Belief Coevolution in a Social Network of Generalist and Specialist Large Language Models
Summary
This paper introduces CoevolveSim, a framework for studying belief diffusion among networked generalist and specialist LLM agents, showing that specialist models and network structure affect consensus and influence dynamics.
arXiv:2607.27512v1 Announce Type: new
Abstract: Large language models (LLMs) are increasingly deployed in multi-agent environments. However, the processes by which beliefs form and propagate among interacting LLMs remain poorly understood. We introduce CoevolveSim, a framework for studying belief diffusion within networked LLM populations. CoevolveSim allows us to isolate and study three factors: domain specialization, social-role assignment, and social network structure. Within this framework, generalist and specialist LLM agents exchange and revise beliefs. In each round, an LLM agent observes a summary of its neighbors' beliefs before updating its own. We run 1,280 controlled simulations spanning four scenarios, two network structures, and 20 medical-indication statements. We find that persona-style role assignment and network structure reshape individual belief revision but have minimal effect on population-level consensus. In contrast, introducing (finetuned) specialist LLMs more than doubles the shift in consensus and gives rise to consistent asymmetries in exerted influence. We further show that simple persistence-based opinion-dynamics models reproduce collective outcomes in all-generalist LLM populations, whereas heterogeneous LLM populations require population-level belief composition to reproduce consensus and agent identity to predict individual belief transitions. Our results indicate that realistic simulation of belief diffusion in multi-agent LLM systems requires a diverse set of underlying LLMs, not persona prompting alone.
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# Belief Coevolution in a Social Network of Generalist and Specialist Large Language Models Source: [https://arxiv.org/html/2607.27512](https://arxiv.org/html/2607.27512) Germans Savcisens1,2,Samantha Dies1,Courtney Maynard1,Tina Eliassi\-Rad1,2,3 1Khoury College of Computer Sciences, Northeastern University, Boston, USA 2Network Science Institute, Northeastern University, Boston, USA 3Santa Fe Institute, Santa Fe, USA Correspondence:[g\.savcisens@northeastern\.edu](https://arxiv.org/html/2607.27512v1/mailto:[email protected]) ###### Abstract Large language models \(LLMs\) are increasingly deployed in multi\-agent environments\. However, the processes by which beliefs form and propagate among interacting LLMs remain poorly understood\. We introduceCoevolveSim, a framework for studying belief diffusion within networked LLM populations\.CoevolveSimallows us to isolate and study three factors: domain specialization, social\-role assignment, and social network structure\. Within this framework, generalist and specialist LLM agents exchange and revise beliefs\. In each round, an LLM agent observes a summary of its neighbors’ beliefs before updating its own\. We run1,2801\{,\}280controlled simulations spanning four scenarios, two network structures, and 20 medical\-indication statements\. We find that persona\-style role assignment and network structure reshape individual belief revision but have minimal effect on population\-level consensus\. In contrast, introducing \(finetuned\) specialist LLMs more than doubles the shift in consensus and gives rise to consistent asymmetries in exerted influence\. We further show that simple persistence\-based opinion\-dynamics models reproduce collective outcomes in all\-generalist LLM populations, whereas heterogeneous LLM populations require population\-level belief composition to reproduce consensus and agent identity to predict individual belief transitions\. Our results indicate that realistic simulation of belief diffusion in multi\-agent LLM systems requires a diverse set of underlying LLMs, not persona prompting alone\. Code and simulation data:[carlomarxdk/coevolve\-sim](https://github.com/carlomarxdk/coevolve-sim)\. Belief Coevolution in a Social Network of Generalist and Specialist Large Language Models Germans Savcisens1,2, Samantha Dies1, Courtney Maynard1, Tina Eliassi\-Rad1,2,31Khoury College of Computer Sciences, Northeastern University, Boston, USA2Network Science Institute, Northeastern University, Boston, USA3Santa Fe Institute, Santa Fe, USACorrespondence:[g\.savcisens@northeastern\.edu](https://arxiv.org/html/2607.27512v1/mailto:[email protected]) ## 1Introduction Figure 1:Schematic overview ofCoevolveSimbelief diffusion\.Given a discussion topic,CoevolveSimfirst asks each agent for its initial belief without providing information about the neighbors \(Round0\)\. Then,CoevolveSimfacilitates the exchange of beliefs and social roles between agents and their immediate neighbors\. In each subsequent round,CoevolveSimevaluates the belief of each agent after providing a summary of the beliefs of its neighbors from the previous round\. AfterTTrounds of interaction, agents reach their final belief states\. In this illustration and in our experiments, we setT=10T=10\.Side note: The discussion statement is factually correct\.Large language models \(LLMs\) are becoming integral to the global information ecosystem\. Nearly two\-thirds of companies now use generative artificial intelligence \(AI\) to produce written contentMcKinsey & Company \([2025](https://arxiv.org/html/2607.27512#bib.bib26)\), with AI\-generated text appearing in contexts ranging from UN press releases to scientific articlesLianget al\.\([2025a](https://arxiv.org/html/2607.27512#bib.bib24),[b](https://arxiv.org/html/2607.27512#bib.bib25)\)\. On social knowledge platforms such asQuora, the share of AI\-generated posts increased from22% in 2022 to3939% by late 2024Sunet al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib5)\)\. At the same time, LLMs are increasingly common in multi\-agent settings, including debate and collaborative reasoningGuoet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib29)\); Wuet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib49)\); Tranet al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib28)\)\. As these applications grow, understanding how beliefs form and spread within populations of interacting LLMs becomes increasingly important\. Questions of collective belief formation have long been studied in the human opinion\-dynamics literature\. Individuals revise beliefs after exposure to others’ opinionsLorenzet al\.\([2011](https://arxiv.org/html/2607.27512#bib.bib62)\)and often reach consensus after repeated interactionsBeckeret al\.\([2017](https://arxiv.org/html/2607.27512#bib.bib63)\)\. Nevertheless, the degree to which individuals influence others’ beliefs varies unevenly within a populationMoussaïdet al\.\([2013](https://arxiv.org/html/2607.27512#bib.bib64)\)\. For example,Baileyet al\.\([2023](https://arxiv.org/html/2607.27512#bib.bib65)\)show that a social label assigned to an advisor \(whether the advisor is described as an expert or a novice\) is the strongest predictor of the extent to which individuals rely on the given advice\. Hence, collective outcomes emerge from aninterplaybetween individual characteristics and social structure rather than from any single mechanism in isolation\. Existing work on multi\-agent LLM systems has largely focused on behavioral outcomes such as task completion, votes, and debate performanceGuoet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib29)\)\. However, LLM\-based agents may exhibit varied behaviors as they are powered by different LLMs, assigned certain social roles \(e\.g\., persona\-style prompting\) or connected to distinct sets of agents in the interaction networks\. The relationship between these factors remains largely understudied, making it difficult to quantify their contributions to agent\-level beliefs, influence, and population\-level dynamicsNget al\.\([2026](https://arxiv.org/html/2607.27512#bib.bib58)\); Yeet al\.\([2026](https://arxiv.org/html/2607.27512#bib.bib59)\)\. We introduceCoevolveSim, a network\-mediated belief diffusion framework in which generalist and specialist LLM agents exchange and revise beliefs over repeated rounds of interaction \(see[Figure˜1](https://arxiv.org/html/2607.27512#S1.F1)\)\. InCoevolveSim, we focus on three factors: - 1\.Domain specialization, which specifies the LLM that powers an agent and determines its specialization \(such as a chemist, a physician, an engineer,etc\)\. - 2\.Social role, which is assigned to each LLM agent\. This persona\-style label is communicated to the agent and its neighbors\. - 3\.Structure of the social network, which determines which LLM agents candirectlyexchange beliefs with each other\. This setup allows us to answer two questions, which we study across four experimental scenarios \(§[4\.4](https://arxiv.org/html/2607.27512#S4.SS4)\): - 1\.Which factors drive belief diffusion in populations of interacting LLM agents? - 2\.Can the resulting dynamics be explained using classical opinion\-dynamics mechanisms? We quantify the resulting belief dynamics in terms of belief revision, exerted influence, and consensus \(§[4\.5\.1](https://arxiv.org/html/2607.27512#S4.SS5.SSS1)\)\. We then assess whether these dynamics can be reproduced by opinion\-dynamics models \(referred to here as surrogate models\) that predict belief transitions using different information, from individual persistence to local social influence and identity\-based characteristics \(§[4\.5\.2](https://arxiv.org/html/2607.27512#S4.SS5.SSS2)\)\. Our findings:LLM heterogeneity is the primary driver of collective belief change\. That is, populations containing a diverse set of LLMs exhibit larger shifts in consensus and stronger influence asymmetries than populations that differ only in social\-role assignment \(all\-generalist populations\)\. Similarly, the factors required to predict individual belief revisions are not necessarily the same as those required to reproduce collective outcomes, highlighting the gap between agent\- and population\-level explanations of belief diffusion\. ##### Contributions - 1\.We introduceCoevolveSim, a framework for studying belief diffusion in populations of networked LLM agents\. - 2\.We disentangle the effects of domain specialization, social\-role assignment, and social network structure through1,2801\{,\}280controlled simulations across four scenarios\. - 3\.We demonstrate that social\-role assignment and network structure each reshape individual belief trajectories, yet leave population\-level consensus nearly unchanged \(§[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)\)\. - 4\.We show that LLM heterogeneity is the primary driver of collective belief change, giving rise to opinion leaders \(§[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)\)\. - 5\.We show that the mechanisms that predict individual belief revisions differ from those that reproduce collective consensus \(§[5\.2](https://arxiv.org/html/2607.27512#S5.SS2)\)\. ## 2Related Work Our work stands at the intersection of \(1\) research on multi\-agent LLM systems, \(2\) heterogeneous agent populations, and \(3\) opinion dynamics\. ### 2\.1Beliefs in Multi\-Agent LLM Systems Multi\-agent LLM systems are typically evaluated through behavioral outcomes such as task completion, voting, and debate performanceGuoet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib29)\); Wuet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib49)\); Chenet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib50)\)\. More recent work focuses directly on the belief states, showing that belief consistency varies across tasks and modelsPalet al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib45)\)\. Similarly, population\-level outcomes such as consensus can also amplify persuasionBilginet al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib44)\), further highlighting that interactions betweenmultiplefactors affect collective behaviorBrockerset al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib60)\)\. However, agent states, local interactions, and population\-level dynamics remain jointly understudiedNget al\.\([2026](https://arxiv.org/html/2607.27512#bib.bib58)\), and existing work rarely isolates the effects of domain specialization, social roles, and network structure\. ### 2\.2Domain Specialization and Social Roles Heterogeneity in multi\-agent LLM populations is commonly introduced through either prompt\-based personas \(that instruct an LLM on how to behave\) or specialized models \(that use various pretrained or finetuned LLMs\)\. Persona\-based approaches simulate diverse social identitiesChuanget al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib2)\); Taubenfeldet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib6)\), but their effects often weaken over extended interactionsBhandariet al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib1)\); Villaet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib56)\)\. Specialized models, by contrast, exhibit greater robustness on domain\-specific tasksTanwaret al\.\([2025](https://arxiv.org/html/2607.27512#bib.bib54)\); Chenet al\.\([2023](https://arxiv.org/html/2607.27512#bib.bib52)\); Mullicket al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib3)\), while homogeneous LLM populations can be vulnerable to consensus collapse and bias amplificationBreumet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib55)\); Estornell and Liu \([2024](https://arxiv.org/html/2607.27512#bib.bib48)\); Xionget al\.\([2023](https://arxiv.org/html/2607.27512#bib.bib7)\)\. So far, existing studies examine personas or specialized models in isolation, making it difficult to separate the effects of portrayed and perceived social roles from those of underlying domain specialization\. ### 2\.3Opinion Dynamics and Network Structure Classical opinion\-dynamics models such as those ofDeGroot \([1974](https://arxiv.org/html/2607.27512#bib.bib38)\)andFriedkin and Johnsen \([1990](https://arxiv.org/html/2607.27512#bib.bib39)\)describe belief revision as a process of repeated social influence\. Empirical studies suggest that local interactions can increase consensusLorenzet al\.\([2011](https://arxiv.org/html/2607.27512#bib.bib62)\); Beckeret al\.\([2017](https://arxiv.org/html/2607.27512#bib.bib63)\), while members of majority groups or those with specialized knowledge produce asymmetric influenceMoussaïdet al\.\([2013](https://arxiv.org/html/2607.27512#bib.bib64)\)\. Network structure further shapes collective outcomes by influencing how information propagates through a populationBakshyet al\.