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Network Effects and Agreement Drift in LLM Debates
Erica Cau, Andrea Failla, Giulio Rossetti
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Summary
This paper investigates the collective behavior of Large Language Model (LLM) agents in multi-round debates using a network generation model. The authors introduce the concept of 'agreement drift'โa directional susceptibility where agents tend to shift toward specific positions on an opinion scale. The study explores how homophily, class size imbalance, and neighborhood information influence opinion dynamics, finding that LLM populations often exhibit systematic biases that can lead to rapid convergence or polarization, depending on network structure.
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Erica Cau โ authored โ Network Effects and Agreement Drift in LLM Debates
confidence 100% ยท Erica Cau et al.: Preprint submitted to Elsevier
LlaMA 3.1 โ usedin โ Network Effects and Agreement Drift in LLM Debates
confidence 100% ยท Unless otherwise stated, results are obtained with Llama 3.1
Agreement Drift โ observedin โ LLM Agents
confidence 90% ยท our findings highlight a particular directional susceptibility that we term agreement drift
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Abstract
Abstract:Large Language Models (LLMs) have demonstrated an unprecedented ability to simulate human-like social behaviors, making them useful tools for simulating complex social systems. However, it remains unclear to what extent these simulations can be trusted to accurately capture key social mechanisms, particularly in highly unbalanced contexts involving minority groups. This paper uses a network generation model with controlled homophily and class sizes to examine how LLM agents behave collectively in multi-round debates. Moreover, our findings highlight a particular directional susceptibility that we term \textit{agreement drift}, in which agents are more likely to shift toward specific positions on the opinion scale. Overall, our findings highlight the need to disentangle structural effects from model biases before treating LLM populations as behavioral proxies for human groups.
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- Source: https://arxiv.org/abs/2604.11312v1
- Canonical: https://arxiv.org/abs/2604.11312v1
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Network Effects and Agreement Drift in LLM Debates โ,โ Erica Cau a,b,โ,1 , Andrea Failla a,b and Giulio Rossetti b a Department of Computer Science, University of Pisa, Largo Bruno Pontecorvo, Pisa, Italy b Institute of Information Science and Technologies โA. Faedoโ (ISTI), National Research Council (CNR), Via Giuseppe Moruzzi 1, Pisa, Italy A R T I C L E I N F O Keywords: LLM Opinion Dynamics Homophily Social Simulation A B S T R A C T Large Language Models (LLMs) have demonstrated an unprecedented ability to simulate human-like social behaviors, making them useful tools for simulating complex social systems. However, it remains unclear to what extent these simulations can be trusted to accurately capture key social mechanisms, particularly in highly unbalanced contexts involving minority groups. This paper uses a network generation model with controlled homophily and class sizes to examine how LLM agents behave collectively in multi-round debates. We show that LLM agents exhibit convergence and polarization patterns that are highly sensitive to network structure and relative group sizes. Moreover, our findings highlight a particular directional susceptibility that we term agreement drift, in which agents are more likely to shift toward specific positions on the opinion scale. Overall, our findings highlight the need to disentangle structural effects from model biases before treating LLM populations as behavioral proxies for human groups. 1. Introduction The introduction of Large Language Models (LLMs) [47, 30, 1, 20] has revolutionized the field of Natural Language Processing (NLP), advancing the ability of language models to solve text-related tasks and generate texts that closely resemble human ones [14]. These models have demonstrated remarkable proficiency across a broad spectrum of NLP tasks [72, 43, 18], marking a transition in the development of general-purpose AI models and progress toward artifi- cial general intelligence (AGI) [40]. In addition to their technical capabilities, LLMs have demonstrated an unprece- dented ability to simulate human social behaviors. When prompted correctly, LLMs demonstrated the ability to mimic user personae with specific demographic and psychological traits [68, 17, 71], occupation [49, 51], political leanings [64, 51, 52], and, in general, human behavior [5], making them valuable tools for studying their potential behavior when interacting in complex simulated societies [49, 54, 2]. As these models become increasingly widespread across var- ious applications, comprehending their collective behavior becomes