wikipedia.org/wiki/Universal_Chess_Interface.
ChatGPT. Blue marks the best-performing strategy under the same society, light blue represents the second-bestperforming strategy, and red indicates the worst-performing strategy. Cost / Cost measures the average tokens consumed by all cases under the same collaborative strategy / society. W-T / W-T tallies the total number of occurrences where performance exceeds the strategy p0p0p0 under the same collaborative strategy / society. The significances test on societies and strategies are respectively shown in Table 6, 7 at Appendix E. The experiments of comparison with the single LLM agent is shown in Figure 21(a)-(f) at Appendix G.2.
consumed by the agents across societies, shedding light on the efficacy of the different collaborative strategies employed. For these evaluations, ChatGPT serves as the LLM agent accessible through the OpenAI API gpt-3.5-turbo-11064. Further comprehensive details on data sampling and result evaluation are introduced in Appendix D.
3 Analysis of Machine Social Collaboration
Our experiments are primarily driven by the following research queries: (RQ1) How does problemsolving effectiveness vary under different collaborative strategies across diverse societies? (RQ2) How to configure the machine society variables for optimal performance? (RQ3) How does machine social collaboration mimic the human society?
3.1 Main Results with Quantitative Analysis To address RQ1, we present the performance of four distinct societies in Table 2, each employing one of eight possible collaborative strategies, evaluated across three datasets with ChatGPT. To make the experimental findings more general, we evaluate on other LLMs, shown in Appendix H. Our experiments yield several pivotal observations:
(1) Societies do not clearly differ in performance but differ significantly in their tendency
4https://platform.openai.com/docs/models/gpt-3-5.
to reach a consensus. As observed from Table 2, among different 3-agent societies S1 ∼ S4 employing the same collaborative strategy (a vertical comparison on Acc), the variations in accuracy are not pronounced. We also conduct a significance test of societies using ChatGPT in Appendix E, and other LLMs in Appendix H, further demonstrating insignificant differences between the societies. Thus we conclude that distinct societies composed of 3 agents possessing varied traits play an indistinctive role in shaping performance. We infer that this is due to LLM alignment (Ouyang et al., 2022), inhibiting agents from displaying extreme overconfidence, which contradicts human alignment (Liu et al., 2022). Sharma et al. (2024) also demonstrate that LLMs tend to show sycophancy, as illustrated in Figure 11, 12. Furthermore, we increase the number of agents (2 to 10), accordingly resulting in more diverse societies, as seen in Figure 14, indicating that the impact of societies on performance remains indistinctive. We further analyze consensus reaching, i.e., agents reach a consistent answer (Chen et al., 2023b), shown in Figure 16 at Appendix E, and find that more diverse societies (5 types of societies, with 2 to 10 agents) observably impact the average quantity of consensus. Generally, a society totally comprising easy-going agents is more likely to reach a consensus.
(2) Permutation of thinking patterns is crucial for collaboration, where debate-initial and debate-dominant strategies exhibit superiority. For instance, on MMLU dataset, debate-dominant collaborative strategies, like p0p0p1, p0p1p0, and p1p0p0, all containing two rounds of debate, display a pronounced outperformance (65.2 for p0p0p1 in S4 versus 34.4 for p1p0p0 in S4). As seen from Table 2, collaborative strategies starting with the thinking pattern of debate p0 (debate-initial), such as p0p0p0, p0p0p1, p0p1p0, and p0p1p1, generally outperform others across all datasets. Furthermore, observed from the performance (i) under strategies with different (3∼10) rounds of collaboration on ChatGPT, as shown in Figure 4 and Figure 18, 19 at Appendix F, debate-initial/dominant strategies are overall better; (ii) on LlaMA2 Chat 13B in Table 14 and Qwen 72B in Table 26, debateinitial stategies are generally superior; (iii) on LlaMA2 Chat 70B in Table 20 and Mixtral 8×7B in Table 32, debate-dominant stategies are superior. Observed from different 3-round collaborative strategies pipjpk applied within the same society (a horizontal comparison on Acc), the variations in accuracy are notably pronounced. Besides, the significance test of different collaborative strategies using ChatGPT in Appendix E and other LLMs in Appendix H demonstrate that the order of thinking patterns significantly impacts the effectiveness.
(3) Tasks behave better under collaborative strategies starting with continuous debate, and debate combined with continuous reflection is superior for difficult tasks. Seen from Table 2, when comparing the best performance (marked in blue) and the worst (marked in red) within the same societies, the difference in results for Chess Move Validity is slight. This stands in sharp contrast to MMLU and MATH, which suggests that the effectiveness of collaborative strategies depends on the task. We then illustrate the performance under different collaborative strategies in view of task domains and difficulty in Figure 13 at Appendix E; on other LLMs in Figure 24, 33, 42, 56 at Appendix H. Figure 13(a) exhibits task-specific impacts and Figure 13(b),(c) reflects domain-dependent impacts under different collaborative strategies, where p0p0p0 and p0p0p1 starting with continuous debate are generally superior. For the mathematics domain seen from Figure 13(d), like MMLU mathematics and MATH level 3 & 4, the performance variations under different strategies are relatively small, but
for the more difficult task, i.e., MATH level 5, the strategies containing debate and continuous reflection (i.e., p0p1p1, p1p1p0) behave superiorly. These nuanced disparities imply that the marginal benefits derived from collaborative strategies may be task-dependent and difficulty-sensitive.
3.2 Impact of Machine Society Settings
To address RQ2, we delve deeper into the variables influencing multi-agent society collaboration, exploring the intricacies of agent composition, collaboration rounds, and collaborative strategies.