\([2011](https://arxiv.org/html/2607.27512#bib.bib61)\)\. However, network structure is rarely manipulated in multi\-agent LLM systemsChuanget al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib2)\); Gaoet al\.\([2023](https://arxiv.org/html/2607.27512#bib.bib57)\)\. These findings suggest that collective belief dynamics emerge from interactions among specialization, social position, and network structure\. Our experimental design operationalizes these three factors within an LLM framework, allowing us to study their individual and combined effects on belief diffusion\. ## 3Belief Diffusion Framework We introduceCoevolveSim, a network\-mediated belief diffusion framework \([Figure˜1](https://arxiv.org/html/2607.27512#S1.F1)\)\. We designed itto isolate the effects of three factors: \(1\) agents’ specialization, \(2\) social\-role assignment, and \(3\) social network structure\. In our framework, generalist LLM agents \(powered by LLMs without finetuning\) and specialist LLM agents \(powered by LLMs finetuned in various fields such as clinical medicine, chemistry, cybersecurity, mathematics, and other fields; see[Table˜A2](https://arxiv.org/html/2607.27512#A2.T2)\) are embedded in an undirected social networkGG\. In each roundtt, LLM agentaia\_\{i\}receives a template message shown in[Figure˜2](https://arxiv.org/html/2607.27512#S3.F2)\. The message includes the agent’s assigned social role, a discussion statement, and a summary of its neighbors’ beliefs from roundt−1t\{\-\}1\. Belief updates are synchronous and Markovian: all agents condition on information from the same previous round, which includesonlythe latest neighborhood summary\. This design allows us to examine how domain specialization, social role, and neighborhood \(social network structure\) shape beliefs overT=10T=10rounds\. In this section, we define domain specialization and social roles \(§[3\.1](https://arxiv.org/html/2607.27512#S3.SS1)\), specify network structures \(§[3\.2](https://arxiv.org/html/2607.27512#S3.SS2)\), formalize belief extraction \(§[3\.3](https://arxiv.org/html/2607.27512#S3.SS3)\), and define the neighborhood summary \(§[3\.4](https://arxiv.org/html/2607.27512#S3.SS4)\)\.[Table˜A1](https://arxiv.org/html/2607.27512#A1.T1)lists the notation used in this section\. ### 3\.1Domain Specialization and Social Roles Each LLM agent is characterized by adomain specializationand asocial role\.Domain specializationreflects an LLM’s finetuning domain\. For example,Llama3\-Med42Christopheet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib10)\)is finetuned on clinical text, so we assume it has a medical specialization\.Social roleis asocial labelassigned to an LLM agent and communicated to both the agent and its immediate neighbors\. Social roles function as social identities, such as “clinical physician,” “mathematician,” or “chemist\.” In our experiments, social roles do not necessarily correspond to specialization\. An LLM agent could specialize in medicine but portray itself as a mathematician\. This separation allows us to test whether belief dynamics are driven by what an LLM agentknows\(domain specialization\) or by what it islabeled as\(social role\)\. ### 3\.2Social Networks We embednnLLM agents in an undirected networkGG, where each agentaia\_\{i\}is a node and edges represent social connections\. Every LLM agentaja\_\{j\}with an edge to agentaia\_\{i\}is part ofaia\_\{i\}’s neighborhood𝒩\(i\)\\mathcal\{N\}\(i\)\. We describe the selection of network structures in §[4\.3](https://arxiv.org/html/2607.27512#S4.SS3)\. ### 3\.3Belief Extraction An LLM agentℳ\\mathcal\{M\}maps an input sequence𝒙\\boldsymbol\{x\}to a distribution𝒫ℳ\\mathcal\{P\}\_\{\\mathcal\{M\}\}\. For any tokenτ∈𝒱ℳ\\tau\\in\\mathcal\{V\}\_\{\\mathcal\{M\}\},𝒫ℳ\(τ∣𝒙\)\\mathcal\{P\}\_\{\\mathcal\{M\}\}\(\\tau\\mid\\boldsymbol\{x\}\)gives the \(uncalibrated\) probability thatτ\\tauis the next token after𝒙\\boldsymbol\{x\}\. We use𝒫ℳ\\mathcal\{P\}\_\{\\mathcal\{M\}\}together with a templated message𝒙\\boldsymbol\{x\}to extract the belief scoresSavcisens and Eliassi\-Rad \([2025](https://arxiv.org/html/2607.27512#bib.bib23)\)\. ##### Templated Message\. Figure 2:Message structure for belief probing\.Each LLM agent receives a message that follows the Hugging Face chat template: \(1\) asystemprompt assigning the agent’s role𝒙r\\boldsymbol\{x\}\_\{r\}and task instructions; \(2\) auserprompt containing the statement𝒙s\\boldsymbol\{x\}\_\{s\}, the neighborhood summary𝒙n\(t\)\\boldsymbol\{x\}\_\{n\}^\{\(t\)\}\(𝒙n0=∅\\boldsymbol\{x\}\_\{n\}^\{0\}=\\emptyset\), and the multiple\-choice question; and \(3\) theassistantprompt from which we extract the next\-token probabilities to obtain belief scores\.At roundtt, LLM agentaia\_\{i\}receives a message𝐦i\(t\)=\(𝒙r,𝒙s,𝒙n\(t\)\)\\mathbf\{m\}\_\{i\}^\{\(t\)\}=\(\\boldsymbol\{x\}\_\{r\},\\boldsymbol\{x\}\_\{s\},\\boldsymbol\{x\}\_\{n\}^\{\(t\)\}\)containing the agent’s role𝒙r\\boldsymbol\{x\}\_\{r\}, the discussion statement𝒙s\\boldsymbol\{x\}\_\{s\}, and a summary𝒙n\(t\)\\boldsymbol\{x\}\_\{n\}^\{\(t\)\}of neighbors’ beliefs from roundt−1t\{\-\}1, with𝒙n\(0\)=∅\\boldsymbol\{x\}\_\{n\}^\{\(0\)\}=\\emptyset\. The message ends with a multiple\-choice question asking the agent to classify the statement𝒙s\\boldsymbol\{x\}\_\{s\}as \(1\)correct, \(2\)incorrect, or \(3\)neither\(see[Figure˜2](https://arxiv.org/html/2607.27512#S3.F2)\)\. ##### Belief\. Given message𝐦i\(t\)\\mathbf\{m\}\_\{i\}^\{\(t\)\}, we operationalize LLM agentii’s belief at roundttas 𝒃i\(t\)\(y∣𝐦i\(t\)\)=𝒫ℳ\(\[ky\]∣𝐦i\(t\)\),\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\\\!\\left\(y\\mid\\mathbf\{m\}\_\{i\}^\{\(t\)\}\\right\)=\\mathcal\{P\}\_\{\\mathcal\{M\}\}\\\!\\left\(\\texttt\{\[\}k\_\{y\}\\texttt\{\]\}\\mid\\mathbf\{m\}\_\{i\}^\{\(t\)\}\\right\),\(1\)whereky∈\{1,2,3\}k\_\{y\}\\in\\\{1,2,3\\\}indexesy∈\{y\\in\\\{correct,incorrect,neither\}\\\}\. The next\-token probability assigned to the corresponding option is thebelief score\. Additionally, any residual probability mass not captured by these tokens is added to𝒃i\(t\)\(neither\)\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\(\\textit\{neither\}\)so that the three scores sum to11\. Further, the LLM agent’sdiscretized beliefis Bi\(t\)=argmaxy𝒃i\(t\)\(y\)\.B\_\{i\}^\{\(t\)\}=\\arg\\max\_\{y\}\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\(y\)\.\(2\) ### 3\.4Neighborhood Summary At roundtt, we collect the previous round’s discretized beliefsBj\(t−1\)B\_\{j\}^\{\(t\-1\)\}fromaia\_\{i\}’s neighbors and group the neighbors into three categories:agree,disagree, andunsure\. For each group, we generate a sentence listing the corresponding neighbor roles and counts \(see[Figure˜2](https://arxiv.org/html/2607.27512#S3.F2)\), and concatenate the three sentences to form a summary of the neighbors’ beliefs𝒙n\(t\)\\boldsymbol\{x\}\_\{n\}^\{\(t\)\}\. To quantify the initial belief of each LLM agent, no neighborhood summary is provided att=0t=0\. To reduce the ordering bias, we randomly shuffle social roles within each sentence and randomize sentence ordering before inserting them into the templated message\. ## 4Experimental Setup In this section, we describe the LLMs used in our study \(§[4\.1](https://arxiv.org/html/2607.27512#S4.SS1)\), discussion statements \(§[4\.2](https://arxiv.org/html/2607.27512#S4.SS2)\), network generation \(§[4\.3](https://arxiv.org/html/2607.27512#S4.SS3)\), simulation scenarios \(§[4\.4](https://arxiv.org/html/2607.27512#S4.SS4)\), as well as details on the descriptive evaluation \(§[4\.5\.1](https://arxiv.org/html/2607.27512#S4.SS5.SSS1)\) and surrogate analysis \(§[4\.5\.2](https://arxiv.org/html/2607.27512#S4.SS5.SSS2)\)\. ### 4\.1Large Language Models To study how domain specialization is associated with belief formation, we use1515LLMs from theLlama\-3Grattafioriet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib8)\)family\.Llama\-3\.1\-8B\-Instructserves as thegeneralist, since it is pretrained without a domain\-specific corpus\. The other1414LLMs serve asspecialistsandarefinetuned on domain\-specific corpora, such as biomedical texts, cybersecurity reports, and programming tasks\. Each LLM has88billion parameters, so performance differences are more likely to come from finetuning rather than model size\.[Table˜A2](https://arxiv.org/html/2607.27512#A2.T2)provides information about the LLMs used in our experiments\. ### 4\.2Discussion Statements We sample2020affirmative statements referencing real\-world medical indications from the corpus introduced bySavcisens and Eliassi\-Rad \([2025](https://arxiv.org/html/2607.27512#bib.bib23)\)\. An example of a sampledtruestatement is“Terbutaline is indicated for the treatment of asthma,”while“Ethinylestradiol is indicated for the treatment of dry cough”is an example of afalsestatement\. We use zero\-shot predictions from a medical LLM111Llama3\-Med42Christopheet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib10)\)is hereafter referred to as the medical LLM\.and1414additional LLMs to construct features that capture \(1\) the binary ground\-truth label of a statement \(true,false\), \(2\) label predicted by the medical LLM, \(3\) accuracy of the medical LLM, \(4\) average accuracy of other LLMs, and \(5\) agreement between the medical LLM and other LLMs\. We apply the maximin criterionJohnsonet al\.\([1990](https://arxiv.org/html/2607.27512#bib.bib33)\)to sample a diverse set of statements\. That is, we maximize the minimum pairwise distance in this feature space\. We provide additional details and a list of statements in[Appendix˜C](https://arxiv.org/html/2607.27512#A3)and[Table˜A4](https://arxiv.org/html/2607.27512#A3.T4)\. ### 4\.3Social Networks We represent social connections between agents via two network structures: \(1\)Erdős and Rényi \([1959](https://arxiv.org/html/2607.27512#bib.bib35)\)\(ER\), and \(2\)Watts and Strogatz \([1998](https://arxiv.org/html/2607.27512#bib.bib34)\)\(WS\)\. In ER,G\(n,p\)G\(n,p\), each pair of LLM agents is connected with a probabilitypp\. It typically produces locally tree\-like networks with low clustering and light\-tailed degree distributionsBarabási and Pósfai \([2016](https://arxiv.org/html/2607.27512#bib.bib40)\)\. In WS,G\(n,β,k\)G\(n,\\beta,k\), the network is constructed by rewiring edges of akk\-regular ring lattice with probabilityβ\\beta\. It generally produces networks with high local clustering and short average path lengths\. We fixn=48n=48for both network structures, withp=0\.3p=0\.3for ERLeskovec \([2017](https://arxiv.org/html/2607.27512#bib.bib36)\)andk=8k=8,β=0\.1\\beta=0\.1for WS\. We select88network instances using the maximin criterion described in[Section˜C\.2](https://arxiv.org/html/2607.27512#A3.SS2)for each network structure and refer to these asnetwork realizations\.222In total, we have1616network realizations\. ### 4\.4Scenarios and Simulations We examine belief diffusion acrossfourscenarios\. These scenarios isolate the effects of domain specialization, social\-role assignment, and role–specialization alignment\. I\. Baseline Generalists\.All LLM agents use the same generalist LLM and receive the same social role, serving as a no\-specialization, no\-role baseline\. II\. Generalists with Random Roles\.All LLM agents use the same generalist LLM, but each is assigned a random social role drawn from[Table˜A2](https://arxiv.org/html/2607.27512#A2.T2)\. This isolates the effect of the role assignment\. III\. Specialists with Random Roles\.LLM agents are powered by generalistandspecialist LLMs with randomly assigned roles\. The list of LLMs and social roles is provided in[Table˜A2](https://arxiv.org/html/2607.27512#A2.T2)\. This scenario isolates the effect of heterogeneity in specialization\. IV\. Specialists with Matched Roles\.LLM agents are powered by generalistandspecialist LLMs\. Further, we assign social roles that match LLMs’ capabilities \(e\.g\., an agent powered by the math LLM is assigned the role of“Mathematician”\)\. Compared with scenario III, here we isolate the marginal effect of role–specialization alignment\. ##### Runs\. Each scenario is simulated multiple times; we refer to each individual simulation as arun\. Each run begins with an initial roundt=0t=0, where we collect LLM agents’ initial beliefs before introducing neighbor information\. It is followed byT=10T=10synchronous belief\-update rounds, yielding 11 statest=0,…,Tt=0,\\dots,T\. In total, we perform1,2801\{,\}280runs:44scenarios,22network structures with88realizations each, and2020discussion statements\. LLMs / SpecializationSocial RolesIGeneralistOnly“LLM”IIGeneralist1515Random rolesIIIGeneralist &1414Specialists1515Random rolesIVGeneralist &1414Specialists1515Matchedroles Table 1:Composition of scenarios\.SpecializationandSocial Rolesshow the number of unique LLMs and social roles, respectively\. Scenarios I vs\. II isolate the effect of the persona\-style role assignment; \{I, II\} vs\. \{III, IV\} isolate the effect of LLM heterogeneity \(introduction of specialists\); III vs\. IV isolate the effect of role–specialization alignment\.These four scenarios allow us to isolate the effects of social role and specialization and are summarized in[Table˜1](https://arxiv.org/html/2607.27512#S4.T1)\. Comparing scenarios I with II isolates persona\-style role assignment; comparing II with III isolates the introduction of specialists \(the specialization effect\); and comparing III with IV isolates role–specialization alignment\. We also report a fourth contrast, the composition effect, for completeness only; it averages over role assignment to contrast the homogeneous scenarios I, II with the heterogeneous III, IV, but our analysis relies on the specialization effect \(II→\\toIII\), which isolates the introduction of specialists with role assignment being fixed\. ### 4\.5Evaluation Our analysis consists of two stages\. We first characterize belief trajectories and compare dynamics across scenarios and network structures \(§[4\.5\.1](https://arxiv.org/html/2607.27512#S4.SS5.SSS1)\)\. We then evaluate the extent to which classical opinion\-dynamics models explain the observed LLM belief dynamics using a hierarchy of increasingly expressive surrogate models \(§[4\.5\.2](https://arxiv.org/html/2607.27512#S4.SS5.SSS2)\)\. #### 4\.5\.1Metrics and Dynamics Analysis We characterize belief trajectories using three agent\-level metrics: magnitude of belief change \(plasticity\), directional consistency of these changes \(directedness\), and outgoinginfluence\. Additionally, we consider theconsensus: a population\-level outcome that quantifies the degree of agreement among all LLM agents in the network\. ##### Agent\-level metrics\. We first examine the metrics that quantify agent\-level belief trajectories\. Hence, we define agentaia\_\{i\}’s per\-round belief change: Δ𝒃i\(t\)=𝒃i\(t\)−𝒃i\(t−1\)\.