essential. A key question is whether LLMs can spontaneously exhibit human-like social behaviors as emergent proper- ties [44] arising from their training processes, rather than through explicit behavioral programming. For instance, LLMs have demonstrated the ability to exhibit simulated Theory of Mind [53], which might enable subjective behav- ioral modeling and the comprehension of ambiguous natural language instructions [69]. There has been considerable debate, with studies offering contradictory evidence [35, 57, โ Corresponding author: A. Failla erica.cau@phd.unipi.it (E. Cau); andrea.failla@phd.unipi.it (A. Failla); giulio.rossetti@isti.cnr.it (G. Rossetti) andreafailla.github.io (A. Failla); giuliorossetti.net (G. Rossetti) ORCID(s): 0009-0005-7267-9870 (E. Cau); 0009-0009-6162-0274 (A. Failla); 0000-0003-3373-1240 (G. Rossetti) 63, 62, 67, 33]. However, even a simulated Theory of Mind could help LLMs interact more naturally with other agents. Such collective behaviors, while useful for better un- derstanding LLMs and human behavior, may introduce previously unknown biases into decision-making processes or exacerbate societal biases embedded in training data, with potentially unknown effects on human-LLM interactions [2]. While much of the literature has focused on defining unstruc- tured agent interactions, such as discussions on controversial topics like climate change [64, 6] or genetically modified food [71], less attention has been given to investigating more structured populations of agents. When we interact with others, we form social ties that can be modelled as edges in a graph, with individuals acting as nodes. Human societies are grounded in unwritten social rules, such as homophily, exemplified by the saying birds of a feather flock together [37]. People tend to gravitate toward those perceived as similar, thereby strengthening their connections with them, while avoiding those perceived as too different. This behavior has various consequences: it might amplify social divisions, strengthen boundaries between groups, and eventually lead to the segregation of populations into homogeneous clusters. Why are these matters important? There are at least two reasons why these questions need to be addressed. By observing how LLM agents respond to topological factors such as homophily and class imbalance, it is possible to char- acterize the latent predispositions that emerge from their col- lective behavior. Understanding these dynamics is essential if we are to interpret their outputs reliably, especially in high- stakes or decision-critical contexts. Second, since LLMs are increasingly employed in agent-based simulations of human social systems [54, 73, 24], it is crucial to evaluate the extent to which their interactions accurately reflect real human behavior. Many recent works position LLMs as proxies for human behavior [23], especially in fields where language is pivotal, such as psychology. However, such usage assumes a Erica Cau et al.: Preprint submitted to ElsevierPage 1 of 13 arXiv:2604.11312v1 [cs.SI] 13 Apr 2026 Network Effects and Agreement Drift degree of behavioral realism that may not hold under closer scrutiny [55]. If LLM populations diverge systematically from known patterns in human opinion formation โ e.g., by converging too quickly, suppressing disagreement, or exhibiting exaggerated sensitivity to class size โ this raises questions about their validity as tools for modeling human collective behavior. Thus, understanding when and how LLMs approximate or deviate from human-like dynamics is critical for both methodological validity and ethical use. Our contribution. This study aims to bridge the gaps outlined above by examining how the degree of homophily and relative class sizes within the interaction network af- fect opinion evolution in LLM societies. Previous work has investigated the homophilic mechanism in networks generated by LLM agents, focusing particularly on how the attributes of LLM agents (e.g., gender, age, or political leaning) influence link formation, leading to assortative structures and clustered communities [38]. In contrast, we model populations of LLMs as agents within a preferential attachment framework augmented with homophilic edge formation [31]. This allows us to manipulate not only traditional network parameters (e.g., degree distribution) but also the social alignment of nodes (via homophily) and the distribution of opinions (via class size imbalance). We simulate debates among agents on a given initial statement and trace how opinions evolve over time. Our investigation is structured around the following research questions: RQ1. How does homophily influence opinion dynamics in balanced LLM agent populations? In this experiment, the agent population is evenly divided (50-50) between two opinion classes. We vary the homophily parameter while keeping all other factors constant, particularly class size, to isolate and observe the impact of homophilic attachment on the