Different Numbers of Agents. To evaluate the impact of different numbers of agents, we analyze performance within societies comprising 2∼10 agents, presented in Figure 3(a). Different numbers of agents would constitute five types of societies, where the agents’ traits could be: totally/mostly easy-going/overconfident; half easygoing/overconfident. We observe that odd numbers of agents generally outperform others within all types of societies, and the possible reason is that odd-number agents can avoid ties. Besides, we also find that the variations of accuracy among odd-number agents are indistinctive. Thus we conclude that the optimal number of agents is 3, considering both performance and efficiency. We also implement a significance test of the number of agents shown in Table 11 at Appendix F, demonstrating that different numbers of agents significantly impact performance. Besides, we illustrate consensus reaching with different numbers of agents in Figure 3(b), demonstrating that more agents are more likely to reach a consensus.
Different Rounds. We then delve into the effects of different numbers of collaboration rounds, and further scale up the rounds of collaboration, presenting the performance under 3 to 10 rounds in Figure 4. Despite some fluctuation in performance from 3 to 10 rounds of collaboration, the variations are not extremely remarkable. Considering both accuracy and cost, we infer that 3-round collaboration is relatively effective and efficient. We also conduct a significance test on different rounds of collaborative strategies, shown in Table 12 at Appendix F, and observe that the impact of rounds significantly relies on the collaborative strategy employed. Generally, the strategies starting or dominating with reflection p1 differ clearly in performance under different rounds.
Other Collaborative Strategies. Venturing into scenarios with more intricate collaboration, we allow agents to adopt varied thinking patterns in each round of collaboration. For example, given three agents, in a specific round of collaboration, two agents engage in debate while the other one engages in reflection. To increase diversity, we perform a random allocation of thinking patterns to agents in each round, steering clear of scenarios where all agents adopt the same thinking pattern. Intriguingly, as shown in Figure 5, the presence of inconsistent thinking patterns within a society tends to negatively impact performance. Given the observation, we claim that maintaining a consistent thinking pattern for all agents in a particular round would maximize collaborative efficacy.
4 Phenomena of Conformity and Consensus Reaching
To address RQ3, we embark on further analysis from a social psychology view (Tajfel, 1982; Tajfel
and Turner, 2004; Johnson and Johnson, 2009), to discern alignment between machine society collaboration and human societal dynamics (Woolley et al., 2010). Our findings indicate that machine society collaboration echoes specific human societal phenomena or theories, such as conformity (Cialdini and Goldstein, 2004; Allen and Levine, 1969; Coultas and van Leeuwen, 2015) and consensus reaching (Scheff, 1967; Degroot, 1974; Baronchelli, 2018) (more analysis are in Appendix G.1). We also analyze group dynamics (Cartwright and Zander, 1968; Alderfer, 1987; Forsyth, 2014; Bion, 2018; Forsyth, 2018) in multiagent collaboration at Appendix G.2 as page limits.
We embark on a detailed analysis, to discern the conformity and consensus-reaching phenomena in collaboration. For instance, as depicted in Figure 8(a) at Appendix D.3, an agent initially responds correctly to a question. However, swayed by the misguided answers and explanations from the other two agents, eventually, the three agents conform to an incorrect answer. This phenomenon
mirrors detriments in “groupthink” (Janis, 1972; Jehn, 1995), suggesting that members of tightknit groups tend to value harmony and consensus over objective critique of divergent views, potentially leading to flawed decisions. Contrastingly, in another scenario illustrated in Figure 8(b) at Appendix D.3, all three agents converge on the right answer after engaging in a society-wide debate. This mirrors benefits in “groupthink” (Jehn, 1995) and “SoM” (Minsky, 1988; Singh, 2003), where a multitude of agents collaboratively yield intelligence. Within such debates, agents furnish varied viewpoints and information. Through these exchanges, conflicts are resolved, ideas are honed, and the group gravitates toward an informed consensus (Fisher et al., 2011; Forsyth, 2018).
We also conduct a quantitative analysis of the prevalence of conformity and consensus-reaching phenomena. We analyze answer correctness changing at each round of collaboration in the situation of conformity, shown in Figure 6 on ChatGPT and Figure 28, 37, 51, 65 on other LLMs at Appendix H. We also present the ratio of consensus reaching at each round in Figure 7 on ChatGPT and Figure 29, 38, 52, 66 on other LLMs at Appendix H. We summarize the following obeservations:
• Conformity is widespread, and the proportion of conformity increases with the round increases in general.
• Overall, considering performance improvement, conformity is beneficial in on ChatGPT, Qwen 72B; and harmful on LlaMA2 Chat 13B/70B, Mixtral 8×7B.
• As the number of rounds increases, benefits of conformity will weaken (the ratio difference between True and False answers becomes smaller); and detriments of conformity enhance (the ratio difference between False and True answers becomes larger).
• Generally, reflection results in increasing the quantity of consensus clusters, demonstrating more difficulty to reach a consensus, while debate is more likely to reach a consensus.
5 Conclusion and Future Work
This study has highlighted the potential of collaboration mechanisms with LLMs. Our findings reveal the impressive collaboration capabilities of LLM agents, with different individual traits, thinking patterns, and collaborative strategies. The emergence of human-like behaviors in these agents, resonating with social psychology theories, further emphasizes the potential of human-AI interaction. Moving forward, a deeper exploration into the multi-agent society is warranted, focusing on collaboration behavior refinement; integrating further insights from social psychology could also guide the development of socially aware NLP systems.