\\Delta\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}=\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\-\\boldsymbol\{b\}\_\{i\}^\{\(t\-1\)\}\.\(3\)Plasticityis the magnitude of an LLM agent’s belief change per round \(averaged over a run\): Plasticity\(i\)=1T∑t=1T12‖Δ𝒃i\(t\)‖1\\mathrm\{Plasticity\}\(i\)=\\frac\{1\}\{T\}\\sum\_\{t=1\}^\{T\}\\tfrac\{1\}\{2\}\\left\\\|\\Delta\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\\right\\\|\_\{1\}\(4\)LLM agents with high plasticity revise beliefs frequently or undergo several large\-magnitude changes in belief, whereas agents with low plasticity remain stable\. Directednesscaptures whether an LLM agent revises belief in a consistent direction: Directedness\(i\)=‖𝒃i\(T\)−𝒃i\(0\)‖1∑t=0T−1‖𝒃i\(t\+1\)−𝒃i\(t\)‖1\\mathrm\{Directedness\}\(i\)=\\frac\{\\left\\\|\\boldsymbol\{b\}\_\{i\}^\{\(T\)\}\-\\boldsymbol\{b\}\_\{i\}^\{\(0\)\}\\right\\\|\_\{1\}\}\{\\sum\_\{t=0\}^\{T\-1\}\\left\\\|\\boldsymbol\{b\}\_\{i\}^\{\(t\+1\)\}\-\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\\right\\\|\_\{1\}\}\(5\)Directedness closer to11indicates that an agent’s beliefs move toward a single label \(e\.g\., increasing the probability assigned to acorrectlabel\) across rounds, while0indicates belief oscillation\.333The denominator is0only for an LLM agent whose belief never changes, yielding an undefined ratio; our implementation is designed to exclude such cases, however, we do not observe this in practice\.Plasticity and directedness characterize theshapeof individual belief trajectories\. An LLM agent that updates frequently but oscillates \(highplasticity, lowdirectedness\) follows a different trajectory than one that updates frequently and monotonically \(highplasticity, highdirectedness\)\. ##### Outgoing Influence\. The agent\-level metrics characterize belief trajectories in isolation and cannot establish whether some agents influence or follow the beliefs of their neighbors, i\.e\., the emergence of opinion\-leader\-like agents \(LLM agents whose own belief changes are associated with larger subsequent changes among beliefs of their neighbors\)\. To capture theinfluence, we measure the average magnitude of neighbors’ belief changes att\+1t\+1, weighted by how much the agentaia\_\{i\}itself moved attt\.444Rounds in whichaia\_\{i\}has a small change in belief make a smaller contribution to the outgoing influence score\.A higher influence in[Equation˜7](https://arxiv.org/html/2607.27512#S4.E7)indicates that belief updates inaia\_\{i\}are associated with greater subsequent updates among its neighbors𝒩\(i\)\\mathcal\{N\}\(i\)\. Let δi\(t\)=12‖Δ𝒃i\(t\)‖1\\delta\_\{i\}^\{\(t\)\}=\\frac\{1\}\{2\}\\left\\\|\\Delta\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\\right\\\|\_\{1\}\(6\)denoteaia\_\{i\}’s absolute per\-round belief change\. Theoutgoing influenceis then defined as Influence\(i\)=∑t=0T−1\[δi\(t\)⋅∑j∈𝒩\(i\)δj\(t\+1\)\]\|𝒩\(i\)\|⋅∑t=0T−1δi\(t\)\.\\mathrm\{Influence\}\(i\)=\\frac\{\\displaystyle\\sum\_\{t=0\}^\{T\-1\}\\left\[\\delta\_\{i\}^\{\(t\)\}\\,\\cdot\\,\\sum\_\{j\\in\\mathcal\{N\}\(i\)\}\\delta\_\{j\}^\{\(t\+1\)\}\\right\]\}\{\|\\mathcal\{N\}\(i\)\|\\,\\cdot\\,\\displaystyle\\sum\_\{t=0\}^\{T\-1\}\\delta\_\{i\}^\{\(t\)\}\}\.\(7\)To assess whether particular agents exert more influence than others, we fit avariance\-components modelScheiplet al\.\([2008](https://arxiv.org/html/2607.27512#bib.bib41)\)to theoutgoing influence\. By treating LLM agents, network realizations, and statements as random effects, we can quantify how much variance in theoutgoing influenceis attributable to each\. For each random\-effects component, we report the intraclass correlation coefficient \(ICC\), which is the proportion of total variance attributable to that component\. A higher agent\-level ICC suggests the presence of opinion leaders555Opinion\-leader\-like agents are LLM agents with persistently high outgoing influence\.and followers\. We provide full model specifications in[Appendix˜D](https://arxiv.org/html/2607.27512#A4)\. ##### Population\-level metrics\. We trackconsensusto estimate the population\-level agreement among the discretized beliefs of LLM agents: Cons\(t\)=1n\(n−1\)∑i≠j𝟙\[Bi\(t\)=Bj\(t\)\]\.\\mathrm\{Cons\}\(t\)=\\frac\{1\}\{n\(n\-1\)\}\\sum\_\{i\\neq j\}\\mathbbm\{1\}\\\!\\left\[B\_\{i\}^\{\(t\)\}=B\_\{j\}^\{\(t\)\}\\right\]\.\(8\)In our analysis, we focus on thechangein consensus between the initial \(t=0t=0\) and final rounds\. A positive value indicates that belief exchange moved the population closer to unanimous agreement, while a negative value indicates that beliefs became more fragmented\. Together, these provide a comprehensive description of belief diffusion that no single metric can provide alone\. For instance, a run with lowchange in consensusmay reflect either near\-zero change in beliefs \(lowplasticity\) or frequent oscillation without convergence toward agreement \(highplasticitywith lowdirectedness\)\. Further, ifplasticityanddirectednessboth have similar values across all LLM agents, theoutgoing influenceshows whether some LLM agents’ belief updates are persistently associated with larger subsequent updates among their neighbors \(opinion\-leader\-like agents\)\. ##### Statistical Inference\. To account for repeated measures across statements and network realizations, we fit linear mixed\-effects models\. Here, we treat scenarios \(I–IV\) and network structures \(ER and WS\) as fixed effects, while statements and network realizations are treated as random effects\. We apply this design toplasticity,directedness, andchange in consensus, and we report estimated marginal means \(EMMs\) with9595% confidence intervals in §[5](https://arxiv.org/html/2607.27512#S5)\. Note that agent\-level metrics are averaged within each run \(n=1,280n=1,280\)\. ##### Contrast Analysis\. To quantify the effect sizes between scenarios, we perform a contrast analysis\. The contrasts include therole effect\(II vs\. I\),specialization effect\(III vs\. II\), androle–specialization alignment\(IV vs\. III\); these are summarized in[Table˜A5](https://arxiv.org/html/2607.27512#A4.T5)\. For each contrast, we report three quantities: - 1\.themarginalcontrast \([Table˜A8](https://arxiv.org/html/2607.27512#A6.T8)\), which averages effects across network structures; - 2\.theconditionalcontrasts \([Table˜A9](https://arxiv.org/html/2607.27512#A6.T9)\), which estimate the same effect separately within ER and WS networks; - 3\.theinteractioncontrast \(Betweenrows in[Table˜A9](https://arxiv.org/html/2607.27512#A6.T9)\), which tests whether a manipulation produces a different effect across two network structures: a non\-significant interaction indicates that we do not detect any differences in the effects\. All contrasts are reported as Cohen’sddwith95%95\\%confidence intervals\. We provide full model specifications and contrast definitions in Appendix[D](https://arxiv.org/html/2607.27512#A4)\. #### 4\.5\.2Surrogate Models of Belief Diffusion To evaluate whether the observed belief dynamics can be explained by classical opinion\-dynamics mechanisms, we fit a hierarchy of surrogate transition models\. Each surrogate predicts an LLM agent’s discretized belief at roundt\+1t\+1from information available at roundtt\. The hierarchy progressively introduces mechanisms such as persistence, social belief composition, and the agent’s identity, allowing us to test which mechanisms are necessary to reproduce the observed dynamics\. Formally, each surrogate estimates Pr\(Bi\(t\+1\)=y∣ϕi\(t\)\),\\Pr\\\!\\left\(B\_\{i\}^\{\(t\+1\)\}=y\\mid\\boldsymbol\{\\phi\}\_\{i\}^\{\(t\)\}\\right\),\(9\)whereBi\(t\)∈\{correct,incorrect,neither\}B\_\{i\}^\{\(t\)\}\\in\\\{\\texttt\{correct\},\\texttt\{incorrect\},\\texttt\{neither\}\\\}denotes the discretized belief of agentaia\_\{i\}at roundtt, andϕi\(t\)\\boldsymbol\{\\phi\}\_\{i\}^\{\(t\)\}is a feature vector encoding information available prior to the update\. ModelFeaturesϕi\(t\)\\phi\_\{i\}^\{\(t\)\}MechanismM1Bi\(t\)B\_\{i\}^\{\(t\)\}Individual persistenceM2Bi\(t\),Γ\(t\)B\_\{i\}^\{\(t\)\},\\varGamma^\{\(t\)\}global belief compositionM3Bi\(t\),Ni\(t\)B\_\{i\}^\{\(t\)\},N\_\{i\}^\{\(t\)\}Local belief compositionM4Bi\(t\),Ni\(t\),Mi,RiB\_\{i\}^\{\(t\)\},N\_\{i\}^\{\(t\)\},M\_\{i\},R\_\{i\}Local influence \+ identity Table 2:Hierarchy of surrogate models\.Γ\(t\)\\varGamma^\{\(t\)\}denotes the population\-level belief distribution at roundtt,Ni\(t\)N\_\{i\}^\{\(t\)\}denotes the belief distribution within agentii’s neighborhood,MiM\_\{i\}denotes the agent’s underlying domain specialization, andRiR\_\{i\}denotes its assigned social role\.M1 serves as an empirical baseline\. It captures the extent to which belief updates can be explained by an agent’s current beliefs aloneBi\(t\)B\_\{i\}^\{\(t\)\}, without access to any other information\. M2 augments the baseline with a population\-level distribution over belief statesΓ\(t\)\\varGamma^\{\(t\)\}\. Each component ofΓ\(t\)\\varGamma^\{\(t\)\}captures the proportion of LLM agents expressing discretized beliefs at roundtt\. Therefore, M2 is closely related to the population\-averaging model ofDeGroot \([1974](https://arxiv.org/html/2607.27512#bib.bib38)\)\. M3 instead incorporates the \(local\) neighborhood\-level distribution over belief statesNi\(t\)N\_\{i\}^\{\(t\)\}\. Each component ofNi\(t\)N\_\{i\}^\{\(t\)\}captures the proportion ofaia\_\{i\}’s neighbors expressing discretized beliefs at roundtt\. This surrogate is analogous to opinion\-dynamics models with localized social belief compositionFriedkin and Johnsen \([1990](https://arxiv.org/html/2607.27512#bib.bib39)\)\. Finally, M4 extends M3 by incorporating an agent’s social roleRiR\_\{i\}and underlying LLMMiM\_\{i\}\. It captures the effect of the LLM agent’s identity on the transition dynamics\. The hierarchy of surrogate models in[Table˜2](https://arxiv.org/html/2607.27512#S4.T2)serves as a controlled ablation\. It allows us to identify which of the mechanisms \(persistence, social belief composition, or agent identity\) are necessary to replicate the observed belief dynamics\. ##### Evaluation of surrogates\. We evaluate surrogate models using two complementary criteria\. First, we assess one\-step predictive performance using theMatthews Correlation Coefficient\(MCC\), a balanced classification metric that accounts for all entries of the confusion matrixChicco and Jurman \([2020](https://arxiv.org/html/2607.27512#bib.bib66)\)\. Higher MCC values indicate a more accurate prediction of individual belief updates\. Second, we evaluate whether a surrogate reproduces population\-level dynamics\. We fit each surrogate on empirical transitions, simulate belief diffusion using the fitted model, and compare the resulting consensus trajectory to the original simulation\. We quantify this agreement usingconsensus fidelity, CF=1−1R∑r=1R\|Cons^r\(T\)−Consr\(T\)\|,\\mathrm\{CF\}=1\-\\frac\{1\}\{R\}\\sum\_\{r=1\}^\{R\}\\left\|\\widehat\{\\mathrm\{Cons\}\}\_\{r\}\(T\)\-\\mathrm\{Cons\}\_\{r\}\(T\)\\right\|,\(10\)whereConsr\(T\)\\mathrm\{Cons\}\_\{r\}\(T\)andCons^r\(T\)\\widehat\{\\mathrm\{Cons\}\}\_\{r\}\(T\)denote the empirical and surrogate consensus levels at the final roundTTof runrr, respectively\. Higher consensus fidelity indicates that the surrogate more accurately reproduces the collective outcome\. Together, MCC values and consensus fidelity distinguish between two forms of success: accurately predicting individual belief updates and accurately reproducing population\-level belief dynamics\. Additional implementation details, feature definitions, fitting procedures, and rollout protocols are provided in Appendix[E](https://arxiv.org/html/2607.27512#A5)\. ## 5Results We first examine which factors drive belief diffusion in LLM populations by comparing the effects of domain specialization, social role assignment, and network structure on belief updating, influence, and consensus formation \(§[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)\)\.666When comparing scenarios or network structures, we also report a standardized effect size via Cohen’sdd, computed from contrasts\.[TableA8](https://arxiv.org/html/2607.27512#A6.T8)showsmarginaleffect sizes, and[TableA9](https://arxiv.org/html/2607.27512#A6.T9)providesconditionalandinteractioneffect sizes\.We then ask whether the resulting belief dynamics can be explained by a hierarchy of classical opinion\-dynamics surrogate models \(§[5\.2](https://arxiv.org/html/2607.27512#S5.SS2)\)\. ### 5\.1What drives belief revisions? We look at two levels of belief dynamics: the agent\-level \(howindividualLLM agents revise their beliefs\) and the population\-level \(consensus\)\. Across four scenarios, these two levels dissociate\. Social role assignment \(scenario II\) reshapes individual belief trajectories but produces only a modest effect on population\-level consensus \(§[5\.1\.1](https://arxiv.org/html/2607.27512#S5.SS1.SSS1)\); LLM heterogeneity \(scenarios III and IV\) produces the largest changes in population\-level consensus \(§[5\.1\.2](https://arxiv.org/html/2607.27512#S5.SS1.SSS2)–§[5\.1\.3](https://arxiv.org/html/2607.27512#S5.SS1.SSS3)\), while aligning role labels to the underlying specialization \(IV\) adds little at either level \(§[5\.1\.4](https://arxiv.org/html/2607.27512#S5.SS1.SSS4)\); finally, network structure modulates agent\-level behavior while having a negligible effect on the population\-level outcome \(§[5\.1\.5](https://arxiv.org/html/2607.27512#S5.SS1.SSS5)\)\. We provide detailed results in[Tables˜A6](https://arxiv.org/html/2607.27512#A6.T6),[A8](https://arxiv.org/html/2607.27512#A6.T8),[A9](https://arxiv.org/html/2607.27512#A6.T9)and[A7](https://arxiv.org/html/2607.27512#A6.T7)\. Figure 3:Belief dynamics across settings and network structures\.Estimated marginal means \(with95%95\\%confidence intervals\) from mixed\-effects models\.Spcsstands forspecialists\. \(A\)Plasticity: average per\-round magnitude of belief change\. Increases from baseline \(I\) through random specialists \(III\); role alignment \(IV\) reduces plasticity in ER but increases it in WS\. \(B\)Directedness: consistency of belief updates across rounds\. Drops sharply once roles are introduced \(I→\\toII\) and reaches its minimum in WS with matched specialists \(IV\)\. \(C\)Consensus change: shift in overall belief agreement between the initial and last rounds\. LLM heterogeneity drives the largest shifts in consensus\.