trajectory and convergence of opinion evolution. RQ2. How does the effect of homophily on LLM opinion dynamics change under increasingly imbalanced class dis- tributions? Building on RQ1, we investigate how skewing the initial class size distribution (i.e., from 70-30 to 90- 10) affects the role of homophily in opinion dynamics. This allows us to examine whether the presence of a minority affects the extent to which homophily influences consensus formation and opinion stability. RQ3. How do the initial stances of minority and majority groups influence opinion dynamics? We compare scenarios in which (i) the majority agrees with the initial statement while the minority disagrees, and (i) the minority agrees with the initial statement while the majority disagrees. Given the LLMsโ tendency toward agreement [58, 9], this question probes whether aligning with the majority on a particular stance amplifies or mitigates its influence on final opinion distributions. RQ4. How does knowledge of neighborsโ opinion distribu- tion affect opinion dynamics? We explore scenarios in which agents have information about their neighborsโ opinion distributions and assess the impact of this knowledge on opinion evolution. Coherently with previous research, we find that LLM pop- ulations exhibit a systematic directional bias in persuasive interactions: when agents holding opposing views interact, movement toward endorsing the discussion statement is more likely than movement toward rejecting it, even in bal- anced populations. At the collective level, its effect depends on exposure: heterogeneous networks allow this bias to prop- agate and produce rapid convergence, whereas homophily and large disagreeing majorities limit cross-opinion encoun- ters and lead to persistent polarization. Providing agents with information about their local neighborhood further reshapes the dynamics by favouring moderate agreement and making opinion change contingent on local alignment. The remainder of this work is organized as follows. In Section 2, we provide an overview of the literature regard- ing opinion dynamics and LLM agents. In Section 3, we introduce the framework for LLM oinion dynamics, and in Section 4, we introduce the experimental setup and results. Finally, in Section 5, we conclude the work by discussing the results and suggesting future research directions. 2. Related Work In this section, we discuss relevant literature on Opinion Dynamics and Large Language Model-augmented social simulations. Opinion Dynamic Models Opinion dynamics (OD) de- scribes computational processes that mimic how individual views evolve over time under empirically observed social in- fluences [7, 59]. In a typical OD simulation, a network of in- teracting agentsโthe populationโholds opinions encoded as real numbers. Empirically grounded social mechanisms are cast as update rules, drawing on techniques from statisti- cal physics, such as graph theory, probability, and statistical modeling. For example, an agent may revise its stance by randomly copying a neighborโs opinion [29] (modeling imi- tation), by averaging the views in its local neighborhood [21] (capturing homophily [37]), or by adopting the most frequent opinion around it [34] (reflecting peer pressure and mutual awareness [16]). OD research asks whether the interplay of these mechanisms drives the system toward one of three mutually exclusive collective states: (i) consensus, when all agents share the same view; (i) polarization, when opinions cluster around two opposing poles; or (i) fragmentation, when more than two distinct clusters form [45, 60]. OD models are also classified by how they encode the opinion variable. In discrete models, opinions can take only a finite set of values, with rules specifying switches among them. The classic Voter Model [15], for instance, considers populations in which agents adopt one of two opposing Erica Cau et al.: Preprint submitted to ElsevierPage 2 of 13 Network Effects and Agreement Drift Figure 1: Graphical schema of the LLM-OD framework. The LLM agents population is initialized as nodes in a network; each agent is an LLM instance with an initial opinion in the range [0, 6] (a). At each iteration, two neighbor agents are chosen and prompted to act as Opponent and Discussant (b). The Discussant is prompted to listen to the opinion of the Opponent around the discussion statement and may then accept, reject, or ignore such opinion (c) and update their current one accordingly byยฑ1 (d). stances (e.g., agree/disagree). By contrast, continuous mod- els treat opinions as points on an uninterrupted spectrum. Canonical examples, such as the DeGroot Model [22], allow any value within a bounded interval โ commonly [-1, 1] โ and interactions move opinions smoothly along that contin- uum. Large Language Models Recent studies have examined the dynamics that arise from interactions among large lan- guage models (LLMs). These LLM agents typically exhibit realistic behavior both individually