Limitations
Although we explored various societies and collaborative strategies, our study still has its limitations. Firstly, limited by expense, we don’t explore the impact of multiple agents respectively based on different LLMs, which may lead to more interesting findings at the social level due to the usage of differently distributed pre-trained data and strategies aligned with human intentions. Furthermore, we traversed all possible scenarios by search alone, lacking a way to let the agents adaptively make autonomous decisions on collaborative strategies in specific scenarios. Although debate can be as close as possible to the upper limit, this approach entails a larger consumption and there exist some strategies that can achieve better performance with less overhead. Additionally, our experimental setup is relatively straightforward, as we have not considered more intricate configurations, such as a broader range of traits or a larger-scale society. Finally, we evaluate performance through manual validation and rule-based matching, which also limits the ability to validate more realistic and creative tasks, such as literary creation.
Reproducibility Statement
All code and data can be found in the GitHub repository5. For specific experimental implementation details, please refer to Appendix D.
Ethics Statement
This research was conducted in line with the highest ethical standards and best practices in research. The data employed were extracted from publicly accessible datasets, ensuring no usage of proprietary or confidential information. Consequently, this research is free from any ethical concerns.
Acknowledgments
We would like to express gratitude to the anonymous reviewers for their kind and helpful comments. We extend our sincere gratitude to MinYen Kan and team members from NUS Web IR / NLP Group advised by Min-Yen Kan; Tao Gui and team members from FudanNLP Group; and Diyi Yang from Stanford University for providing insightful and constructive feedback on this paper. This work was supported by the National Natural Science Foundation of China (No.
5https://github.com/zjunlp/MachineSoM.
62206246), the Fundamental Research Funds for the Central Universities (226-2023-00138), Zhejiang Provincial Natural Science Foundation of China (No. LGG22F030011), Yongjiang Talent Introduction Programme (2021A-156-G), Tencent AI Lab Rhino-Bird Focused Research Program (RBFR2024003), Information Technology Center and State Key Lab of CAD&CG, Zhejiang University, and NUS-NCS Joint Laboratory (A-000854200-00).
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Overview of Appendices
We summarize the overview of Appendices below: §A: Key Takeaways. §B: Related Work. §C: Potential Real-World Applications. §D: Implementation Details.
Experimental Setup (§D.1) Experimental Evaluation (§D.2) Illustration of Agent Collaboration (§D.3)
§E: Further Analysis on Machine Social Collaboration (Backbone: ChatGPT). §F: Analysis on Machine Society Settings (Backbone: ChatGPT). §G: A Social Psychology View on Conformity, Consensus Reaching, and Group Dynamics (Backbone: ChatGPT).
Conformity, Consensus Reaching (§G.1) Group Dynamics (§G.2)
§H: Analysis on Different Backbone LLMs. LlaMA2 Chat 13B (§H.1) LlaMA2 Chat 70B (§H.2) Qwen 72B (§H.3) Mixtral 8×7B (§H.4)
§I: Assessing the Effectiveness of Prompts.
A Key Takeaways
Drawing from our comprehensive analysis, we distill valuable insights for future multi-agent collaboration designs concerning Strategy Selection, Society Settings, and Social Psychology View.
Regarding Strategy Selection,
• Starting or dominating multi-agent collaboration with debate, yields relatively optimal outcomes, as seen from Table 2, 8, 14, 20, 26, 32.
• Totally-reflection strategy like p1p1p1 is generally worst in performance, as observed from Table 2, 8, 14, 20, 26, 32.
• For difficult tasks, debate combined with continuous reflection is superior; for simple tasks, self-consistency or reflection is enough, as seen from Figure 13, 24, 33, 42, 56.
Regarding Society Settings,
• Surprisingly, “overconfident” agents lose that trait in groups, as observed from word clouds in Figure 11, 22, 31, 40, 54 and answer keeping in Figure 12, 23, 32, 41, 55!
• Setting agent numbers to 3 is generally advantageous in performance and cost, as seen from Figure 15, 25, 34, 43, 57.
• The rounds of collaboration are relatively suitable to set as 3 since it’s both effective and efficient, as seen from Figure 18, 4, 19 on ChatGPT; Figure 26, 35 on LlaMA 13B/70B; Figure 47, 48, 49 on Qwen 72B; Figure 61, 62, 63 on Mixtral 8×7B.
• Employing the uniform thinking patterns across all agents within a round enhance efficacy, as seen from Figure 5, 20, 27, 36, 50, 64.
Regarding Social Psychology View,
• Collaboration is generally effective in the group, especially for tackling difficult tasks, as observed from Figure 13, 24, 33, 42, 56; and Figure 21, 30, 39, 53, 67.
• Collaboration widely leads to conformity, either beneficial or harmful in performance. As observed from Figure 6, 28, 37, 51, 65.
• As the number of rounds increases, the benefits of conformity will decrease, and the detriments of conformity will increase, as observed from Figure 6, 28, 37, 51, 65.
• The totally easy-going society is more likely to reach a consensus, debate helps to consensus reaching while reflection impedes it, as observed from Figure 16, 45, 59; and Figure 7, 29, 38, 52, 66.
B Related Work
Multi-Agent Collaboration. With the development of Large Language Models (LLMs) (Zhao et al., 2023; Yin et al., 2023; Zhu et al., 2023), study on LLM-based agents (Wang et al., 2024c; Xi et al., 2023; Gao et al., 2023a; Cheng et al., 2024), has drawn considerable attention. Recently there has been a proliferation of various agent systems, such as Generative Agents (Park et al., 2023), MetaGPT (Hong et al., 2024), ProAgent (Zhang et al., 2024), Agents (Zhou et al., 2023), OpenAgents (Xie et al., 2023), AutoAgents (Chen et al., 2023a), MAgIC (Xu et al., 2023), AgentBoard (Ma et al., 2024a), InterAct (Chen and Chang, 2023), and AutoAct (Qiao et al., 2024). These works have primarily focused on the elaborate design/evaluation of agent components, such as memory, environment, and planning. There are also some works
exploring what kind of mindset can fully exploit the comprehensive performance of the multi-agent system (Guo et al., 2024; Pezeshkpour et al., 2024; Du et al., 2024; Han et al., 2024), including debate (Du et al., 2023b; Liang et al., 2023) and reflection (Shinn et al., 2023; Madaan et al., 2023).