#### 5\.1\.1Social roles changehowLLM agents revise beliefs Plasticity\([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)A\) is lowest in the baseline scenario \(I\) with estimated means of0\.030\.03for ER and0\.030\.03for WS\. Assigning social roles to generalist agents \(I→\\toII\) increasesplasticityto0\.070\.07in ER and0\.050\.05in WS, with the marginal role effectd=0\.32d=0\.32\. Scenario II also produces the largest drop indirectedness, from0\.970\.97to0\.440\.44in ER and0\.960\.96to0\.500\.50in WS, with the marginal role effectd=−1\.86d=\-1\.86\. LLM agents exhibit more belief“movement,”but this movement is not monotonic \([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)B\): the few revisions that occur do not move toward a specific belief label\. This is further supported by thechange in consensusin[Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)C, where scenario II produces a minimalchange in consensusof0\.040\.04for ER and0\.050\.05for WS, with the marginal effectd=0\.51d=0\.51\. Social roles \(persona\-style prompting\) substantially alterhowLLM agents revise beliefs but produce only a modest consensus shift relative to the baseline scenario \(I\)\. #### 5\.1\.2LLM heterogeneity is a driver of collective change Introducing specialist LLMs alongside generalists \(II→\\toIII\) further increasesplasticityfrom0\.070\.07to0\.130\.13in ER and from0\.050\.05to0\.110\.11in WS, with the marginal \(II→\\toIII\) effectd=0\.53d=0\.53\. Here,directednessfalls to0\.270\.27in ER and0\.350\.35in WS with the marginal effectd=−0\.62d=\-0\.62\. Likewise, scenario III results in a higherconsensus change\([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)C\) with0\.190\.19for ER and0\.180\.18for WS, with the marginal \(II→\\toIII\) effectd=1\.39d=1\.39\. Unlike social role assignment \(II\), introducing specialist LLMs \(III\) has a larger effect on both agent\- and population\-level dynamics\. #### 5\.1\.3LLM heterogeneity introduces between\-agent differences in influence The shift from scenario II→\\toIII is accompanied by the emergence of opinion\-leader\-like agents \([Figure˜4](https://arxiv.org/html/2607.27512#S5.F4)\)\. In generalist scenarios \(I, II\), the agent\-level ICC777Agent\-level ICC quantifies the proportion of variance in theoutgoing influenceattributable to the LLM agent identity\.foroutgoing influenceis statistically indistinguishable from zero, indicating that no LLM agents systematically exert more influence than others\. Once specialist LLMs are introduced, the agent\-level ICC rises to4\.974\.97% in scenario III and2\.732\.73% in scenario IV \(p<0\.001p<0\.001for both\)\. That is, introducing LLM heterogeneity produces a subset of agents with persistent between\-agent differences in outgoing influence\. We do not observe this asymmetry in persona\-style role assignment with generalist LLMs \(scenario II\)\. Figure 4:Variance decomposition of outgoing influence\.Intraclass correlations \(with95%95\\%confidence intervals\) from mixed\-effects models with random intercepts for agent, network realization, and discussion statement\.Spcsstands forspecialists\.Agentcomponent shows the proportion of total outgoing influence variance attributable to agent\-level differences; thenetworkcomponent measures variance attributed to network realizations\. Statement and residual components are not shown\.Agentcomponent is statistically zero in generalist LLM scenarios \(I, II\) and rises to4\.97%4\.97\\%and2\.73%2\.73\\%in specialist scenarios \(III and IV, respectively;[Table˜A7](https://arxiv.org/html/2607.27512#A6.T7)\)\. That is, agent\-level differences in outgoing influence emerge only when specialist LLMs are present\. #### 5\.1\.4Role\-specialization alignment leaves trajectories largely intact but dampens the consensus change Aligning social roles with the underlying domain specialization \(III→\\toIV\) has negligible marginal effects on belief trajectories \([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)\): the marginal effectd=0\.06d=0\.06onplasticityandd=−0\.09d=\-0\.09ondirectedness\. However, we observe a small marginal effect inconsensus change\(d=−0\.36d=\-0\.36\), where values drop \(III→\\toIV\) from0\.190\.19to0\.160\.16in ER and from0\.180\.18to0\.140\.14in WS\.888Agents still move about three times farther from their initial agreement than under random roles alone \(II→\\toIV\)\. Once LLM heterogeneity is introduced \(II→\\toIII\),furtheralignment of social labels with specialization \(III→\\toIV\) has little effect on agent\-level trajectories,reducesrather than increases the consensus \([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)C\) and does not amplify the leader–follower effect \([Figure˜4](https://arxiv.org/html/2607.27512#S5.F4)\)\. #### 5\.1\.5Social roles interact with the network structure at the agent level but not at the population level The effect of introducing specialist LLMs does not differ between ER and WS networks: the \(II→\\toIII\) interaction contrast is non\-significant for every outcome \(plasticityp=0\.94p=0\.94, directednessp=0\.38p=0\.38, outgoing influencep=0\.26p=0\.26, and consensus changep=0\.10p=0\.10\)\. However, social role assignment \(I→\\toII\)ismodulated by network structure: the increase in plasticity is twice as large in ER \(d=0\.43d=0\.43\) as in WS \(d=0\.21d=0\.21\), with an interaction effectd=0\.22d=0\.22\. Similarly, the directedness has a larger drop in ER \(d=−1\.99d=\-1\.99\) than in WS \(d=−1\.74d=\-1\.74\), with an interaction effectd=−0\.26d=\-0\.26\. Role–specialization alignment \(III→\\toIV\) is the only manipulation for which network structure produces opposite effects at the agent level: plasticity decreases in ER \(d=−0\.15d=\-0\.15\) but increases in WS \(d=0\.26d=0\.26\), with an interaction effectd=−0\.41d=\-0\.41; while directedness increases in ER \(d=0\.13d=0\.13\) but decreases in WS \(d=−0\.32d=\-0\.32\), with an interaction effectd=0\.45d=0\.45\. Consensus change, by contrast, is network\-structure\-invariant: the interaction effect is non\-significant for every contrast \(role, I→\\toII:p=0\.21p=0\.21; LLM heterogeneity, II→\\toIII:p=0\.10p=0\.10; role–specialization alignment, III→\\toIV:p=0\.95p=0\.95\)\. Network structure, therefore, reshapeshowindividual agents revise their beliefs but does not affectwherethe agents collectively converge\. Figure 5:Final\-state MCC across scenarios and surrogate models\.It measures the accuracy of the surrogate’s predicted final belief against the observed final belief\.Spcsstands forspecialists\. Each panel corresponds to one of four experimental settings: \(A\) Base LLMs, \(B\) Random roles, \(C\) Specialists with random roles, and \(D\) Specialists with matched roles\. Each line connects mean estimates \(with 95% bootstrap confidence intervals\) across surrogate models of increasing complexity for Erdős–Rényi \(ER\) and Watts–Strogatz \(WS\)\. Surrogate models with additional social information \(M3 and M4\) provide limited benefit in generalist scenarios but modestly improve predictive accuracy in specialist scenarios \(III and IV\)\. We provide detailed statistics in[Table˜A10](https://arxiv.org/html/2607.27512#A6.T10)\.Figure 6:Consensus fidelity across scenarios and surrogate models\.Spcsstands forspecialists\. Each panel corresponds to one of four experimental settings: \(A\) Base LLMs, \(B\) Random roles, \(C\) Specialists with random roles, \(D\) Specialists with matched roles, and each line connects mean estimates \(95% bootstrap confidence intervals\) across surrogate models of increasing complexity for Erdős–Rényi \(ER\) and Watts–Strogatz \(WS\) networks\. In generalist scenarios \(I, II\), simpler surrogates achieve the highest consensus fidelity, while specialist scenarios \(III, IV\) require at least global or local belief composition to reproduce observed consensus dynamics\. We provide detailed statistics in[Table˜A11](https://arxiv.org/html/2607.27512#A6.T11)\. ### 5\.2Can classical opinion\-dynamics models explain these dynamics? Section[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)established a dissociation between agent\- and population\-level dynamics: social roles primarily reshapehowagents update their beliefs, while LLM heterogeneity additionally produces changes inwherethe population converges \(changes in consensus\)\. We now ask what mechanisms are needed to predict individual belief transitions and to reproduce population\-level outcomes \(consensus\)\. We evaluate the surrogate hierarchy introduced in §[4\.5\.2](https://arxiv.org/html/2607.27512#S4.SS5.SSS2), where M1 captures individual persistence; M2 combines individual persistence with the population\-level belief composition; M3 combines individual persistence with the local neighborhood belief composition; and M4 extends M3 with an LLM agent’s domain specialization and social\-role information\. We provide an overview of the results in[Tables˜A10](https://arxiv.org/html/2607.27512#A6.T10)and[A11](https://arxiv.org/html/2607.27512#A6.T11)\. #### 5\.2\.1Generalist populations are explained by simple dynamics The generalist LLM scenarios \(I, II\) exhibit high predictive performance across the entire surrogate hierarchy\. In scenario I \([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)A\), the final\-state MCC is high under M1 with92\.4%92\.4\\%for ER and90\.290\.2% for WS; and in scenario II, M1 achieves86\.1%86\.1\\%for ER and94\.7%94\.7\\%for WS \([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)B\)\. Overall, the performance gain from M1→\\toM4 is modest in both scenarios \(I:\+4\.8\+4\.8percentage points \(pp\) for ER,\+2\.3\+2\.3pp for WS; II:\+4\.2\+4\.2pp for ER and0\.00\.0pp for WS\)\. Consensus fidelity reveals that individual persistence \(M1\) is sufficient to explain population\-level dynamics in generalist scenarios \([Figure˜6](https://arxiv.org/html/2607.27512#S5.F6)A–B\)\. In the baseline scenario \(I\), M1 achieves the highest consensus fidelity \(91\.1%91\.1\\%ER and90\.4%90\.4\\%WS\), with performance decreasing once additional features are introduced \(M4:81\.0%81\.0\\%for ER and78\.5%78\.5\\%for WS\)\. In the random\-role scenario \(II\), M2 performs best \(84\.7%84\.7\\%for ER and86\.7%86\.7\\%for WS\), but its confidence intervals overlap with M1 \(80\.1%80\.1\\%ER,82\.1%82\.1\\%WS; see[Table˜A11](https://arxiv.org/html/2607.27512#A6.T11)\)\. Here, surrogates with richer features \(M3, M4\) also have lower consensus fidelity, e\.g\., M4 achieves77\.6%77\.6\\%ER and76\.6%76\.6\\%WS \([Figure˜6](https://arxiv.org/html/2607.27512#S5.F6)B\)\. Individual persistence and the population’s belief composition are sufficient to capture agent\-level belief transitions in generalist scenarios\. Explicitly modeling local neighborhood composition or agent identity provides little additional explanatory power\. Meanwhile, consensus in scenarios I and II appears to emerge from nearly independent belief trajectories: adding social features \(M2–M4\) does not improve consensus fidelity\. This is consistent with the descriptive findings in §[5\.1\.1](https://arxiv.org/html/2607.27512#S5.SS1.SSS1)\. #### 5\.2\.2Heterogeneous LLM populations require belief composition Descriptive evaluation \(§[5\.1\.2](https://arxiv.org/html/2607.27512#S5.SS1.SSS2)\) showed that specialist scenarios \(III, IV\) produced richer belief dynamics than the generalist scenarios \(I, II\)\. We now ask whether these dynamics require more expressive surrogate models\. Final\-state MCC increases with feature richness \([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)C–D\): in scenario III from76\.3%76\.3\\%\(ER\) and84\.4%84\.4\\%\(WS\) under M1 to82\.5%82\.5\\%and89\.1%89\.1\\%under M4\. We observe a similar pattern in scenario IV: from81\.7%81\.7\\%\(ER\) and79\.6%79\.6\\%\(WS\) to84\.7%84\.7\\%and82\.0%82\.0\\%\. Hence, domain specialization and social\-role features enhance prediction of individual belief transitions\. Consensus fidelity, however, exhibits a different pattern\. M1 achieves72\.1%72\.1\\%\(ER\) and73\.3%73\.3\\%\(WS\) in scenario III, and73\.7%73\.7\\%\(ER\) and73\.4%73\.4\\%\(WS\) in scenario IV\. Adding population\-level belief composition \(M2\) increases consensus fidelity to≥92%\\geq 92\\%across both scenarios and network structures, while M3 and M4 provide no further improvements \(confidence intervals overlap;[Table˜A11](https://arxiv.org/html/2607.27512#A6.T11)\)\. Here, surrogate analysis shows that heterogeneous LLMs produce belief dynamics that cannot be captured by persistencealone\. Features tied to the collective belief composition and agent identity \(domain specialization and social roles\) shapehowindividual agents revise beliefs, and thus improve prediction ofindividualtransitions\. This extends the agent\- and population\-level dissociation in §[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)\. However, unlike the generalist scenarios \(I, II\), where individual persistence \(M1\) largely reproduces consensus, the heterogeneous scenarios \(III, IV\) require features that account for the“collective”belief composition: consensus emerges as a process in which belief revisions depend on the beliefs circulating in the population or neighborhood\. #### 5\.2\.3Agent\-level prediction does not guarantee population\-level fidelity The two evaluation metrics recover the agent–population dissociation in §[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)\. In heterogeneous scenarios \(III, IV\), final\-state MCC generally increases with feature richness, peaking at M4 \(III:82\.5%82\.5\\%ER,89\.1%89\.1\\%WS;[Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)C–D\)\. However, these gains are not mirrored in consensus fidelity, where M2–M4 perform nearly identically \(M2 for III:94\.5%94\.5\\%ER and93\.3%93\.3\\%WS;[Figure˜6](https://arxiv.org/html/2607.27512#S5.F6)C–D\)\. The same gap appears in homogeneous LLM scenarios \(I, II\), but in the opposite direction\. Consensus fidelity ishighestunder the simplest surrogate anddecreasesin more complex surrogates\. For example, in scenario I, fidelity decreases from91\.1%→81\.0%91\.1\\%\\to 81\.0\\%\(ER;[Figure˜6](https://arxiv.org/html/2607.27512#S5.F6)A\); however, final\-state MCC has a modest increase as we add more features:92\.4%→97\.2%92\.4\\%\\to 97\.2\\%\([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)A\)\. #### 5\.2\.4Network structure informs individual transitions but not consensus Finally, surrogate analysis mirrors §[5\.1\.5](https://arxiv.org/html/2607.27512#S5.SS1.SSS5): network structure primarily influenceshowindividual agents revise their beliefs while leaving collective outcomes unchanged\. Final\-state MCC differs between ER and WS networks: in scenario III, WS has consistently higher scores than ER \(by8\.18\.1,4\.14\.1,5\.85\.8, and6\.66\.6percentage points across M1–M4;[Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)C\)\. Comparable separation appears in scenarios I and II \([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)A–B\)\. Consensus fidelity, by contrast, shows no such separation: the ER and WS point estimates are close and their confidence intervals overlap \(see[Figure˜6](https://arxiv.org/html/2607.27512#S5.F6)and[Table˜A11](https://arxiv.org/html/2607.27512#A6.T11)\) across