and collectively [49, 51], with human-like patterns naturally emerging from their in- teractions. Examples include the formation of scale-free net- works [19], dissemination of information [28], and the devel- opment of trust [70]. When supplied with demographic back- grounds and personality traits, LLMs can more accurately mimic human behavior [50, 49, 4], including reflecting hu- man biases and political inclinations [11]. Integrating LLMs with traditional agent-based modeling approaches [36], as demonstrated in [66], has shown how recommender systems can influence the quality of discourse. Specifically, agents exposed to popular content tend to exhibit increased toxicity and interparty engagement, mirroring the toxicity levels seen in U.S. Twitter discourse circa 2019. Further simulations reveal that confirmation bias among agents contributes to social fragmentation [12], aligning with established findings in opinion dynamics. LLMs are also capable of emulat- ing persuasive communication [6, 41], generating coherent arguments based on psycho-linguistic theories of opinion change, and can be utilized for comprehensive social media simulations [54]. Nonetheless, LLMs have a natural incli- nation toward factual correctness and often resist generating content that contradicts scientific knowledge unless explic- itly prompted [12]. This tendency may cause them to dis- regard assigned roles or personality traits [64], resulting in less authentic behavior. Additionally, LLM agents generally avoid intense conflict [13, 66] and display sensitivity toward various social and political issues [56, 27]. 3. LLM-powered Opinion Dynamics We present a general framework to describe how pop- ulations of large language model (LLM) agents develop and revise opinions through structured interactions [8]. The system is represented by the tuple: ํ = โจ๎ณ,๎ฟ,๎ป,ํ,ํ,๎ฐโฉ, where each element captures a specific component of the simulation: โข ๎ณ = โจํ ,ํธโฉ denotes the interaction network, where ํ is the set of LLM agents and ํธ โ ํ ร ํ is the set of undirected pairs of agents that can interact. The topology may be fully connected (i.e., mean-field) or follow an empirical or synthetic configuration. โข ๎ฟ is the discussion prompt or proposition that defines the initial subject of deliberation. It establishes the se- mantic dimension along which opinions are assessed. โข ๎ป represents the space of admissible opinions. This space can be discrete (e.g., ๎ป = 0,1) or continuous (e.g., ๎ป = [0,1]), encoding positions from complete disagreement to full agreement with the statement ๎ฟ. โข ํ โถ ๎ป ํ รโ ํ โ ๎ป is the opinion update function. It specifies how an agent revises its opinion as a function of its current position, the opinions of ํ neighboring agents, and additional features or external variables in โ ํ . โข ํ is the temporal domain of the simulation, defined as an ordered sequence of discrete time steps ํก โโค + . Erica Cau et al.: Preprint submitted to ElsevierPage 3 of 13 Network Effects and Agreement Drift โข ๎ฐ(ํก) = ํ ํ (ํก) โฃ ํ โ ํ denotes the opinion state at time ํก, where ํ ํ (ํก) โ ๎ป is the opinion of agent ํ at that time. This framework supports a wide variety of network topologies, interaction mechanisms, and opinion evolution rules. In what follows, we describe a particular instantiation of the model adopted in our experimental setting. A general overview of its rationale is provided in Al- gorithm 1. In detail, we define the graph topology, the Algorithm 1 LLM Opinion Dynamics Require: Graph: ๎ณ, Statement: ๎ฟ, Initial opinions: ๎ฐ(0) = ํ ํ (0) โฃ ํ โ ํ , Time steps: ํ max , Ensure: Opinion Distribution Evolution ๎ฐ ํํ 1: Init ๎ฐ ํํ as an empty list 2: ๎ฐ ํํ .append(๎ฐ(0)) 3: for ํก = 0 to ํ max โ 1 do 4: for each agent ํ โ ํ do 5:Select random neighbor ํฃ ํ โ ํํํํโํํํํ (ํ) 6:ฮํ ํ (ํก) = ํํํํํกํ(ํ ํ (ํก),ํ ํ (ํก),๎ฟ) 7:Update opinion: ํ ํ (ํก + 1) = ํ ํ (ํก) + ฮํ ํ (ํก) 8: end for 9: Update opinion distribution: ๎ฐ(ํก + 1) = ํ ํ (ํก + 1) โฃ ํ โ ํ 10: ๎ฐ ํํ .append(๎ฐ(ํก + 1)) 11: end for 12: return ๎ฐ ํํ initial statement, the opinion distribution, and the number of iterations. Each agent is initialized with a discrete opinion on a 7-point Likert scale, such that 0 corresponds with strong disagreement with ํ, 3 corresponds with neutrality, and 6 denotes strong agreement. At each time step, for each agent ํ โ ํ , a neighbor ํ is randomly selected to engage in a debate on ๎ฟ. As a result of the debate, ํโs opinion is either (i) brought closer to ํโs if they agree, (i) brought farther from ํโs if they disagree, or (i) not modified if ํโs arguments are ignored. Opinion updates are stored at each iteration and returned at the end. The debate unfolds according to Algorithm 2. The selected agents are first assigned one of two mutually exclusive roles, namely discussant (agent i) or opponent (agent j). The dis- cussant is the agent who starts the conversation. It does so by expressing and justifying its opinion on ํ. The discussant is