AgentVerse (Chen et al., 2024) draws on the above two types of work to explore the multi-agent architecture and design two collaboration patterns: Horizonal Communication (similar to debate (Du et al., 2023b; Liang et al., 2023)) and Vertical Communication (similar to self-refine (Madaan et al., 2023)). These two collaboration patterns are included in our experiment framework. In addition, we have also explored a variety of other societies and collaborative strategies. Besides, there are also some researches focusing on exploring cooperation between agents constituted by different model compositions, such as ReConcile (Chen et al., 2023c). Although we do not demonstrate this kind of method, our work can easily expand to it.
Human-Agent Simulation. When the pretrained LLMs (e.g., LLM-empowered agents) are socially aligned (Duéñez-Guzmán et al., 2023; Liu et al., 2024; Gao et al., 2023b), they could exhibit human-like intelligence (Minsky, 1988; Singh, 2003; Zhuge et al., 2023; Li et al., 2023a; Xu et al., 2024; Talebirad and Nadiri, 2023). Specifically, agents can simulate human-like behaviors (Mei et al., 2024; Wang et al., 2024a; Xiao et al., 2023; Li et al., 2023b; Zhang et al., 2023b,a; Chuang et al., 2023; Chuang and Rogers, 2023; Crouse et al., 2023; Xie et al., 2024; Liang et al., 2024), play roles like humans (Shanahan et al., 2023; Hou et al., 2023; He et al., 2023), and even collaborate with humans (Fuchs et al., 2023; Gao et al., 2024; Feng et al., 2024; Alberts et al., 2024).
Notably, multi-agent collaboration can echo human society phenomena or theories in a social psychology view (Binz and Schulz, 2023; Demszky et al., 2023; Hagendorff, 2023; Kuribayashi et al., 2024), such as conformity (Cialdini and Goldstein, 2004; Allen and Levine, 1969; Coultas and van Leeuwen, 2015), consensus reaching (Scheff, 1967; Degroot, 1974; Baronchelli, 2018), group dynamics (Cartwright and Zander, 1968; Alderfer, 1987; Seal et al., 1998; Forsyth, 2014; Bion, 2018; Forsyth, 2018) and social science (Gilbert and Terna, 2000; Epstein, 2012; Flache et al., 2017; Lorenz et al., 2021; Smaldino, 2023; Lanctot et al., 2023).
C Potential Real-world Applications
In this section, we present some potential applications (Ke et al., 2024) of our work, which could benefit from the LLM agents’ ability to collaborate effectively, similar to how human collaboration is enriched inspired by social psychology.
• Social Research: LLM agents can be used to simulate social interactions to study phenomena like conformity, leadership, or group decision-making.
• Negotiation and Mediation: LLMs could simulate multiple parties in a negotiation so that offering fair solutions based on social psychology principles.
• AI Ethics and Governance: By understanding the dynamics of social behaviors, LLM agents could help in forming guidelines for AI ethics, ensuring AI systems are developed and deployed responsibly.
• Advanced Team Collaboration Tools: By understanding social dynamics, LLM agents could facilitate better team collaboration, suggesting initiatives, mediating discussions, and optimizing workflow.
• Intelligent Tutoring Systems: Collaborative LLM agents could personalize education by interacting with students in a more human-like manner, adapting to individual learning styles and requirements.
• Healthcare Coordination: LLM agents could collaborate to provide care advice, cross-referencing patient data, and medical knowledge to assist healthcare professionals.
• Crisis Management: During emergencies, LLM agents could work together to analyze data, manage communications, and provide real-time information to the public.
• Content Creation: Collaborative LLMs could produce complex content, such as scripts or articles, by dividing tasks based on different expertise areas or writing styles.
• Interactive Entertainment: In gaming and virtual reality, LLM agents could provide more dynamic and responsive narratives, by collaborating to adapt the storyline to the players’ actions and intentions.
Experiment Type Model Dataset
Collaboration Round Number of Agents Society
Different Number of Agents
gpt-3.5-turbo-1106 Mixtral 8x7B Qwen 72B Chess Move Validity 3 2∼10 See the Figure 15 and Table 11.
LlaMA-13B-Chat LlaMA-70B-Chat
MMLU Chess Move Validity 3 2∼4
Only one easy-going agent in the society
Different Collboration Rounds
gpt-3.5-turbo-1106 Mixtral 8x7B Qwen 72B MMLU MATH Chess Move Validity 10 3 S2
LlaMA-13B-Chat LlaMA-70B-Chat
MMLU Chess Move Validity 4 3 S2
Different Strategy
gpt-3.5-turbo-1106 LlaMA-13B-Chat LlaMA-70B-Chat Mixtral 8x7B Qwen 72B MMLU MATH Chess Move Validity 3 3 S2
The detailed society settings of the experiments in §3.2 are shown in Table 3. Due to the context length constraints of the LlaMA2 Chat 13B and LlaMA2 Chat 70B, which support a maximum of 4096 tokens, it’s challenging to scale up the number of agents and the rounds of collaboration. Consequently, we have capped the collaboration rounds at 4 and also restricted the maximum agent number to 4. We select MMLU and Chess Move Validity datasets in our analysis. Nevertheless, a small fraction of cases still exceed the maximum length constraint. To address this, we strategically prune content from the earlier rounds to ensure compliance with the length limitation. As for other LLMs (ChatGPT, Mixtral 8×7B, and Qwen 72B), in terms of experiments on the number of agents, adding an additional agent results in substantial costs. This is due to the necessity of conducting 5 replicate experiments and accommodating 8 collaborative strategies. Therefore, our experiments on these LLMs are carried out on the less token-intensive dataset: Chess Move Validity. As for trials con-
cerning the rounds of collaboration, the quantity of viable collaborative strategies increases exponentially with each additional round – for instance, 10 rounds would yield 210 unique strategies. Considering the complexity, we analyze on 8 strategies that are representative of the broader set of possibilities.