every scenario \(I–IV\) and surrogate \(M1–M4\)\. ## 6Discussion FindingEvidence from §[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)Evidence from §[5\.2](https://arxiv.org/html/2607.27512#S5.SS2)Social roles changehowLLM agents revise beliefsIntroducing random social roles \(I→\\toII\) alters agent\-level trajectories but has much smaller effects on consensus than introducing specialist LLMs \(II→\\toIII\) \([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)\)\.Generalist scenarios \(I, II\) are well explained by simple surrogates, whereas specialist scenarios \(III, IV\) require collective belief composition to reproduce consensus \([Figures˜5](https://arxiv.org/html/2607.27512#S5.F5)and[6](https://arxiv.org/html/2607.27512#S5.F6)\)\.LLM heterogeneity drivesbothagent\- and population\-level dynamicsIntroducing specialist LLMs \(II→\\toIII\) changes both agent\- \(plasticity\) and population\-level \(consensus\) dynamics \([Figure˜3](https://arxiv.org/html/2607.27512#S5.F3)\)\.Specialist scenarios differ from generalist scenarios in both transition predictability and consensus fidelity \([Figures˜5](https://arxiv.org/html/2607.27512#S5.F5)and[6](https://arxiv.org/html/2607.27512#S5.F6)\)\.Specialist LLMs produce a leader–follower structureVariance in outgoing influence attributed to the agent identity is significant only in specialist scenarios \([Figure˜4](https://arxiv.org/html/2607.27512#S5.F4)\)\.Identity and local\-neighborhood features improve individual transition prediction \(final\-state MCC\) primarily in specialist scenarios \([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)C–D\)\.Role–specialization alignment leaves trajectories largely intact but dampens the consensus changeMatching social roles to specialization \(III→\\toIV\) has only minor effects on belief dynamics \([Figures˜3](https://arxiv.org/html/2607.27512#S5.F3)and[4](https://arxiv.org/html/2607.27512#S5.F4)\)\.Surrogate model predictability \(final\-state MCC,[Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)C–D\) and consensus fidelity \([Figure˜6](https://arxiv.org/html/2607.27512#S5.F6)C–D\) are similar across the two specialist scenarios\.Network structurefurthermodulates agent\- but not population\-level outcomesNetwork structure modulates agent\-level belief revision under the role \(I→\\toII\) and alignment \(III→\\toIV\) manipulations, but the effect of specialist LLMs \(II→\\toIII\) is network\-invariant \([Table˜A9](https://arxiv.org/html/2607.27512#A6.T9)\)\.ER and WS differ in final\-state MCC \([Figure˜5](https://arxiv.org/html/2607.27512#S5.F5)\), but not in consensus fidelity\.Table 3:Summary of the core findings\.The dynamics analysis \(§[5\.1](https://arxiv.org/html/2607.27512#S5.SS1)\) identifies factors associated with belief diffusion in LLM populations, while the surrogate analysis \(§[5\.2](https://arxiv.org/html/2607.27512#S5.SS2)\) evaluates which opinion\-dynamics mechanisms are required to reproduce them\. Despite addressing different questions, both analyses converge on the same qualitative conclusions\.Our results suggest that belief diffusion in networked LLM populations is driven more by underlying LLM heterogeneity than by persona\-style prompting alone\. We provide a summary of findings in[Table˜3](https://arxiv.org/html/2607.27512#S6.T3)\. ### Persona\-style role assignment is a weak driver of population\-level diversity The predominant way to introduce behavioral diversity in LLM multi\-agent simulations is through persona\-style role assignment: assigning distinct social roles to otherwise identical LLMsChuanget al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib2)\); Taubenfeldet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib6)\)\. Our analysis shows that social rolesdoreshape individual trajectories: LLM agents revise their beliefs more often, but instead of converging monotonically toward a specific belief label, they oscillate\. This added movement does not propagate to the population level, as the consensus shift stays far below that of introducing heterogeneous LLMs \([Table˜A8](https://arxiv.org/html/2607.27512#A6.T8)\)\. Persona\-style prompting therefore alters how individual LLM agents update, but it does not by itself produce substantial population\-level diversity: it“excites”individual LLM agents without carrying them far from their baseline beliefs That is, assigning roles is not sufficient to simulate a population of agents with diverse behavior\. ### LLM heterogeneity is the stronger driver of population\-level change The effect of introducing specialist LLMs among the generalists \(II→\\toIII,d=1\.39d=1\.39\) on consensus change is2\.7×2\.7\\timesthat of a social\-role assignment \(I→\\toII,d=0\.51d=0\.51;[Table˜A8](https://arxiv.org/html/2607.27512#A6.T8)\)\. Because specialists are finetuned on different data and with different methods, they bring different knowledge priors into the interaction\. While persona labels \(II\) only rename otherwise identical“belief generators”, specialists introducediversebeliefs\. In heterogeneous scenarios \(III, IV\), LLMs differ not only in their embedded knowledge, but also in how they respond to their neighbors’ beliefs\. LLM agents exhibit patterns of outgoing influence that are absent in all\-generalist scenarios \(I, II\): some adopt their neighbors’ beliefs, while others hold to their initial position \(emergence of opinion\-leader\-like agents,[Figure˜4](https://arxiv.org/html/2607.27512#S5.F4)\)\. The surrogate analyses explain this distinction \(§[5\.2\.2](https://arxiv.org/html/2607.27512#S5.SS2.SSS2)\)\. For homogeneous scenarios \(I, II\), simpler surrogate models reproduce the observed dynamics, but heterogeneous scenarios \(III, IV\) require surrogates that incorporate evolving belief composition \(not persistence alone\) to recover the collective outcome\. ### Network structure primarily modulates individual belief revision Network structure further shapes the belief trajectories, but its effect is more limited than that of LLM heterogeneity\. That is, network structure changes how individual LLM agents revise beliefs and how outgoing influence is distributed, yet it does not affect the consensus \([Table˜A8](https://arxiv.org/html/2607.27512#A6.T8)\)\. In particular, the evaluation metrics for ER and WS networks separate more clearly in agent\-level outcomes than in consensus, indicating that network structure mainly affects who revises beliefs and who influences whom\. This pattern is consistent with the surrogate analysis\. For individual belief transitions, incorporating network information improves prediction in heterogeneous scenarios \(especially when agent identity and local neighborhood composition are included\)\. By contrast, consensus fidelity is insensitive to adding more detailed features, and the main gains come from accounting for population\-level belief composition \(§[5\.2\.2](https://arxiv.org/html/2607.27512#S5.SS2.SSS2)\)\. ### Agent\-level and population\-level explanations are only partially aligned The factors that best predict individual belief transitions are not always the same as those needed to reproduce population\-level consensus\. These findings align with research in human opinion dynamics, which demonstrates that belief diffusion is influenced by both social factors and the structure of the interacting populationLorenzet al\.\([2011](https://arxiv.org/html/2607.27512#bib.bib62)\); Beckeret al\.\([2017](https://arxiv.org/html/2607.27512#bib.bib63)\)\. Specifically, human\-centered studies have established that influence is often distributed unevenly and that local network interactions can shape collective agreement in ways not captured by simple contagion modelsMoussaïdet al\.\([2013](https://arxiv.org/html/2607.27512#bib.bib64)\); Bakshyet al\.\([2011](https://arxiv.org/html/2607.27512#bib.bib61)\)\. Our results reveal a similar pattern in LLM populations: while role labels and neighborhood structure affect individual updating, the underlying composition of the LLM agent population is the primary driver of changes in collective consensus\. Our results suggest that the mechanisms governing individual belief revision and collective belief formation overlap only partially, making both levels of analysis necessary for understanding belief diffusion in LLM populations\. ## 7Conclusion CoevolveSimallows us to disentangle the effects of domain specialization, social\-role assignment, and network structure on belief diffusion within populations of interacting LLM agents, and answer the following two questions: 1. 1\.Which factors drive belief diffusion?LLM heterogeneity, rather than persona\-style role assignment, emerges as the primary driver of collective change\. Introducing specialist LLMs more than doubles the shift in consensus compared to social role labels alone and leads to the emergence of high\-influence LLM agents, a pattern not observed in all\-generalist scenarios\. Social roles and network structure reshapehowindividual agents revise their beliefs \(plasticity, directedness\) but leavewherethe population converges nearly unchanged\. 2. 2\.Can the resulting dynamics be explained by classical opinion\-dynamics models?Only partially: the mechanisms that best predict individual belief transitions \(agent identity, local neighborhood composition\) are not necessarily the same as those that reproduce collective consensus, so agent\- and population\-level predictability diverge\. Realistic simulation of belief diffusion in multi\-agent LLM systems requires a diverse set of underlying LLMs\. Persona prompting alone does not produce variation in collective beliefs\. ## Limitations ##### Scope of the experiments\. Our study deliberately tradesbreadthforcontrol, and several design choices limit the generalizability of our conclusions\. Statements are chosen from a single domain \(affirmative medical indications\), which keeps the ground truth verifiable but leaves open how dynamics would change for contested, vague, or compositional claims\. The LLM agent pool is narrow by design to better control for confounding factors such as family or scale\. Similarly, our study does not separate the effects of finetuning data from those of optimization choices\. We examine small populations \(n=48n=48\) over a short timeline \(T=10T=10rounds\), which are large enough to observe rapid belief revisions \(or changes in consensus\) but insufficient to capture slow drifts or behavior at realistic community scales\. No human participants were involved\. Embedding humans into the same framework and comparing their update behavior with that of LLM agents under identical conditions is a natural next step\. ##### Interaction protocol\. We deliberately use minimal update rules\. Our protocol is synchronous, Markovian, and broadcast\-style\. Each LLM agent conditions only on the neighborhood summary from the previous round, not the entire interaction history\. This design isolates the effects of social influence from memory and dialogue\. However, it excludes practical mechanisms such as asynchronous turn\-taking, persistent context, free\-form messaging, and persuasion effects\. ##### Belief inference\. We read beliefs from next\-token probabilities over a small discrete label set\. This produces a tractable, comparable signal across heterogeneous models, but it cannot characterize what happens inside an LLM \(its inner representations\) or address its sensitivity to prompt structure\. Representation\-based probes of latent truth or epistemic stability would complement this output view\. These could help disentangle genuine belief revision from response conformity\. ##### Causality scope\. Our causal claims are similarly bounded: the dynamics analysis detects social role, specialization, role–specialization alignment, and composition effects across the scenarios\. However, we do not use formal mediation analysis or targeted interventions to localize the mechanism\. ## Ethical Considerations CoevolveSimis a simulation of LLM\-agent belief dynamics, not a study of human subjects\. Therefore, the results should not be interpreted as evidence about human behavior or used as a basis for human\-facing policy claims\. Our findings are limited to a singleLlama\-3family and may not generalize to other model families, sizes, languages, or cultural settings\. ##### Use of AI\. We used Claude Code and GitHub Copilot for code annotations and formatting assistance and Grammarly for grammar and style support\. After drafting the manuscript, we used Claude Fable 5 and GPT\-5\.6\-sol to proofread it, incorporating their feedback where appropriate\. ## Author Contributions Conceptualization:TER \(lead, framing & original idea: network\-based coevolution of LLM beliefs\), GS \(lead, experimental paradigm; supporting, framing & initial feasibility exploration\), SD \(lead, experimental paradigm; supporting, framing & research questions\), CM \(lead, experimental paradigm; supporting, framing\) Data Curation:GS \(lead, maximin selection, statement selection, network realization\), SD \(lead, surrogate data quality\) Formal Analysis:GS \(lead, descriptive analysis, mixed\-effects models, ICC, contrast analysis; supporting, exploratory analysis, surrogate analysis\), SD \(lead, surrogate analysis; supporting, descriptive & exploratory analysis\), CM \(supporting, surrogate analysis, descriptive & exploratory analysis\) Funding Acquisition:TER Investigation:GS \(lead, analysis, simulations\), SD \(lead, analysis; supporting, simulations\), CM \(supporting, simulations\) Methodology:GS \(lead, experimental scenarios & evaluation metric, mixed\-effects models, contrasts, variance decomposition; supporting, framing, surrogate models\), SD \(lead, framing, experimental scenarios & evaluation metric, surrogate models\), TER \(lead, framing\), CM \(supporting, framing, experimental scenarios & evaluation metric\) Project Administration:TER Resources:TER Software:SD \(lead, simulation logic, network generation, surrogate models; responsible for the initial codebase\), GS \(lead, logging, scaling, configuration & setup, descriptive/statistical analysis, GitHub maintenance; supporting, simulation logic, evaluation metrics\), CM \(supporting, network generation, evaluation metrics, logging\) Supervision:TER \(lead\), GS \(supporting\) Validation:GS Visualization:GS Writing – Original Draft:GS \(lead, introduction, methods & setup, results & descriptive analysis, limitation & ethics; supporting, discussion\), SD \(lead, discussion, results & surrogate models; supporting, introduction, methods & setup, literature review, discussion, results & descriptive analysis\), CM \(lead, literature review\) Writing – Review & Editing:GS \(lead\), TER \(lead\), SD \(supporting\) ## References - A\. 