the only agent allowed to change its opinion (after engaging with the opponent). The opponent is tasked with producing a persuasive argument to convince the discussant. It is a stubborn agent, i.e., it is not allowed to change opinion. The debate proceeds in rounds, where each round consists of one interaction from each agent. The total number of rounds is capped by a maximum limit, max_rounds, to ensure the debate does not continue indefinitely. Initially, the Discussant is prompted to express its opinion on ๎ฟ. During each round, the Opponent first evaluates the Discussantโs message and then decides whether to ACCEPT, REJECT, or IGNORE the Discussantโs viewpoint. If the Opponent chooses to IGNORE or ACCEPT, the debate concludes. Otherwise, the Discussant evaluates the Opponentโs argument, and the debate continues. The final opinion shift of the Discussant, ํ ฮ+ ํ , is determined based on its final choice. If the Discussant ACCEPTs, its opinion is brought closer to the Opponentโs, and if it REJECTs, it is Algorithm 2 Debate Require: Initial opinions: ํ ํ , ํ ํ , Statement: ๎ฟ, Maximum number of interaction rounds: max_rounds Ensure: Final opinion delta of the Discussant: ํ ฮ+ ํ 1: Init Discussantโs Opinion Delta ํ ฮ+ ํ โ 0 2: Discussant states its opinion ํ ํ on ๎ฟ 3: for round = 1 to max_rounds = 3 do 4: Opponentโs Turn: 5: Opponent evaluates Discussantโs argument 6: Opponent decides and justifies: ACCEPT, REJECT, IGNORE 7: if decision is IGNORE or ACCEPT then 8:break 9: end if 10: Discussantโs Turn: 11: Discussant evaluates Opponentโs argument 12: Discussant decides and justifies: ACCEPT, REJECT, IGNORE 13: if decision is ACCEPT then 14:ํ ฮ+ ํ โ 1 if ํ ํ > ํ ํ else -1 15:break 16: else if decision is REJECT then 17:ํ ฮ+ ํ โ -1 if ํ ํ > ํ ํ else 1 18:break 19: end if 20: end for 21: return ํ ฮ+ ํ brought further (e.g., backfire effect [46]). If the Discussant does neither, or if the debate terminates earlier, their opinion remains unchanged. 4. Results We conduct a series of simulations within the LLM-based opinion dynamics framework introduced in Section 3. We generate scale-free networks of 100 agents in which nodes belong to two mutually exclusive classes, with tunable class sizes and assortativity [31]. For further information on the network generation process, please refer to Appendix A. The discussion prompt is based on the paradox of Theseusโ Ship, first reported in Plutarchโs Parallel Lives [25], which questions whether an object that has had all its components replaced retains its identity. The statement is deliberately non-empirical to avoid convergence driven by factual cor- rectness and to preserve argumentative diversity [12, 9]. Un- less otherwise stated, results are obtained with Llama 3.1 [1], and the neighborhood-pressure condition is additionally replicated with Gemma3 [65]. For each parameter con- figuration we run a single simulation on a fixed network realization in order to isolate the structural effect of the experimental parameters and to avoid compounding sources of stochasticity. Experimental design. We begin with a symmetric con- figuration in which the two opinion groups are equally represented, providing a baseline to evaluate how homophily (โ โ [0,0.25,0.5,0.75,1]) affects opinion diffusion in the absence of numerical advantage (RQ1). We then introduce asymmetric populations in which one group constitutes 30% and 10% of the agents to assess the impact of minority size on global dynamics (RQ2). Each imbalance condition is repeated in a reverse configuration, where the initial majority and minority positions are swapped, to test whether the out- comes depend on the opinion side rather than on group size alone (RQ3). Finally, we provide agents with information Erica Cau et al.: Preprint submitted to ElsevierPage 4 of 13 Network Effects and Agreement Drift about the opinion distribution in their ego network during the interaction to evaluate the effect of local social pressure on opinion change (RQ4). We first examine the temporal evolution and final distribu- tion of opinions across all scenarios, thereby identifying the macro-level effects of homophily and group composition. We then focus on the neighborhood-pressure condition and estimate opinion transition probability matrices to uncover the micro-level mechanisms driving the observed patterns. These probabilities quantify the likelihood that a Discussant moves toward the Opponentโs position under different initial configurations and neighborhood states. To assess whether the observed transition probabilities differ from what would be expected by chance, we employ a permutation-based null model. Specifically, we randomly reshuffle the post- interaction opinions among interaction events while keeping fixed (i) the pre-interaction opinions of both agents and (i) the neighborhood composition. This procedure preserves the marginal distributions and the interaction structure but removes any systematic association between interaction context and