The decoding parameters for various models are detailed in Table 4. In gpt-3.5-turbo-1106, we align our approach with Du et al. (2023b) by setting the temperature to 0, while adhering to the default settings for the remaining parameters. For Qwen 72B, we utilize the default parameters as furnished by the official documentation. For the remaining models, we configure the temperature to 0.7 and respectively adjust the Top P and Top K values to 50 and 0.95. This configuration is primarily based on insights from Demszky et al. (2023), which advocates for the recognition and integration of the inherent stochastic nature of LLM outputs into analytical frameworks, in a manner akin to the treatment of stochastic variables in psychological studies. It is noteworthy that even with the temperature parameter set to 0, gpt-3.5-turbo-1106 may still exhibit randomness in the outputs.
The prompts used in our experiments are shown in Table 5. On the MMLU dataset, we curated questions from 6 domains (statistics, mathematics, computer science, biology, chemistry, and physics) and performed a random sampling of 50 samples, maintaining a proportion of 8 : 8 : 8 : 8 : 9 : 9 for each domain. On the MATH dataset, we randomly selected 50 cases from Level 3, 4, and 5, distributing them in a ratio of 22 : 22 : 6. On the
Chess Move Validity dataset, we similarly selected 50 samples for testing.
D.2 Experimental Evaluation
The evaluation process involves two fundamental steps: (i) A unified answer is selected from the machine society. To achieve this, we employ the majority vote method to ascertain the consensus reached by the society after multiple rounds of collaboration. If the unanimity among agents is not achieved, it will be considered as an error. Additionally, if an individual agent provides multiple answers without following our prompts, its response will be disregarded. (ii) Answer responses from agents are matched against the ground truth. This step presents two main challenges. Firstly, there is the concern of non-compliance with instructions. Despite providing explicit prompts and specifying the desired output format for evaluation, it’s inevitable that agents may occasionally deviate from the given instructions. Secondly, the answers may manifest in non-unique forms, leading to potential variations, such as the equivalence between “3/4” and “0.75” in the MATH (Hendrycks et al., 2021b) dataset. To address these challenges, a comprehensive set of matching rules is employed. Nonetheless, it is important to acknowledge the possibility of encountering a small number of values that fall outside the purview of these rules.
D.3 Illustration of Multi-Agent Collaboration
As seen from Figure 8, the conformity phenomenon in multi-agent collaboration can be both beneficial (i.e., changing the answer from wrong to correct) and harmful (i.e., changing the answer from correct to wrong) in problem-solving.
We also illustrate the detailed conversation process for multi-agent collaboration in Figure 9 and Figure 10, regarding the conformity phenomenon presented in Figure 8.
E Further Analysis on Machine Social Collaboration (Backbone: ChatGPT)
We conduct a rigorous significance test for the main experiment in §3.1. Given our experimental design incorporating two key factors, namely collaborative strategy and society, we respectively opt for a one-way analysis of variance. Before delving into the analysis, we ensured that the data adhered to a normal distribution and satisfied the assumption of homogeneity of variance. We present
the p-values for society and collaborative strategy across three datasets in Table 6, 7.
We then present the main results and significance tests of societies andcollaborative strategies on ChatGPT (with the engine of gpt-3.5-turbo employed between July 10 and July 23, 2023) in Table 8, 9, 10.
Notably, the p-value of the collaborative strategy (on ChatGPT, engine: gpt-3.5-turbo-1106; gpt-3.5-turbo in July) is significantly below the threshold of 0.05, indicating that collaborative strategies have substantial impact on performance. Besides, on the backbone LLM of ChatGPT, the p-value of the society (with the engine of gpt-3.5-turbo-1106) is smaller than 0.05 in 17 out 24 cases, in contrast, the p-value of the society (with the engine of gpt-3.5-turbo employed between July 10 and July 23, 2023) is larger than 0.05 in 23 out 24 cases. Generally, this corroborates our earlier conclusion in §3.1, emphasizing that the influence of collaborative strategies outweighs that of societies.
We also present the word clouds in Figure 11, and answer changing of agents with different traits in Figure 11, to reveal that indistinctive impact of 3-agent societies on performance. Furthermore, we demonstrate that the tasks with different
ChatGPT (with engine of gpt-3.5-turbo employed between July 10 and July 23, 2023). Blue marks the best-performing strategy under the same society, light blue represents the second-best-performing strategy, and red indicates the worst-performing strategy. Cost / Cost measures the average tokens consumed by all cases under the same collaborative strategy / society. W-T / W-T tallies the total number of occurrences where performance exceeds the strategy p0p0p0 under the same collaborative strategy / society. The significances test on societies and strategies are respectively shown in Table 9, 10.
subjects and difficulty display varying sensitivity to collaborative strategies, as presented with radar maps in Figure 13.