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Ferrara \(2026\)Stop drawing scientific claims from LLM social simulations without robustness audits\.arXiv\.External Links:[Document](https://dx.doi.org/10.48550/arxiv.2605.18890),[Link](https://arxiv.org/abs/2605.18890)Cited by:[§1](https://arxiv.org/html/2607.27512#S1.p4.1)\. ## Appendix ## Appendix ANotations SymbolDescriptionNotesℳ\\mathcal\{M\}Large language model \(LLM\)𝒱\\mathcal\{V\}Vocabulary of modelℳ\\mathcal\{M\}, consisting of tokens\[τ1,…,τ\|𝒱\|\]∈𝒱\[\\tau\_\{1\},\\dots,\\tau\_\{\|\\mathcal\{V\}\|\}\]\\in\\mathcal\{V\}τ\\tauToken from the vocabulary𝒱ℳ\\mathcal\{V\}\_\{\\mathcal\{M\}\}e\.g\. tokens \[1\], \[2\]𝒫ℳ\(τ∣𝒙\)\\mathcal\{P\}\_\{\\mathcal\{M\}\}\\left\(\\tau\\mid\\boldsymbol\{x\}\\right\)Output ofℳ\\mathcal\{M\}: a conditional probability distribution over tokensAgents and NetworksG\(n,p\)G\(n,p\)Erdős–Rényi \(ER\) network structureG\(n,β,k\)G\(n,\\beta,k\)Watts–Strogatz \(WS\) network structurennNumber of nodes in a networkGGppProbability of an edge between two nodes in an ER networkβ\\betaEdge rewiring probability in a WS networkkkInitial degree \(i\.e\., number of nearest neighbors\) in the WS ring latticeaia\_\{i\}ii\-th agent/node in a networkGG𝒩\(i\)\\mathcal\{N\}\(i\)Neighbors of a nodeiiBelief𝒃i\(t\)\\boldsymbol\{b\}^\{\(t\)\}\_\{i\}\(Uncalibrated\) belief scores of a modelℳ\\mathcal\{M\}at roundtt∑y𝒃ℳ\(t\)\(y\|input\)=1\\sum\_\{y\}\\boldsymbol\{b\}\_\{\\mathcal\{M\}\}^\{\(t\)\}\(y\|\\text\{input\}\)=1Δ𝒃i\(t\)\\Delta\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}Agentaia\_\{i\}’s belief change between roundsttandt−1t\-1Δ𝒃i\(t\)=𝒃i\(t\)−𝒃i\(t−1\)\\Delta\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}=\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\-\\boldsymbol\{b\}\_\{i\}^\{\(t\-1\)\}δi\(t\)\\delta\_\{i\}^\{\(t\)\}Magnitude of the per\-round belief changeδi\(t\):=12‖Δ𝒃i\(t\)‖1\\delta\_\{i\}^\{\(t\)\}:=\\frac\{1\}\{2\}\\left\\\|\\Delta\\boldsymbol\{b\}\_\{i\}^\{\(t\)\}\\right\\\|\_\{1\}Bi\(t\)B\_\{i\}^\{\(t\)\}Discretized belief label of theii\-th agentBi\(t\)=argmaxy𝒃i\(y∣𝐦i\(t\)\)B\_\{i\}^\{\(t\)\}=\\arg\\max\_\{y\}\\boldsymbol\{b\}\_\{i\}\(y\\mid\\mathbf\{m\}\_\{i\}^\{\(t\)\}\)B^i\(t\+1\)\\hat\{B\}\_\{i\}^\{\(t\+1\)\}Predicted next\-round belief for agentaia\_\{i\}TTTotal number of roundsT=10T=10rrSimulation run indexccContrast between two scenariosc=EMM1−EMM2c=\\mathrm\{EMM\}\_\{1\}\-\\mathrm\{EMM\}\_\{2\}Δc\\Delta cInteraction contrast between two networksΔc=cER−cWS\\Delta c=c\_\{\\mathrm\{ER\}\}\-c\_\{\\mathrm\{WS\}\}ddCohen’s effect size[Section˜D\.3](https://arxiv.org/html/2607.27512#A4.SS3)Inputs and Text𝐦i\(t\)\\mathbf\{m\}\_\{i\}^\{\(t\)\}Message toii\-th agent at roundtt𝐦i\(t\)=\(𝐱r,𝐱s,𝐱n\(t\)\)\\mathbf\{m\}\_\{i\}^\{\(t\)\}=\(\\mathbf\{x\}\_\{r\},\\mathbf\{x\}\_\{s\},\\mathbf\{x\}\_\{n\}^\{\(t\)\}\)𝐱r\\mathbf\{x\}\_\{r\}Role specification[Table˜A2](https://arxiv.org/html/2607.27512#A2.T2)𝐱s\\mathbf\{x\}\_\{s\}Statement \(topic of discussion\)[Table˜A4](https://arxiv.org/html/2607.27512#A3.T4)𝐱n\(t\)\\mathbf\{x\}\_\{n\}^\{\(t\)\}Summary of neighbors’ beliefs at roundtt𝐱n\(0\)=∅\\mathbf\{x\}\_\{n\}^\{\(0\)\}=\\emptysetyyGround\-truth label for the statement𝐱s\\mathbf\{x\}\_\{s\}Surrogate \(Opinion\-dynamics\) ModelsPrPrProbability given by surrogate modelsΓ\(r,t\)\\varGamma^\{\(r,t\)\}Global belief\-state composition at a roundttin a runrr\(f1\(r,t\),f2\(r,t\),f3\(r,t\)\)\(f\_\{1\}^\{\(r,t\)\},f\_\{2\}^\{\(r,t\)\},f\_\{3\}^\{\(r,t\)\}\)Ni\(r,t\)N\_\{i\}^\{\(r,t\)\}Neighborhood belief\-state composition for an agentaia\_\{i\}\(ni,1\(r,t\),ni,2\(r,t\),ni,3\(r,t\)\)\(n\_\{i,1\}^\{\(r,t\)\},n\_\{i,2\}^\{\(r,t\)\},n\_\{i,3\}^\{\(r,t\)\}\)MiM\_\{i\}LLM assigned to an agentaia\_\{i\}RiR\_\{i\}Role assigned to an agentaia\_\{i\}ϕi\(t\)\\boldsymbol\{\\phi\}\_\{i\}^\{\(t\)\}Feature vector used to predict the next\-round belief of agentaia\_\{i\} Table A1:Notations used throughout the paper\.Symbols are grouped by category\. ## Appendix BSelection of Large Language Models We select large language models \(LLMs\) according to the following criteria: 1. 1\.The finetuned LLM must be based onLlama\-3\-InstructorLlama\-3\.1\-InstructGrattafioriet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib8)\)\. 2. 2\.The finetuning must use conversational or instruction\-based datasets to maintain the LLM’s chat\-like capabilities\. 3. 3\.The LLM must be publicly available on the[Hugging Face](https://huggingface.co/)platform\. 4. 4\.The developers must provide documentation describing the data sources \(e\.g\., URLs and data cards\)\. 5. 5\.The model card or associated manuscript must report benchmark results demonstrating that the finetuning yields comparable or improved performance relative to the chat\-basedLlama\-3model \(for a domain\-specific task\)\. Model NameSpecialization \(Domain\)Social RoleDeveloper & SourceLlama\-3\.1\-8B\-InstructGeneralist \(Base Model\)LLM or Human ParticipantGrattafioriet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib8)\)Bio\-Medical\-Llama\-3\-8BBiomedical ResearchBiomedical ResearcherContact Doctor \([2024](https://arxiv.org/html/2607.27512#bib.bib9)\)Llama3\-Med42\-8BClinical MedicineClinical PhysicianChristopheet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib10)\)Llama\-3\.1 OpenScholar\-8BScientific LiteratureAcademic ScholarAsaiet al\.\([2026](https://arxiv.org/html/2607.27512#bib.bib11)\)Llama3Dictionary\-MergeLexicography / DefinitionsLexicographerPeritiet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib4)\)Llama\-3\.1\-Hawkish\-8BFinancial MarketsFinancial Analystmukaj \([2024](https://arxiv.org/html/2607.27512#bib.bib12)\)Llama3\-KALE\-LM\-Chem\-1\.5\-8BChemistryChemistDaiet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib13)\)Foundation\-Sec\-8B\-InstructCybersecuritySecurity AnalystFDTN AI \([2024](https://arxiv.org/html/2607.27512#bib.bib14)\)UserLM\-8BSocial ConversationOnline FriendNaouset al\.\([2026](https://arxiv.org/html/2607.27512#bib.bib15)\)OpenMath2\-Llama3\.1\-8BMathematicsMathematicianToshniwalet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib16)\)Human\-Like\-Llama3\-8B\-InstructHuman\-like ConversationAssistantÇalık and Akkuş \([2025](https://arxiv.org/html/2607.27512#bib.bib17)\)Hermes\-3\-Llama\-3\.1\-8BStrategic ReasoningStrategic PlannerTekniumet al\.\([2024](https://arxiv.org/html/2607.27512#bib.bib18)\)Suzume\-Llama\-3\-8B\-MultilingualMultilingual DialogueLanguage MediatorDevine \([2024](https://arxiv.org/html/2607.27512#bib.bib19)\)Code\-Llama\-3\-8BCoding and MathsSoftware EngineerBawase \([2024](https://arxiv.org/html/2607.27512#bib.bib20)\)Roleplay\-Llama\-3\-8BRoleplay / StorytellingStorytellerGallego \([2024](https://arxiv.org/html/2607.27512#bib.bib21)\) Table A2:Summary of the1515LLMs used as agents in our study\.Each model is characterized by its specialization \(i\.e\., the datasets on which it was finetuned\), the social role assigned to it within the experiments, and its developer or source\. The selection includes both general\-purpose \(a\.k\.a\. generalist\) and finetuned \(a\.k\.a\. specialist\)Llama\-3andLlama\-3\.1models\.Note:Although the generalist LLM can take the social role of aHuman Participant, this designation refers only to its social identity in the experiment and does not imply human\-like qualities; in scenario I, we only use the“LLM”role\. In scenarios II and III, social roles are assigned at random and thus do not necessarily correspond to the specialization categories shown here\. ## Appendix CSampling with Maximin Criterion The design space of our experiments requires around10510^\{5\}simulations \(statements×\\timesnetwork realizations×\\timesscenarios×\\timesnetwork structures\), which is infeasible given our time and resource constraints\. To reduce the number of simulations while ensuring that we select a diverse set of statements and network realizations, we use themaximin criterionJohnsonet al\.\([1990](https://arxiv.org/html/2607.27512#bib.bib33)\)\. This appendix describes the algorithm, its application, and the diagnostics we use to verify coverage\. ### C\.1Maximin Criterion Given a candidate pool𝒳=\{x1,…,xN\}⊂ℝd\\mathcal\{X\}=\\\{x\_\{1\},\\ldots,x\_\{N\}\\\}\\subset\\mathbb\{R\}^\{d\}of sizeNN, we select a subsetS⋆⊆𝒳S^\{\\star\}\\subseteq\\mathcal\{X\}of sizeKKwhose minimum pairwise Euclidean distance is as large as possible: S⋆\\displaystyle S^\{\\star\}=argmaxS⊆𝒳\|S\|=Kdmin\(S\),\\displaystyle=\\;\\arg\\max\_\{\\begin\{subarray\}\{c\}S\\subseteq\\mathcal\{X\}\\\\ \|S\|=K\\end\{subarray\}\}d\_\{\\min\}\(S\),\(A1\)dmin\(S\)\\displaystyle d\_\{\\min\}\(S\):=minx,y∈Sx≠y∥x−y∥2\.\\displaystyle:=\\min\_\{\\begin\{subarray\}\{c\}x,y\\,\\in S\\\\ x\\neq y\\end\{subarray\}\}\\,\\lVert x\-y\\rVert\_\{2\}\.\(A2\)We use the farthest\-point greedy algorithm ofGonzalez \([1985](https://arxiv.org/html/2607.27512#bib.bib32)\)to perform the iterative selection in[Algorithm˜1](https://arxiv.org/html/2607.27512#alg1)\. ##### Procedure\. We start by standardizing features of𝒳\\mathcal\{X\}to zero mean and unit variance\. We then either select the sample with the largest norm or provide an initial setS0S\_\{0\}\. We iteratively select the candidates from𝒳\\mathcal\{X\}whose pairwise minimum distance to the already\-selected setS⋆S^\{\\star\}is greatest\. Algorithm 1Greedy maximin selection1:Pool 𝒳=\{x1,…,xN\}⊂ℝd\\mathcal\{X\}=\\\{x\_\{1\},\\ldots,x\_\{N\}\\\}\\subset\\mathbb\{R\}^\{d\}, target size KK, optional starting set S0S\_\{0\}\. 2: S⊆𝒳S\\subseteq\\mathcal\{X\}approximating S⋆S^\{\\star\}in \([A1](https://arxiv.org/html/2607.27512#A3.E1)\)\. 3: 𝒳←standardize\(𝒳\)\\mathcal\{X\}\\leftarrow\\texttt\{standardize\}\(\\mathcal\{X\}\) 4:if S0S\_\{0\}is non\-emptythen 5: S←S0S\\leftarrow S\_\{0\} 6:else 7: S←\{argmaxx∈𝒳∥x∥2\}S\\leftarrow\\\{\\,\\arg\\max\_\{x\\in\\mathcal\{X\}\}\\lVert x\\rVert\_\{2\}\\,\\\} 8:endif 9:while \|S\|<K\|S\|<Kdo 10:foreach x∈𝒳∖Sx\\in\\mathcal\{X\}\\setminus Sdo 11: d\(x\)←minx′∈S∥x−x′∥2d\(x\)\\leftarrow\\min\_\{x^\{\\prime\}\\in S\}\\,\\lVert x\-x^\{\\prime\}\\rVert\_\{2\} 12:endfor 13: S←S∪\{argmaxx∈𝒳∖Sd\(x\)\}S\\leftarrow S\\cup\\\{\\,\\arg\\max\_\{x\\in\\mathcal\{X\}\\setminus S\}d\(x\)\\,\\\} 14:endwhile 15:return SS ### C\.2Sampling Network Realizations with Maximin Criterion Seedℓ¯\\bar\{\\ell\}CCk¯\\bar\{k\}σk\\sigma\_\{k\}k0k\_\{0\}Erdős–Rényi\(n=48n=48,p=0\.3p=0\.3\)20121557231\.7550\.23312\.3752\.8331122921232361\.6660\.35315\.7503\.38820430192161\.7340\.32213\.5423\.937719820185731\.6970\.29514\.4582\.2731137810929451\.7070\.28913\.9583\.0412727013269891\.6860\.34715\.4583\.974937982791631\.7250\.28413\.6253\.289156015357741\.6750\.30715\.4172\.45721Watts–Strogatz\(n=48n=48,k=8k=8,β=0\.1\\beta=0\.1\)17696747412\.2780\.4188\.0001\.307103658601062\.6150\.5738\.0000\.50073950364302\.3020\.4318\.0001\.041538306402762\.3520\.4688\.0000\.645910937738362\.4560\.4978\.0001\.137813560442892\.4470\.5068\.0000\.79168513506172\.6210\.5388\.0000\.816942629342052\.2770\.4088\.0000\.9798 Table A3:Overview of the structural features of the eight networks selected per network structurevia Algorithm[1](https://arxiv.org/html/2607.27512#alg1)\. These networks are generated using our network generators \(ER and WS\)\. Features:\(ℓ¯\)\(\\bar\{\\ell\}\)mean shortest\-path length;\(C\)\(C\)global clustering coefficient;\(k¯\)\(\\bar\{k\}\)mean degree;\(σk\)\(\\sigma\_\{k\}\)standard deviation of the degree distribution;\(k0\)\(k\_\{0\}\)degree of node0\.We consider two network structures: Erdős–Rényi \(ER\) and Watts–Strogatz \(WS\)\. For each structure, we run simulations across multiple network realizations to ensure the findings are not driven by a single sample \(i\.e\., we want a structurally diverse set of realizations for each network structure\)\. Specifically, we generateNpool=1000N\_\{\\text\{pool\}\}=1000candidate realizations by drawing independent seeds for the corresponding generator while holding the following parameters fixed:n=48n=48for both network structures,p=0\.3p=0\.3for ER, andk=8k=8,β=0\.1\\beta=0\.1for WS\. For each sampled network realization, we compute five structural features: 1. 1\.mean shortest\-path length, 2. 2\.global clustering coefficient, 3. 3\.mean degree, 4. 4\.standard deviation of the degree distribution, 5. 5\.degree of node0, the node reserved for the Clinical Physician agent \(so that the specialist’s local connectivity varies across replicates\)\. We discard candidate network realizations with more than one connected component\. The resulting per\-structure feature matrices are passed to[Algorithm˜1](https://arxiv.org/html/2607.27512#alg1)withK=8K=8\. That is, as a result of the maximin sampling, we obtain eight network realizations per network structure\.[Table˜A3](https://arxiv.org/html/2607.27512#A3.T3)provides an overview of the selected network realizations\. ### C\.3Sampling Discussion Statements with Maximin Criterion IDStatementy^doc\\hat\{y\}\_\{\\text\{doc\}\}adoca\_\{\\text\{doc\}\}aothera\_\{\\text\{other\}\}ccFalse statements\(y=0y=0\)false\_0Silver is indicated for the treatment of keratosis pilaris\.00\.9990\.8000\.948false\_1Terbutaline is indicated for the treatment of cramps\.10\.0780\.0670\.966false\_2Isosorbide is indicated for the treatment of ischemia\.10\.0120\.8670\.024false\_3Atorvastatin is indicated for the treatment of aggression\.01\.0000\.0000\.022false\_4Manidipine is indicated for the treatment of septic\.01\.0000\.3330\.554false\_5VLTS\-589 is indicated for the treatment of diabetic macular edema\.10\.3830\.8670\.386false\_6Nandrolone decanoate is indicated for the treatment of Duchenne muscular dystrophy\.01\.0000\.6670\.608false\_7Vitamin E is indicated for the treatment of pulmonary coccidioidomycosis\.01\.0000\.2670\.191false\_8Tetracycline is indicated for the treatment of throat\.00\.7550\.9330\.763false\_9Ethinylestradiol is indicated for the treatment of dry cough\.01\.0000\.0670\.301True statements\(y=1y=1\)true\_0Methyl nicotinate is indicated for the treatment of aches\.10\.7730\.9330\.869true\_1Terbutaline is indicated for the treatment of asthma\.00\.0000\.1330\.986true\_2Warfarin is indicated for the treatment of pulmonary embolism\.11\.0000\.2000\.006true\_3Tetracycline is indicated for the treatment of Q fever\.00\.0470\.9330\.188true\_4Theophylline is indicated for the treatment of asthma\.10\.5310\.2670\.773true\_5Sildenafil is indicated for the treatment of pulmonary hypertension\.11\.0000\.5330\.510true\_6Polymyxin B is indicated for the treatment of infections of the urinary tract\.00\.4380\.1330\.571true\_7SNS\-314 is indicated for the treatment of tumors\.00\.0160\.5330\.589true\_8Valomaciclovir is indicated for the treatment of viral infection\.00\.3180\.4000\.920true\_9Linezolid is indicated for the treatment of nosocomial pneumonia\.10\.7030\.2000\.307 Table A4:List of 20 discussion statements selected via[Algorithm˜1](https://arxiv.org/html/2607.27512#alg1)and their corresponding ground\-truth label and four features\. We divide the statements into false \(y=0y=0\) and true \(y=1y=1\) subtables\. The four maximin features are the medical specialist’s predicted label\(y^doc\)\(\\hat\{y\}\_\{\\text\{doc\}\}\), the medical specialist’s accuracy\(adoc\)\(a\_\{\\text\{doc\}\}\), the mean accuracy of the other 14 LLMs\(aother\)\(a\_\{\\text\{other\}\}\), and the consensus score\(c\)\(c\)between the medical specialist and the1414other LLMs:1−\|pdoc\(true∣s\)−p~other\(true∣s\)\|1\-\\lvert p\_\{\\text\{doc\}\}\(\\textsc\{true\}\\mid s\)\-\\tilde\{p\}\_\{\\text\{other\}\}\(\\textsc\{true\}\\mid s\)\\rvert, wherep~other\\tilde\{p\}\_\{\\text\{other\}\}is the median probability of the1414other LLMs\.Note: We do not correct the template\-induced grammatical artifacts so that prompts remain uniformly formatted across conditions\.Our statements are drawn from the medical\-indication data introduced inSavcisens and Eliassi\-Rad \([2025](https://arxiv.org/html/2607.27512#bib.bib23)\)\. We restrict selection to non\-negated statements that reference real\-world entities\.999We exclude neither\-valued statements with synthetic entities\.An example of such a statement is“Heparin is indicated for the treatment of pulmonary embolism\.” Before applying the maximin criterion, we compute zero\-shot predictions for each statementssfrom the medical specialist \(Llama3\-Med42\-8B\) and from 14 other LLMs in[Table˜A2](https://arxiv.org/html/2607.27512#A2.T2)\. In addition, we define the following features for each statementss: 1. 