opinion change. For each entry of the transition matrix, we generate a null distribution from 1000 permuta- tions and retain only those probabilities that are significantly different from the null expectation (ํ < 0.01). Details on the estimation and validation procedure are reported in Appendix B. 4.1. Effect of homophily and group size imbalance Opinion trajectories for all configurations are shown in Figures 2 and 3. We first discuss the symmetric population (RQ1), then introduce class imbalance (RQ2), and finally analyze the reverse configurations (RQ3). Balanced Scenario (RQ1). With equal group sizes, all networks with 0 โค โ โค 0.75 rapidly converge toward the positive side of the opinion scale, typically within 20โ40 iterations (Figure 2a). Lower homophily accelerates con- vergence, with heterophilic networks reaching agreement almost immediately. As โ increases, convergence becomes slower, but the final outcome remains unchanged. A qualita- tively different regime emerges at complete homophily (โ = 1), where interactions occur almost exclusively within like- minded groups, and the system stabilizes in a segregated, polarized state. Imbalanced Scenario (RQ2). Introducing a minority strength- ens the convergence toward agreement. With a 70โ30 split, the system reaches consensus in about 20-30 iterations across all homophily levels, with only minor fluctuations between agree and strongly agree (Figure 2b). Similarly to the balanced scenario, high homophily (โ = 0.75) slows convergence speed; nonetheless, the agents reach perfect adherence to the strongly agree opinion. Reducing the minority to 10% further accelerates its disappearance, especially for 0 โค โ โค 0.25, while higher homophily temporarily preserves small opposing clusters before con- vergence (Figure 2c). At โ = 1, segregation persists because cross-group interactions are rare. Reversed Imbalanced Scenario (RQ3). Interestingly, when moving to the reverse class distribution scenario, where the minority now holds the strongly agree opinion, trends show a clear pattern that diverges from simple symmetry (Figure 3). With ํํํ = 0.3, disagreeing agents form a dominant cluster, with small neutral and agreeing clusters surviving for several iterations. Although the latter gradually decreases in size after 40 iterations, the dominant opinion does not reach full consensus. This pattern persists for 0.25 โค โ โค 0.75, indicating that negative majorities are more resistant to complete convergence. Strengthening the imbalance at ํํํ = 0.1 heightens the dominance of strongly disagreeing opinion clusters across all homophily levels, with only small residual agreeing clusters. Only in the case of โ = 1, agents behave almost symmetrically to what was previously observed in the base imbalanced scenario, which we attribute to strong structural constraints. 4.2. Effect of neighborhood awareness Providing agents with the distribution of opinions in their ego network results in systematically faster opinion change and shifts the dynamics toward moderate agreement (Figure 4a). In the balanced population, convergence is al- most immediate but typically stops at agree, also preventing the full convergence observed without neighborhood infor- mation. Under complete homophily (โ = 1), agents ini- tially maintain separation between the two extreme clusters; then, an additional cluster with the agree opinion emerges. With moderate class imbalance, neighborhood awareness eliminates the rapid dominance of extreme positive opinions observed in the base scenario and allows small neutral and mildly positive clusters to persist across homophily levels (Figure 4b). Under extreme class imbalance, the majority of opinions stabilize on agree, followed by a few strongly agree and minimal other clusters (Figure 4c). Interestingly, the polarized outcome between extreme stances observed so far atโ = 1 does not hold in this scenario; here, we note an agree majority followed by small mildly agree and neutral clusters. In other words, unlike other high-homophily settings, the minority slowly moves toward the majorityโs opinion under extreme class imbalance and known neighborhood config- uration. In the reverse configurations, where the minority initially holds the positive stance (Figures 5a and 5b), the dynamics become asymmetric. For ํํํ = 0.3, negatively oriented majorities progressively shift toward moderate and positive positions, indicating that access to neighborhood opinion distributions mitigates the dominance of negative opinions; a stable negative cluster persists only under com- plete homophily (โ = 1), where interactions remain within groups. In the extreme imbalance (ํํํ = 0.1), however, the negative majority instead consolidates and converges, a process reinforced by homophily, while the small positive Erica Cau et al.: Preprint submitted to ElsevierPage 5 of 13 Network Effects and Agreement Drift (a) ํํํ=0.5 (b) ํํํ=0.3 (c) ํํํ=0.1 Figure 2: Opinion trends for the base scenario (strongly-agreeing majority) across different homophily levels for minority fraction min=0.5 (a), min = 0.3 (b) and min = 0.1 (c) Each panel shows the proportion of agents holding different opinion states over 100 iterations. All points of the opinion scale are mapped to the colors in the legend, from Strongly Disagree (dark red) to Strongly Agree (dark green). minority survives only in fully homophilic networks without changing its stance. 