F Analysis on Machine Society Settings (Backbone: ChatGPT)
In this section, we conduct significance tests for the experiments outlined in §3.2. The chosen method is one-way analysis of variance. Prior to the analysis, we performed a check for homogeneity of variance, with only one entry in Table 13 deviating from the criteria. The significance tests for the number of agents, the number of rounds, and different collaborative strategies are respectively detailed in Table 11, Table 12 and Table 13.
Different Numbers of Agents. According to the results of the p-values in Table 11, the conclusion in §3.2 is confirmed, namely, different number of agents results in a significant correlation on performance. By integrating the results in Figure 3, it becomes evident that the presence of three agents is relatively optimal.
We also analyze the consensus reaching with different numbers of agents, and present the results in Figure 16, 17.
Different Rounds of Collaboration. As
varied subjects and difficulty, using ChatGPT. The symbol ‘ ’ represents that there is at least one collaborative strategy whose accuracy is better than self-consistency, while the symbol ‘ ’ indicates that there is no collaborative strategy whose accuracy is worse than self-consistency. Both of these symbols represent the accuracy of selfconsistency. The accuracy under each collaborative strategy is a summation within all 3-agent societies.
observed from Table 12, we find that the impact of rounds significantly relies on the employed collaborative strategy. For MMLU and Chess Move Validity, collaborative strategies where p-values < 0.05 are {p0p1p1p0, p0p1p1p1, p1p0p1p0, p1p0p1p1} and {p0p1p1p0, p0p1p1p1, p1p0p1p1, p1p1p0p0, p1p1p0 p1, p1p1p1p0}. We also increase the rounds of collaboration, from 3 to 10, and present the results in Figure 18, 19. We find that although there would be some fluctuations in performance if we scale up the round of collaboration, the outperformance is not obvious enough. While increasing rounds of collaboration will result in more consumption of tokens, which is not economic. Thus we infer that the 3-round collaboration is relatively optimal considering both performance and cost.
Furthermore, as seen from Figure 7, the strategy after a round of debate tends to yield fewer consensus clusters compared to the preceding rounds. Conversely, the strategy subsequent with a round of reflection at the same juncture will increase consensus clusters. Adding an extra round of debate at this juncture, as the conclusions in §4, is not anticipated to bring about a discernible enhancement in performance. This confirms the efficacy of the early-stopping mechanism implemented in Liu et al. (2023), drawing inspiration from Byzantine Consensus theory (Castro and Liskov, 1999).
Moreover, we scrutinize the consensus reaching of these strategies in three rounds where pvalues are below 0.05, as shown in Figure 7. Also seen from Figure 7 and Figure 18, 4, 19, it becomes apparent that these collaborative strategies exhibit substantial fluctuations in consensus reaching, demonstrating notably low answer consistency.
For p0p0p0p0 on Chess Move Validity, although continuous reflection results in a gradual increase in the number of consensus clusters, a more stable trend with smaller fluctuations renders it less sensitive to the rounds of collaboration. Conversely, collaborative strategies where p-values> 0.05 often display higher levels of answer consistency.
Other Collaborative Strategies. We show the results of all agents in a society executing the same or inconsistent thinking pattern(s) at one round in Figure 20. Seen from Table 13, we observe pronounced impacts of keeping a consistent thinking pattern on Chess Move Validity, while its influence
on MMLU and MATH is less significant.
G A Social Psychology View on Conformity, Consensus Reaching, and Group Dynamics
G.1 Conformity and Consensus Reaching
Figures 6, 28, 37, 65, and 51 illustrate the conformity. Figures 7, 28, 37, 65, and 51 illustrate the consensus. This section provides a detailed explanation of the methodologies used to calculate both conformity and consensus.
For conformity, we solely focus on agents actively engaging in debate, disregarding those in re-
flection during a given round. Let the answer of the i-th agent at j-th round be denoted as ai,j . For the k-th agent at j-th round, if “Frequency ( {ai,j−1|i ∈
[1, n]} )
= ak,j”, we identify this as the occurrence of conformity by agent k at j-th round, where Frequency(·) represents the most frequently given answer (excluding instances where all answers occur only once, as such cases are considered as nonconformity). Additionally, we categorize the correctness of answers both before and after conformity into four cases, with ‘True’ denoting correct and ‘False’ denoting incorrect.
For consensus, we examine the evolution of the number of distinct answers (i.e., consensus clusters) with increasing rounds of collaboration. Let the answer of the i-th agent at time j be denoted as ai,j . For the j-th round, consensus clusters is defined as ‖Set({ai,j |i ∈ [1, n]})‖, where ‖Set(·)‖ represents the count of different answers. This computational approach has been utilized in the analysis presented in Figures 17, 16, 60, 59, 46, 45.
G.2 Group Dynamics
We seek to elucidate how performance is impacted by group dynamics, i.e., the patterns of interaction between group members and different processes that may occur within a social group.
Diving into the intricacies of collaboration, each agent generates four answers, including the initial answer without collaboration, as shown in Figure 2(d). To determine the answer for each round, we employ the majority vote (Cobbe et al., 2021; Li et al., 2022). Given ‘T’ and ‘F’ respectively denoting a round that yields a correct and an incorrect answer, we could obtain 24=16 possible answer sequences over the four rounds. We select 10 sequences6 of them and categorize them into 3 groups: Correcting Mistakes (FFFT, FFTT, FTTT ), Changing Correct Answers (TFFF, TTFF, TTTF ), and Wavering Answers (FTFT, FTTF, TFTF, TFFT ). Particularly, Wavering Answers resemble model hallucination (Rawte et al., 2023; Zhang et al., 2023c; Ji et al., 2023; Luo et al., 2024) due to the occurrence of self-contradictory answers. Our categorization is under society-agnostic collaborative strategies, considering the performance variance between societies is negligible. From the results on ChatGPT shown in Figure 21, and on other LLMs shown in Appendix H, we summarize the following findings:
(1) Debate-initial/dominant collaborative 6The selected 10 sequences adhere to patterns: (1) [F ]i>0[T ]j>0, e.g., FFFT ; (2) [T ]i>0[F ]j>0, e.g., TFFF ; (3) [TF ]i≥0[FT ]j≥0, e.g., FTFT , where [·]i, [·]j respectively denotes repetition for i, j times.
strategies are generally effective. As seen from the red bars in Figure 21 30, 39, 53, 67(d-f), we find that the collaborative strategies starting from or dominant with debate p0 are more effective than other, and mostly outperform self-consistency, even though they cost more tokens (seen from blue bars).