1\.The binary ground\-truth label: y∈\{false,true\}y\\in\\\{\\textsc\{false\},\\textsc\{true\}\\\}or\{0,1\}\\\{0,1\\\}, respectively, 2. 2\.Label predicted by a medical specialist, 3. 3\.Medical specialist’s accuracy, based on next\-token probabilities:1−\|y−pdoc\(true∣s\)\|1\-\\lvert y\-p\_\{\\text\{doc\}\}\(\\textsc\{true\}\\mid s\)\\rvert, 4. 4\.Label\-level \(averaged\) accuracy of other LLMs, 5. 5\.Consensus between the medical specialist and other models=1−\|pdoc\(true∣s\)−p~other\(true∣s\)\|=1\-\\lvert p\_\{\\text\{doc\}\}\(\\textsc\{true\}\\mid s\)\-\\tilde\{p\}\_\{\\text\{other\}\}\(\\textsc\{true\}\\mid s\)\\rvert, wherep~other\\tilde\{p\}\_\{\\text\{other\}\}denotes the median probability assigned by the 14 other models\. The first two features are binary; the remaining three are continuous in the range\[0,1\]\[0,1\]\. Note that feature\#4\\\#4is computed from the binary label predictions, while feature\#5\\\#5compares probability distributions, so the two are not redundant\. Since we want to have an equal number of true and false statements, we add a constraint to[Algorithm˜1](https://arxiv.org/html/2607.27512#alg1)that enforces aK/2K/2quota per ground\-truth label \(we setK=20K=20\)\. That is, we ensure that we select1010true and1010false statements\.[Table˜A4](https://arxiv.org/html/2607.27512#A3.T4)displays selected statements with the corresponding features\. ## Appendix DAdditional Details on Descriptive Analysis This section expands on the methodology described in §[4\.5](https://arxiv.org/html/2607.27512#S4.SS5)\. Here, we useR’s mixed\-model \(lme4\) formula notationBateset al\.\([2015](https://arxiv.org/html/2607.27512#bib.bib68)\)\. A termy ˜ x \+ \(1\|g\)fits a fixed effect forxand a random intercept for each level of grouping factorg\(a separate baseline offset per level ofg, which accounts for repeated measures within each level\)\. Meanwhile,\(1\|g1:g2\)denotes a random intercept for each combination of levels ofg1andg2; it is used wheng2’s labels are only meaningful jointly withg1\. For instance,“network realization 3”refers to a different network under ER vs\. WS\. Finally,n\-strstands for thenetwork structure\(ER or WS\) andn\-realizationstands for thenetwork realization; each network structure has eight network realizations \([Table˜A3](https://arxiv.org/html/2607.27512#A3.T3)\)\. We use two identifiers for a network realization, depending on the analysis:n\-realizationindexes a realizationwithinits network structure \(values 1–8, reused across ER and WS\) andn\-realization\-idis a globally unique identifier assigned to each of the 16 realizations across both structures\. ### D\.1Linear Mixed\-Effects Models Estimated marginal means \(EMMs\), or least\-squares means, are model\-based predicted means adjusted for the other terms in the mixed model\. To estimate the coefficients, EMMs, and confidence intervals, we fit the following linear mixed\-effects model for plasticity, directedness, consensus \(and consensus change\), and outgoing influence \(see §[4\.5\.1](https://arxiv.org/html/2607.27512#S4.SS5.SSS1)for definitions\): <var\-name\> ˜ scenario \* n\-str \+ \(1 \| statement\) \+ \(1 \| n\-str:n\-realization\)\. The random\-effects structure includes\(1\|statement\)to account for repeated measures across statements and\(1\|n\-str:n\-realization\)to capture variation due to different realizations of each network structure\. We provide an overview of results in[Table˜A6](https://arxiv.org/html/2607.27512#A6.T6)\. Here, we include the marginal estimates where the mixed\-effects model is specified as: <var\-name\> ˜ scenario \+ \(1 \| statement\) \+ \(1 \| n\-str:n\-realization\)\. ### D\.2Variance Decomposition To assess whether some agents exert more influence than others, we fit a variance‑components model to the agent‑level outgoingInfluence\(i\)\\mathrm\{Influence\}\(i\), with intercept‑only fixed effects and random intercepts foragent\(nested within networks\),network realization, andstatement\(we fit models separately for each scenario\)\. The model formula is influence ˜ 1 \+ \(1 \| n\-realization\-id\) \+ \(1 \| statement\) \+ \(1 \| agent:n\-realization\-id\)\. It allows us to quantify the variance inoutgoing influenceattributed to agent identity relative to network realization and statement\. For each random‑effects component, we report the intraclass correlation coefficient \(ICC\) as the proportion of total variance attributable to that component\. A higher agent‑level ICC suggests asymmetry in the outgoing influence \(presence of opinion leaders and followers\), whereas a near‑zero value indicates that influence is largely exchangeable across agents \(no opinion leaders\)\. In[Figure˜4](https://arxiv.org/html/2607.27512#S5.F4), we report 95% confidence intervals estimated via a parametric bootstrap \(1,0001\{,\}000resamples\)\. To test whether the agent‑level variance component is distinguishable from zero, we use an exact restricted likelihood ratio test \(RLRsim;Scheiplet al\.,[2008](https://arxiv.org/html/2607.27512#bib.bib41)\), which accounts for the boundary problem in testingσagent2=0\\sigma^\{2\}\_\{\\text\{agent\}\}=0\. The null distribution is simulated with10,00010\{,\}000Monte Carlo draws\. ### D\.3Contrast Analysis We define four planned contrasts on the four scenarios \(I, II, III, and IV\), each corresponding to a single‑degree‑of‑freedom effect on the outcome\. These four contrasts were specified a priori, before inspecting the fitted models\. We define the contrast asc=EMM1−EMM2c=\\mathrm\{EMM\}\_\{1\}\-\\mathrm\{EMM\}\_\{2\}, where EMMs are based on the outcomes of two scenarios\.[Table˜A5](https://arxiv.org/html/2607.27512#A4.T5)specifies the contrast weights, and below we provide the contrast definitions: Role Effect:Random Roles \(II\) vs\. Baseline \(I\) Specialization Effect:Random Specialists \(III\) vs\. Random Roles \(II\) Role–specialization \(alignment\) effect:Matched Specialists \(IV\) vs\. Random Specialists \(III\) Composition Effect:comparing the average of homogeneous scenarios \(I and II\) and the average of heterogeneous scenarios \(III and IV\)\. ContrastNotationI\. BaselineII\. RandomRolesIII\. RandomSpecialistsIV\. MatchedSpecialistsRole effectI→\\toII−1\-1\+1\+100Specialization effectII→\\toIII0−1\-1\+1\+10Role–specialization alignmentIII→\\toIV00−1\-1\+1\+1Composition effect\{I, II\}→\\to\{III,IV\}−0\.5\-0\.5−0\.5\-0\.5\+0\.5\+0\.5\+0\.5\+0\.5 Table A5:Contrast weights for the four contrasts between scenarios\.Each row defines a linear combination of the four scenarios as a single degree\-of\-freedom contrast\. Resulting effect sizes are visualized in[Figure˜A1](https://arxiv.org/html/2607.27512#A4.F1)and reported in[Tables˜A8](https://arxiv.org/html/2607.27512#A6.T8)and[A9](https://arxiv.org/html/2607.27512#A6.T9)\.For each contrast above, we compute three quantities: - •Marginalcontrast \([Table˜A8](https://arxiv.org/html/2607.27512#A6.T8)\): the contrast averaged across both network structures, showing the overall effect of a manipulation\. - •Conditionalcontrast \([Table˜A9](https://arxiv.org/html/2607.27512#A6.T9)\): the same linear combination estimated separately within each network structure \(ER or WS\)\. - •Interactioncontrast \(theBetweenrows in[Table˜A9](https://arxiv.org/html/2607.27512#A6.T9)\): the difference between the ER and WS conditional contrasts,cER−cWSc\_\{\\text\{ER\}\}\-c\_\{\\text\{WS\}\}\. A non\-significant interaction indicates that we do not detect differences between manipulation effects when comparing two network structures\. For all contrasts, we report Cohen’sdd,95%95\\%confidence intervals, standard errors, andtt\-statistics\. Figure A1:Effect sizes for the four planned contrasts\.We provide marginal and conditional estimates for ER and WS network structures\. The results are provided in[Tables˜A9](https://arxiv.org/html/2607.27512#A6.T9)and[A8](https://arxiv.org/html/2607.27512#A6.T8)\.##### Computations and effect sizes\. We compute themarginalandconditionalcontrastsccand their95%95\\%confidence intervals from the fitted mixed\-effects model withemmeans\(Lenth and Piaskowski,[2026](https://arxiv.org/html/2607.27512#bib.bib69)\), using Satterthwaite\-approximated degrees of freedom \(lmerTest;Kuznetsovaet al\.,[2017](https://arxiv.org/html/2607.27512#bib.bib67)\)\. For each contrast, we report Cohen’sdd: the estimated marginal\-mean \(EMM\) contrastccstandardized by the*total*standard deviation of the mixed\-effects model, d=cσ^total,withσ^total=σ^ϵ2\+∑gτ^g2,d=\\frac\{c\}\{\\hat\{\\sigma\}\_\{\\mathrm\{total\}\}\},\\quad\\text\{with\}\\quad\\hat\{\\sigma\}\_\{\\mathrm\{total\}\}=\\sqrt\{\\,\\hat\{\\sigma\}^\{2\}\_\{\\epsilon\}\+\\textstyle\\sum\_\{g\}\\hat\{\\tau\}^\{2\}\_\{g\}\\,\},\(A3\)where we sum over the random\-intercept variance componentsτ^g2\\hat\{\\tau\}^\{2\}\_\{g\}\(e\.g\., statement and network realization for the agent\-level outcomes\) andσ^ϵ2\\hat\{\\sigma\}^\{2\}\_\{\\epsilon\}is the residual variance\(Westfallet al\.,[2014](https://arxiv.org/html/2607.27512#bib.bib70)\)\. InR, it is computed as the square root of the summedVarCorrcomponents \(valid for this purpose, since all random effects are intercept\-only\)\. Note that because the components enteringσ^total\\hat\{\\sigma\}\_\{\\mathrm\{total\}\}differ by observational level,ddis comparable across scenarios within an outcome but not directly across the agent and population levels\. Theinteractioncontrast \(theBetweenrows in[Table˜A9](https://arxiv.org/html/2607.27512#A6.T9)\) is the difference between the ER and WS conditional contrasts,Δc=cER−cWS\\Delta c=c\_\{\\mathrm\{ER\}\}\-c\_\{\\mathrm\{WS\}\}, standardized by the sameσ^total\\hat\{\\sigma\}\_\{\\mathrm\{total\}\}\(values near zero indicate a network\-invariant effect\)\. The standard error forΔc\\Delta c\(SE\) is obtained from the variance–covariance matrix of the EMMs\. ## Appendix ESurrogate Model Details The surrogate analysis evaluates whether the belief dynamics observed inCoevolveSimcan be reproduced using a hierarchy of transition models\. ### E\.1Feature Construction LetBi\(r,t\)∈\{1,2,3\}B\_\{i\}^\{\(r,t\)\}\\in\\\{1,2,3\\\}denote the discretized belief of agentaia\_\{i\}in runrrat roundtt, where11,22, and33correspond to accepting, rejecting, or abstaining from the statement, respectively\. All models condition on the agent’s current belief stateBi\(r,t\)B\_\{i\}^\{\(r,t\)\}\. Additional features are defined as follows\. ##### Global belief composition\. For runrrand roundtt, we define Γ\(r,t\)=\(f1\(r,t\),f2\(r,t\),f3\(r,t\)\),\\varGamma^\{\(r,t\)\}=\\left\(f\_\{1\}^\{\(r,t\)\},f\_\{2\}^\{\(r,t\)\},f\_\{3\}^\{\(r,t\)\}\\right\),\(A4\)wherefc\(r,t\)f\_\{c\}^\{\(r,t\)\}denotes the fraction of agents holding belief statecc\. ##### Neighborhood belief composition\. For agentaia\_\{i\}, we define Ni\(r,t\)=\(ni,1\(r,t\),ni,2\(r,t\),ni,3\(r,t\)\),N\_\{i\}^\{\(r,t\)\}=\\left\(n\_\{i,1\}^\{\(r,t\)\},n\_\{i,2\}^\{\(r,t\)\},n\_\{i,3\}^\{\(r,t\)\}\\right\),\(A5\)whereni,c\(r,t\)n\_\{i,c\}^\{\(r,t\)\}denotes the fraction of neighbors in𝒩\(i\)\\mathcal\{N\}\(i\)holding belief statecc\. ##### Identity features\. For model M4, we additionally includeMiM\_\{i\}andRiR\_\{i\}, the underlying LLM and social role assigned to agentaia\_\{i\}, respectively\. ### E\.2Model Specification Each surrogate estimates a conditional distribution over next\-round beliefs, Pr\(Bi\(t\+1\)=c∣ϕi\(t\)\),c∈\{1,2,3\},\\Pr\\\!\\left\(B\_\{i\}^\{\(t\+1\)\}=c\\mid\\boldsymbol\{\\phi\}\_\{i\}^\{\(t\)\}\\right\),\\;c\\in\\\{1,2,3\\\},\(A6\)whereϕi\(t\)\\boldsymbol\{\\phi\}\_\{i\}^\{\(t\)\}is a model\-specific feature vector\. Models are fit separately for each experimental scenario and network structure\. ##### M1: Empirical persistence baseline\. M1 estimates one\-step transition probabilities directly from observed transition frequencies: Pr\(Bi\(t\+1\)=c∣Bi\(t\)\)\.\\Pr\\\!\\left\(B\_\{i\}^\{\(t\+1\)\}=c\\mid B\_\{i\}^\{\(t\)\}\\right\)\.\(A7\) ##### M2: Global belief composition\. M2 conditions on the agent’s current belief and the global belief composition: Pr\(Bi\(t\+1\)=c∣Bi\(t\),Γ\(t\)\)\.\\Pr\\\!\\left\(B\_\{i\}^\{\(t\+1\)\}=c\\mid B\_\{i\}^\{\(t\)\},\\varGamma^\{\(t\)\}\\right\)\.\(A8\) ##### M3: Local belief composition\. M3 conditions on the agent’s current belief and local neighborhood \(belief\) composition: Pr\(Bi\(t\+1\)=c∣Bi\(t\),Ni\(t\)\)\.\\Pr\\\!\\left\(B\_\{i\}^\{\(t\+1\)\}=c\\mid B\_\{i\}^\{\(t\)\},N\_\{i\}^\{\(t\)\}\\right\)\.\(A9\) ##### M4: Local belief composition \+ identity\. M4 augments M3 with agent\-level identity features: Pr\(Bi\(t\+1\)=c∣Bi\(t\),Ni\(t\),Mi,Ri\)\.\\Pr\\\!\\left\(B\_\{i\}^\{\(t\+1\)\}=c\\mid B\_\{i\}^\{\(t\)\},N\_\{i\}^\{\(t\)\},M\_\{i\},R\_\{i\}\\right\)\.