4.2.1. Model Comparison The Gemma-based simulations reveal a systematically stronger drift toward positive opinions than observed with Llama. In balanced populations, negatively oriented agents disappear rapidly for all 0 โค โ โค 0.75, and the system con- verges either to strongly agree or to a polarized configuration dominated by a large positive cluster (Figure 6). Even under complete homophily, where Llama agents remain segregated at the two extremes, Gemma agents predominantly reinforce the positive side, indicating a higher intrinsic propensity to accept upward shifts. This tendency is further amplified in imbalanced settings: when the positive class is the majority, intermediate opinions vanish quickly, and convergence to- ward the positive extreme is faster and more stable than in the corresponding Llama runs. The asymmetry persists in the reverse configurations, where negative agents form the numerical majority. Although neg- ative clusters initially survive for several iterations, upward transitions remain frequent and the dynamics eventually lead to either strong polarization or to the re-emergence of a dominant positive cluster. This behavior suggests that Gemma agents are less sensitive to structural constraints and more responsive to persuasive interactions that point toward agreement. At the micro level, this is reflected in transition probabilities close to 1 for low-to-high shifts and in the high stability of high-opinion states, confirming a stronger and more persistent bias toward positive opinions compared with Llama. 4.2.2. Neighborhood Awareness and Interaction Dynamics To connect the aggregate opinion trajectories with the underlying interaction dynamics, we analyze conditional transition probability matrices for balanced populations (ํํํ = 0.5). Across all homophily levels and model variants, upward transitions (lowโ high) are consistently more likely than downward ones (highโ low), indicating that persuasion is structurally asymmetric and biased toward positive opinions (Figure 7). This asymmetry, which we will refer to as agreement drift, persists even when group Erica Cau et al.: Preprint submitted to ElsevierPage 6 of 13 Network Effects and Agreement Drift (a) ํํํ=0.3 (b) ํํํ=0.1 Figure 3: Opinion trends for the reversed scenario (strongly-disagreeing majority) across different homophily levels for minority fraction min=0.5 (a), min = 0.3 (b), and min = 0.1 (c) Each panel shows the proportion of agents holding different opinion states over 100 iterations with different levels of homophily. All points of the opinion scale are mapped to the colors in the legend, from Strongly Disagree (dark red) to Strongly Agree (dark green). sizes are equal, showing that it is not a consequence of numerical dominance, but likely an intrinsic feature of the LLM interaction dynamics. Increasing homophily reduces the frequency of cross-opinion encounters and leads to structural segregation, yet the imbalance between upward and downward shifts remains visible whenever interactions between opposite opinions occur. Providing agents with knowledge of their neighborsโ opinion distributions (Figure 7, mid row) produces distinc- tive behavior: agents seem to change their opinion when facing a higher-opinion opponent, but become more resistant to changing their opinion when facing a lower-opinion oppo- nent. The most interesting scenario is โ = 1, as discussants holding a low opinion prefer high-opinion opponents (83%), while the reverse transition occurs (100%), indicating that persuasion remains active despite structural segregation. Maintaining a high opinion, however, seems difficult for high-opinion agents, as their likelihood of retaining it is relatively low (30%), especially compared with the base scenario. The effect is even stronger for Gemma agents (Fig- ure 7, bottom row), for which upward transitions approach probability 1 and high-opinion states become highly stable. To further assess the impact of agentsโ knowledge of their neighborsโ opinion distribution, we quantify the like- lihood of the deviation of the discussantsโ final opinions in relation to their neighbors in the opinion-distribution-aware setting. These matrices were created for both Llama (Figure 8) and Gemma simulations (Figure 9). For Llama agents, opposing neighborhoods strongly stabilize high-opinion discussants, whose probability of maintaining their position remains close to one across all โ. At the same time, upward shifts from low to high emerge even when the local environment discourages them, becoming deterministic