(2) Reflection experiences greater instability (a heightened risk of model hallucination). As observed from the purple bars in Figure 21 30, 39, 53, 67(g-h), comparing pipjp0 & pipjp1; pip0pj & pip1pj , pipjp0 and pip0pj are more likely to wavering answers than pipjp1 and pip1pj , demonstrating that reflection is more likely to cause model hallucination than debate.
H Analysis on Different Backbone LLMs
To make the findings in this paper more general, we also implement all the experiments with some other open-resource backbone LLMs, such as LlaMA2 Chat 13B (Touvron et al., 2023), LlaMA2 Chat 70B (Touvron et al., 2023), Qwen 72B (Bai et al., 2023) and Mixtral 8×7B (Jiang et al., 2023, 2024).
H.1 LlaMA2 Chat 13B Analysis on Machine Social Collaboration. We present the main results and significance tests of societies and strategies on LlaMA2 Chat 13B in Table 14, 15, 16. We present the word clouds of LlaMA2 Chat 13B in Figure 22, and proportion of agents with different traits keeping answers in different societies on LlaMA2 Chat 13B in Figure 23. Furthermore, we demonstrate that the tasks with different subjects and difficulty display varying sensitivity to collaborative strategies, as presented with radar maps on LlaMA2 Chat 13B in Figure 24.
Analysis on Different Numbers of Agents. We present the significance test for different numbers of agents with LlaMA2 Chat 13B in Table 17. We also show the performance varying from agent numbers in Figure 25.
Analysis on Different Rounds. We present the significance test for different rounds of collaboration with LlaMA2 Chat 13B in Table 18. We also show the performance varying from collaboration rounds in Figure 26.
Analysis on Other Collaborative Strategies. We present the significance test for other collaborative strategies (executing the same or hybrid thinking patterns in a certain round) with LlaMA2 Chat 13B in Table 19. We also show the performance varying from other strategies in Figure 27.
A Social Psychology View on Conformity, Consensus Reaching and Group Dynamics. We then show the variation of answer correctness in the situation of conformity in Figure 28; and the quantity of consensus clusters among 3-agent answers in Figure 29. We present group dynamics reflected by different answer-changing behaviors on LlaMA2 Chat 13B in Figure 30.
varied subjects and difficulty, using LlaMA2-13B-chat. The symbol ‘ ’ represents that there is at least one collaborative strategy whose accuracy is better than self-consistency, while the symbol ‘ ’ indicates that there is no collaborative strategy whose accuracy is worse than self-consistency. Both of these symbols represent the accuracy of self-consistency. The accuracy under each collaborative strategy is a summation within all 3-agent societies.
H.2 LlaMA2 Chat 70B Analysis on Machine Social Collaboration. We present the main results and significance tests of societies and strategies on LlaMA2 Chat 70B in Table 20, 21, 22. We present the word clouds of LlaMA2 Chat 70B in Figure 31, and proportion of agents with different traits keeping answers in different societies on LlaMA2 Chat 70B in Figure 32. Furthermore, we demonstrate that the tasks with different subjects and difficulty display varying sensitivity to collaborative strategies, as presented with radar maps on LlaMA2 Chat 70B in Figure 33.
Analysis on Different Numbers of Agents. We present the significance test for different numbers of agents with LlaMA2 Chat 70B in Table 23. We also show the performance varying from agent numbers in Figure 34.
Analysis on Different Rounds. We present the significance test for different rounds of collaboration with LlaMA2 Chat 70B in Table 24. We also show the performance varying from collaboration rounds in Figure 35.
Analysis on Other Collaborative Strategies. We present the significance test for other collaborative strategies (executing the same or hybrid thinking patterns in a certain round) with LlaMA2 Chat 70B in Table 25. We also show the performance varying from other strategies in Figure 36.
A Social Psychology View on Conformity, Consensus Reaching and Group Dynamics. We then show the variation of answer correctness in the situation of conformity in Figure 37; and the quantity of consensus clusters among 3-agent answers in Figure 38. We present group dynamics reflected by different answer-changing behaviors on LlaMA2 Chat 70B in Figure 39.
varied subjects and difficulty, using LlaMA2-70B-chat. The symbol ‘ ’ represents that there is at least one collaborative strategy whose accuracy is better than self-consistency, while the symbol ‘ ’ indicates that there is no collaborative strategy whose accuracy is worse than self-consistency. Both of these symbols represent the accuracy of self-consistency. The accuracy under each collaborative strategy is a summation within all 3-agent societies.
H.3 Qwen 72B Analysis on Machine Social Collaboration. We present the main results and significance tests of societies and strategies on Qwen 72B in Table 26, 27, 28. We present the word clouds of Qwen 72B in Figure 40, and proportion of agents with different traits keeping answers in different societies on Qwen 72B in Figure 41. Furthermore, we demonstrate that the tasks with different subjects and difficulty display varying sensitivity to collaborative strategies, as presented with radar maps on Qwen 72B in Figure 42.