\(A10\) ### E\.3Fitting Procedure For each network structure and experimental scenario, we construct transition\-level examples from the empirical belief trajectories generated byCoevolveSim\. Transitions are partitioned into training, validation, and test sets at the run level so that observations from the same simulation run do not appear in multiple splits\. M1 estimates transition probabilities directly from observed transition counts\. Models M2–M4 are implemented as multinomial logistic regressions predicting the next\-round belief state from the corresponding feature set\. ### E\.4Evaluation We evaluate the surrogate hierarchy using both held\-out prediction and behavioral rollouts\. ##### Held\-out transition prediction\. For each transition, the fitted model predictsB^i\(t\+1\)\\widehat\{B\}\_\{i\}^\{\(t\+1\)\}from information available at roundtt\. Predictive performance is evaluated using the Matthews Correlation Coefficient \(MCC\); specifically, we look at whether the final belief state from the surrogate rollout agrees with the observed final\-round state\. We refer to this agreement as a final\-state MCC\. ##### Rollout evaluation\. For each held\-out run, we initialize the surrogate from the empirical round\-0belief state and iteratively generate subsequent belief states by sampling from the fitted transition model\. This procedure produces a complete surrogate belief trajectory\. We compare empirical and surrogate trajectories using consensus fidelity, which measures agreement between the final\-round consensus levels of the empirical and surrogate simulations\. Higher consensus fidelity indicates that the surrogate more accurately reproduces the collective outcome\. We provide an overview of the results in[Tables˜A10](https://arxiv.org/html/2607.27512#A6.T10)and[A11](https://arxiv.org/html/2607.27512#A6.T11)\. ## Appendix FTables In this section, we provide detailed tables for 1. 1\.Estimated marginal means \(EMMs\) in[Table˜A6](https://arxiv.org/html/2607.27512#A6.T6), 2. 2\.Variance decomposition for the outgoing influence in[Table˜A7](https://arxiv.org/html/2607.27512#A6.T7), 3. 3\.Contrast analysis: marginal effect sizes in[Table˜A8](https://arxiv.org/html/2607.27512#A6.T8)and conditional effects by network structure in[Table˜A9](https://arxiv.org/html/2607.27512#A6.T9), 4. 4\.Surrogate analysis: final\-state Matthews Correlation Coefficient \(final\-state MCC\) in[Table˜A10](https://arxiv.org/html/2607.27512#A6.T10)and consensus fidelity in[Table˜A11](https://arxiv.org/html/2607.27512#A6.T11)\. Estimate95%95\\%CIlower95%95\\%CIupperSEdfOutcomeScenarioNetworkPlasticityI\. Base LLMsER0\.030\.000\.050\.0120\.00WS0\.030\.000\.060\.0120\.00Marginal0\.030\.000\.050\.0119\.50II\. Random rolesER0\.070\.050\.100\.0120\.00WS0\.050\.030\.080\.0120\.00Marginal0\.060\.040\.090\.0119\.50III\. Random SpecialistsER0\.130\.110\.160\.0120\.00WS0\.110\.090\.140\.0120\.00Marginal0\.120\.100\.150\.0119\.50IV\. Matched SpecialistsER0\.120\.090\.140\.0120\.00WS0\.140\.110\.170\.0120\.00Marginal0\.130\.100\.150\.0119\.50DirectednessI\. Base LLMsER0\.970\.911\.030\.0319\.90WS0\.960\.901\.020\.0319\.90Marginal0\.960\.911\.020\.0319\.80II\. Random rolesER0\.440\.380\.500\.0319\.90WS0\.500\.440\.560\.0319\.90Marginal0\.470\.410\.530\.0319\.80III\. Random SpecialistsER0\.270\.210\.330\.0319\.90WS0\.350\.290\.410\.0319\.90Marginal0\.310\.250\.370\.0319\.80IV\. Matched SpecialistsER0\.310\.250\.360\.0319\.90WS0\.260\.200\.320\.0319\.90Marginal0\.280\.230\.340\.0319\.80Outgoing InfluenceI\. Base LLMsER0\.02\-0\.010\.040\.0119\.90WS0\.02\-0\.010\.050\.0119\.90Marginal0\.02\-0\.010\.050\.0119\.40II\. Random rolesER0\.070\.050\.100\.0119\.90WS0\.050\.030\.080\.0119\.90Marginal0\.060\.040\.090\.0119\.40III\. Random SpecialistsER0\.130\.110\.160\.0119\.90WS0\.120\.090\.150\.0119\.90Marginal0\.130\.100\.160\.0119\.40IV\. Matched SpecialistsER0\.120\.090\.140\.0119\.90WS0\.150\.120\.170\.0119\.90Marginal0\.130\.100\.160\.0119\.40Consensus ChangeI\. Base LLMsER0\.00\-0\.030\.020\.0132\.00WS\-0\.01\-0\.040\.010\.0132\.00Marginal\-0\.01\-0\.030\.020\.0124\.20II\. Random rolesER0\.040\.010\.070\.0132\.00WS0\.050\.020\.080\.0132\.00Marginal0\.040\.020\.070\.0124\.20III\. Random SpecialistsER0\.190\.170\.220\.0132\.00WS0\.180\.150\.210\.0132\.00Marginal0\.190\.160\.210\.0124\.20IV\. Matched SpecialistsER0\.160\.130\.180\.0132\.00WS0\.140\.110\.170\.0132\.00Marginal0\.150\.120\.170\.0124\.20 Table A6:Estimated marginal means \(EMMs\) of agent\- and population\-level outcomesby scenario and network structure \([Appendix˜D](https://arxiv.org/html/2607.27512#A4)\)\. EMMs with95%95\\%confidence intervals are estimated with the linear mixed\-effects models, reported per network structure \(ER, WS\) and marginally \(averaged over both structures with equal weights\)\. Agent\-level outcomes \(plasticity, directedness, outgoing influence\) are fit with random intercepts for statement and network realization, while consensus change is fit at the run level;dfdenotes Satterthwaite\-approximated degrees of freedom \(which is why marginal and per\-network rows differ\)\.SEis the standard error of the EMM; in thenetworkcolumn ER stands for Erdős–Rényi and WS for Watts–Strogatz\.Agent\-level ICC \(95% CI\)Network\-level ICC \(95% CI\)ScenarioICCLowerUpperICCLowerUpperRLRTppI\. Baseline0\.000\.000\.050\.270\.090\.660\.50II\. Random Roles0\.000\.000\.121\.320\.492\.870\.49III\. Random Specialists4\.973\.507\.082\.961\.125\.96<0\.001IV\. Matched Specialists2\.731\.904\.044\.981\.909\.35<0\.001Table A7:Variance decomposition of outgoing influence by scenario: intraclass correlations \(ICC, %\) show the ratio of variance in outgoing influence that is attributed to agent identities \(agent\-level\) or network realizations \(network\-level\)\. Additionally, we provide the likelihood\-ratio test results \(RLRT\)\. The variation in influence due to the LLM agents’ identities \(emergence of persistent opinion leaders and followers\) appears only when specialist LLMs are introduced; that is, in scenarios III and IV\.Cohen’sdd95%95\\%CIlower95%95\\%CIupperSEtt\-statpp\-valdfSigOutcomeContrastPlasticityRole effect0\.320\.250\.380\.0049\.55<0\.0011253\*Specialization effect0\.530\.460\.590\.00415\.83<0\.0011253\*Role–spec\. alignment0\.06\-0\.010\.120\.0041\.660\.0981253Composition effect0\.710\.670\.760\.00330\.30<0\.0011253\*DirectednessRole effect\-1\.86\-1\.94\-1\.790\.010\-48\.59<0\.0011253\*Specialization effect\-0\.62\-0\.69\-0\.540\.010\-16\.14<0\.0011253\*Role–spec\. alignment\-0\.09\-0\.17\-0\.010\.010\-2\.350\.0191253\*Composition effect\-1\.60\-1\.65\-1\.540\.007\-58\.85<0\.0011253\*Outgoing InfluenceRole effect0\.530\.440\.620\.00411\.19<0\.0011253\*Specialization effect0\.730\.640\.820\.00415\.36<0\.0011253\*Role–spec\. alignment0\.04\-0\.050\.130\.0040\.850\.3941253Composition effect1\.010\.951\.080\.00330\.24<0\.0011253\*Consensus ChangeRole effect0\.510\.380\.650\.0077\.52<0\.0011253\*Specialization effect1\.391\.261\.530\.00720\.46<0\.0011253\*Role–spec\. alignment\-0\.36\-0\.49\-0\.230\.007\-5\.27<0\.0011253\*Composition effect1\.471\.371\.560\.00530\.53<0\.0011253\* Table A8:Marginaleffects for the four contrasts on agent\- and population\-level outcomes\([Appendix˜D](https://arxiv.org/html/2607.27512#A4)\)\. Each contrast is a single\-degree\-of\-freedom comparison between scenarios, averaged across network structures:role effect\(II vs\. I\),specialization effect\(III vs\. II\),role–specialization alignment\(IV vs\. III\), andcomposition effect\(\{III, IV\} vs\. \{I, II\}\)\. Effect sizes are reported as Cohen’sddwith95%95\\%confidence intervals; larger\|d\|\|d\|indicates a larger standardized difference; the sign ofddindicates the direction of the effect\.SEis the standard error of the unstandardized contrastcc,tt\-stat is the associatedtt\-statistic, thepp\-value testsH0\\text\{H\}\_\{0\}:d=0d=0,dfdenotes Satterthwaite\-approximated degrees of freedom, and∗\*in theSigcolumn denotesp<0\.05p<0\.05\.Cohen’sdd95%95\\%CIlower95%95\\%CIupperSEtt\-statpp\-valdfSigOutcomeNetworkContrastPlasticityERRole effect0\.430\.340\.520\.0059\.09<0\.0011253\*Specialization effect0\.530\.440\.620\.00511\.24<0\.0011253\*Role–spec\. alignment\-0\.15\-0\.24\-0\.060\.005\-3\.170\.0021253\*Composition effect0\.670\.600\.740\.00420\.09<0\.0011253\*WSRole effect0\.210\.120\.300\.0054\.41<0\.0011253\*Specialization effect0\.530\.430\.620\.00511\.14<0\.0011253\*Role–spec\. alignment0\.260\.170\.350\.0055\.52<0\.0011253\*Composition effect0\.760\.690\.820\.00422\.77<0\.0011253\*BetweenRole effect0\.220\.090\.350\.0073\.31<0\.0011253\*Specialization effect0\.01\-0\.130\.140\.0070\.070\.9411253Role–spec\. alignment\-0\.41\-0\.54\-0\.280\.007\-6\.15<0\.0011253\*Composition effect\-0\.09\-0\.180\.000\.005\-1\.900\.0581253DirectednessERRole effect\-1\.99\-2\.10\-1\.890\.014\-36\.73<0\.0011253\*Specialization effect\-0\.65\-0\.76\-0\.550\.014\-12\.03<0\.0011253\*Role–spec\. alignment0\.130\.030\.240\.0142\.470\.0141253\*Composition effect\-1\.58\-1\.66\-1\.510\.01\-41\.24<0\.0011253\*WSRole effect\-1\.74\-1\.84\-1\.630\.014\-31\.99<0\.0011253\*Specialization effect\-0\.59\-0\.69\-0\.480\.014\-10\.79<0\.0011253\*Role–spec\. alignment\-0\.32\-0\.42\-0\.210\.014\-5\.80<0\.0011253\*Composition effect\-1\.61\-1\.69\-1\.540\.01\-41\.98<0\.0011253\*BetweenRole effect\-0\.26\-0\.41\-0\.110\.020\-3\.36<0\.0011253\*Specialization effect\-0\.07\-0\.220\.080\.020\-0\.880\.3821253Role–spec\. alignment0\.450\.300\.600\.0205\.84<0\.0011253\*Composition effect0\.03\-0\.080\.140\.0140\.520\.6021253Outgoing InfluenceERRole effect0\.680\.540\.810\.00610\.06<0\.0011253\*Specialization effect0\.680\.540\.810\.00610\.07<0\.0011253\*Role–spec\. alignment\-0\.20\-0\.33\-0\.070\.006\-2\.960\.0031253\*Composition effect0\.910\.821\.010\.00419\.27<0\.0011253\*WSRole effect0\.390\.260\.520\.0065\.76<0\.0011253\*Specialization effect0\.780\.650\.910\.00611\.65<0\.0011253\*Role–spec\. alignment0\.280\.150\.410\.0064\.17<0\.0011253\*Composition effect1\.111\.021\.210\.00423\.50<0\.0011253\*BetweenRole effect0\.290\.100\.470\.0083\.040\.0021253\*Specialization effect\-0\.11\-0\.290\.080\.008\-1\.120\.2631253Role–spec\. alignment\-0\.48\-0\.66\-0\.290\.008\-5\.04<0\.0011253\*Composition effect\-0\.20\-0\.33\-0\.070\.006\-3\.000\.0031253\*Consensus ChangeERRole effect0\.430\.240\.620\.0104\.44<0\.0011253\*Specialization effect1\.501\.311\.690\.01015\.63<0\.0011253\*Role–spec\. alignment\-0\.35\-0\.54\-0\.170\.010\-3\.69<0\.0011253\*Composition effect1\.541\.411\.670\.00722\.64<0\.0011253\*WSRole effect0\.600\.410\.790\.0106\.20<0\.0011253\*Specialization effect1\.281\.091\.470\.01013\.31<0\.0011253\*Role–spec\. alignment\-0\.36\-0\.55\-0\.170\.010\-3\.77<0\.0011253\*Composition effect1\.401\.261\.530\.00720\.54<0\.0011253\*BetweenRole effect\-0\.17\-0\.440\.100\.014\-1\.250\.2131253Specialization effect0\.22\-0\.040\.490\.0141\.640\.1001253Role–spec\. alignment0\.01\-0\.260\.280\.0140\.060\.9551253Composition effect0\.14\-0\.050\.330\.0101\.480\.1381253 Table A9:Conditionalandinteractioneffects for the four contrasts on agent\- and population\-level outcomes\([Appendix˜D](https://arxiv.org/html/2607.27512#A4)\)\. Each contrast is estimated separately within each network structure \(ER stands for Erdős–Rényi, and WS stands for Watts–Strogatz\)\. TheBetweenrows report interaction contrasts \(ER conditional contrast−\-WS conditional contrast\); a non\-significantBetweenrow indicates that the manipulation does not produce any detectable differences between the two network structures\. The contrasts includerole effect\(II vs\. I\),specialization effect\(III vs\. II\),role–specialization alignment\(IV vs\. III\), andcomposition effect\(\{III, IV\} vs\. \{I, II\}\)\. Effect sizes are reported as Cohen’sddwith95%95\\%confidence intervals; larger\|d\|\|d\|indicates a larger standardized difference; the sign ofddindicates the direction of the effect\.SEis the standard error of the unstandardized contrastcc,tt\-stat is the associatedtt\-statistic, thepp\-value testsH0\\text\{H\}\_\{0\}:d=0d=0,dfdenotes Satterthwaite\-approximated degrees of freedom, and∗\*in theSigcolumn denotesp<0\.05p<0\.05\.NetworkFinal\-stateMCC \(%\)95%95\\%CIlower95%95\\%CIupperScenarioSurrogateI\. BaselineM1ER92\.490\.094\.5WS90\.287\.792\.6M2ER98\.297\.099\.3WS90\.287\.792\.6M3ER97\.295\.798\.4WS92\.590\.394\.6M4ER97\.295\.798\.4WS92\.590\.394\.6II\. Random RolesM1ER86\.183\.088\.9WS94\.792\.896\.5M2ER87\.584\.790\.2WS94\.892\.796\.5M3ER90\.888\.493\.2WS93\.891\.895\.8M4ER90\.387\.792\.8WS94\.792\.896\.5III\. Random SpecialistsM1ER76\.372\.879\.7WS84\.481\.387\.2M2ER80\.777\.683\.9WS84\.881\.987\.7M3ER80\.677\.483\.8WS86\.483\.689\.1M4ER82\.579\.385\.5WS89\.186\.591\.6IV\. Matched SpecialistsM1ER81\.778\.584\.7WS79\.675\.983\.1M2ER79\.976\.383\.1WS78\.775\.082\.3M3ER81\.578\.584\.6WS80\.677\.083\.8M4ER84\.781\.787\.6WS82\.078\.785\.3Table A10:Final\-state Matthews Correlation Coefficient \(final\-state MCC\) by scenario, surrogate model, and network structure\([Appendix˜E](https://arxiv.org/html/2607.27512#A5)\)\. We report MCC with95%95\\%bootstrapped confidence intervals for agreement between each surrogate’s predicted final belief state and the observed final belief state\. Surrogate models are M1 \(persistence\), M2 \(persistence \+ global belief composition\), M3 \(persistence \+ local neighborhood composition\), and M4 \(M3 \+ agent identity and social role\); see[Table˜2](https://arxiv.org/html/2607.27512#S4.T2)\. Higher final\-state MCC indicates more accurate prediction of individual final\-round beliefs\. In the network column, ER stands for Erdős–Rényi, and WS stands for Watts–Strogatz\.NetworkConsensusFidelity \(%\)95%95\\%CIlower95%95\\%CIupperScenarioSurrogateI\. BaselineM1ER91\.188\.793\.6WS90\.488\.392\.7M2ER80\.178\.681\.4WS81\.779\.684\.1M3ER81\.178\.184\.2WS78\.475\.281\.7M4ER81\.077\.984\.3WS78\.575\.281\.7II\. Random RolesM1ER80\.177\.882\.5WS82\.179\.884\.4M2ER84\.781\.787\.7WS86\.783\.989\.3M3ER77\.875\.480\.1WS76\.073\.878\.1M4ER77\.675\.080\.2WS76\.674\.278\.8III\. Random SpecialistsM1ER72\.169\.575\.2WS73\.370\.476\.9M2ER94\.593\.195\.6WS93\.390\.595\.6M3ER92\.991\.694\.2WS90\.989\.092\.6M4ER93\.892\.594\.8WS92\.190\.593\.4IV\. Matched SpecialistsM1ER73\.770\.677\.2WS73\.469\.678\.2M2ER93\.691\.395\.5WS92\.489\.094\.9M3ER91\.188\.593\.3WS90\.588\.991\.9M4ER92\.590\.694\.1WS89\.887\.991\.8Table A11:Consensus fidelity by scenario, surrogate model, and network structure\([Appendix˜E](https://arxiv.org/html/2607.27512#A5)\) with95%95\\%bootstrapped confidence intervals\. Consensus fidelity is defined as the similarity between observed and surrogate final\-round consensus levels across runs; higher values indicate that a surrogate more accurately reproduces the population\-level agreement observed inCoevolveSim\. Surrogate models are M1 \(persistence\), M2 \(persistence \+ global belief composition\), M3 \(persistence \+ local neighborhood composition\), and M4 \(M3 \+ agent identity and social role\); see[Table˜2](https://arxiv.org/html/2607.27512#S4.T2)\. In the network column, ER stands for Erdős–Rényi, and WS stands for Watts–Strogatz\.
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