Analysis on Different Numbers of Agents. We present the significance test for different numbers of agents with Qwen 72B in Table 29. We also show the performance varying from agent numbers in Figure 43, varying from societies containing 2∼10 agents in Figure 44. We also analyze the consensus reaching with different numbers of agents, and present the results in Figure 45, 46.
Analysis on Different Rounds. We present the significance test for different rounds of collaboration with Qwen 72B in Table 30. We also show the performance varying from collaboration rounds in Figure 47, 48, 49.
Analysis on Other Collaborative Strategies. We present the significance test for other collaborative strategies (executing the same or hybrid thinking patterns in a certain round) with Qwen 72B in Table 31. We also show the performance varying from other strategies in Figure 50.
A Social Psychology View on Conformity, Consensus Reaching and Group Dynamics. We then show the variation of answer correctness in the situation of conformity in Figure 51; and the quantity of consensus clusters among 3-agent answers in Figure 52. We present group dynamics reflected by different answer-changing behaviors on Qwen 72B in Figure 53.
varied subjects and difficulty, using Qwen 72B. The symbol ‘ ’ represents that there is at least one collaborative strategy whose accuracy is better than self-consistency, while the symbol ‘ ’ indicates that there is no collaborative strategy whose accuracy is worse than self-consistency. Both of these symbols represent the accuracy of selfconsistency. The accuracy under each collaborative strategy is a summation within all 3-agent societies.
H.4 Mixtral 8×7B Analysis on Machine Social Collaboration. We present the main results and significance tests of societies and strategies on Mixtral 8×7B in Table 32, 33, 34. We present the word clouds of Mixtral 8×7B in Figure 54, and the proportion of agents with different traits keepging answers in different societies on Mixtral 8×7B in Figure 55. Furthermore, we demonstrate that the tasks with different subjects and difficulty display varying sensitivity to collaborative strategies, as presented with radar maps on Mixtral 8×7B in Figure 56.
Analysis on Different Numbers of Agents. We present the significance test for different numbers of agents with Mixtral 8×7B in Table 35. We also show the performance varying from agent numbers in Figure 57, varying from societies containing 2∼10 agents in Figure 58. We also analyze the consensus reaching with different numbers of agents, and present the results in Figure 59, 60.
Analysis on Different Rounds. We present the significance test for different rounds of collaboration with Mixtral 8×7B in Table 36. We also show the performance varying from collaboration rounds in Figure 61, 62, 63.
Analysis on Other Collaborative Strategies. We present the significance test for other collaborative strategies (executing the same or hybrid thinking patterns in a certain round) with Mixtral 8×7B in Table 37. We also show the performance varying from other strategies in Figure 64.
A Social Psychology View on Conformity, Consensus Reaching and Group Dynamics. We then show the variation of answer correctness in the situation of conformity in Figure 65; and the quantity of consensus clusters among 3-agent answers in Figure 66. We present group dynamics reflected by different answer-changing behaviors on Mxitral-8×7B in Figure 67.
varied subjects and difficulty, using Mixtral-8×7B. The symbol ‘ ’ represents that there is at least one collaborative strategy whose accuracy is better than self-consistency, while the symbol ‘ ’ indicates that there is no collaborative strategy whose accuracy is worse than self-consistency. Both of these symbols represent the accuracy of self-consistency. The accuracy under each collaborative strategy is a summation within all 3-agent societies.
I Assessing the Effectiveness of Prompts
In this section, we conduct a sanity check to ensure that the agents’ actions reflect align with our instruction, such as reflecting easy-going or overconfident traits.
Prompts play a critical role in our experiments and are the primary focus of this sanity check. The word cloud analysis presented in Figure 11 supports the appropriateness of the “easy-going” prompt. Consequently, confirming the effectiveness of the “overconfident” prompt is crucial. We use “reflecting the overconfident trait” as a case study to explore the validity of our prompts. In the absence of established validation techniques, we combine experimental results and experiential insights to evaluate prompt effectiveness from three perspectives:
• Granularity of Description. As illustrated in Table 5, we describe two behaviors, i.e., “being confident in your answer” and “persuading other agents to believe in you”, both aligning with the behavioral facets of “overconfident”.
• Model Response. We employ the role-play method to prompt the model and subsequently inquire its awareness, as illustrated in Table 5. If the prompts potentially instruct the model to generate harmful content, the model refuses to comply with the prompt. Upon reviewing our logs, it is noteworthy that the model ac-
cepted all prompts without refusal. Instead, it responded with “OK” as corroborated by the ‘role-play’ part in Figure 9 and Figure 10.
• Ask Again. We revisit the initial scenarios and responses using the role-play format. We then query the model again: “If one agent’s answer differs from yours, what should you do?” The model replies: “In a situation where another agent’s answer differs from mine, I should respectfully present my perspective, providing supporting evidence or reasoning to demonstrate confidence in my response. It’s important to engage in constructive dialogue and potentially find common ground, but maintaining clarity and conviction in my position is crucial to persuading others to consider my viewpoint.” This response, emphasizing overconfidence, demonstrates the rationality of our prompts. The complete conversation record is illustrated in Figure 68.
Example Analysis. We further validate the “Ask Again” method with specific interactions involving an overconfident and an easy-going agent, by showing a concrete example. We provide the conversation records with an overconfident agent and an easy-going agent, respectively in Figure 69 and Figure 70. Despite the model’s response being incorrect and our prompted answer being accurate, the model consistently maintains its viewpoint, reaffirming our prompt design’s effectiveness.

heading: Future Work