for โ = 0.75. Mixed neighborhoods display the most symmetric dynamics, with statistically significant transitions in both directions for โ โค 0.75, For โ โค 0.75, transitions from high to low become more signif- icant, allowing a downward movement from high to low. In supporting neighborhoods, opinion change largely follows the local consensus: shifts aligned with the neighborhood are reinforced, while the persistence of low-opinion states in low-to-low interactions remains rare. Overall, peer pressure acts as a selective amplifier [42], strengthening changes that are locally consistent, while still allowing occasional counter-aligned upward moves. Gemma exhibits a qualitatively different regime. Most cross- class shift probabilities are not significant, especially when the direction of the shift is supported or opposed by neigh- boring agents. The most noticeable patterns appear in the first (opposing) and third (supporting) rows of the matri- ces in Figure 9. In opposing neighborhoods, statistically significant shifts in probability occur from low to high opinions, indicating that Gemma agents can adjust upward even when surrounded by opposing agents. Conversely, with supporting agents and in all homophily configurations, discussants move from high to low. Agents in this case are susceptible to neighborhood alignment and change their opinion when their peers reinforce this transition. Addi- tionally, with high homophily values (0.75 โค โ โค 1), only shifts probabilities consistent with each agentโs ego network are allowed. According to this dynamic, opinion change is allowed only when contextual reinforcement is sufficiently strong. Therefore, Gemma exhibits a different Erica Cau et al.: Preprint submitted to ElsevierPage 7 of 13 Network Effects and Agreement Drift (a) ํํํ=0.5 (b) ํํํ=0.3 (c) ํํํ=0.1 Figure 4: Opinion trends for the base scenario (strongly-agreeing majority) under neighborhood opinion awareness across different homophily levels for minority fraction min=0.5 (a), min = 0.3 (b), and min = 0.1 (c) Each panel shows the proportion of agents holding different opinion states over 100 iterations. All points of the opinion scale are mapped to the colors in the legend, from Strongly Disagree (dark red) to Strongly Agree (dark green). behavior to Llama, with rare opinion shifts in which agents are subjected to peer pressure from the neighborhood during class changes. The bias toward acceptance is more evident in Gemma, where low-to-high transitions are allowed even in the presence of an opposing neighborhood. In the mixed scenario, Gemmaโs agents exhibit more varied behavior, as they are not exposed to a single dominant opinion. The matrices show interaction probabilities that are statistically significant across all homophily levels, with a preference for agents to accept high-to-high opinion shifts. 5. Discussion This work investigates how network structure, class imbalance, and local social information shape opinion dy- namics in populations of LLM agents, and to what extent the resulting collective behavior resembles mechanisms known from human social systems. This study identifies two main results that jointly explain the collective behavior of LLM- based opinion dynamics. First, we observe a systematic bias we term agreement drift: in pairwise interactions, agents are more likely to shift from lower to higher positions on the opinion scale than in the opposite direction. Across homophily levels, class distribu- tions, and model variants, upward transitions occur more frequently than downward ones whenever agents holding opposing views interact. A similar effect was reported in previous work [9, 39]; here we show that it generalizes across different models and heterogeneous network configurations. We find that this asymmetry is present even in balanced populations, indicating that it is not dependent on numerical dominance and cannot be reduced to a majority effect. At the same time, it does not automatically produce convergence toward agreement at the collective level: when cross-opinion encounters are limited (either because the disagreeing group forms a large majority or because homophily segregates the network) the directional tendency remains locally ob- servable but cannot spread through the system. Collective outcomes, therefore, emerge from the interaction between an intrinsic persuasive bias and the opportunity structure for exposure created by the network. Importantly, the agreement drift effect is distinct from the Erica Cau et al.: Preprint submitted to ElsevierPage 8 of 13 Network Effects and Agreement Drift (a) ํํํ=0.3 (b) ํํํ=0.1 Figure 5: Opinion trends for the reversed scenario (strongly-disagreeing majority) under neighborhood awareness across different homophily levels for minority fraction min=0.5 (a), min = 0.3 (b), and min = 0.1 (c) Each panel shows the proportion of agents holding different opinion states over 100 iterations. All points of the opinion scale are mapped to the colors in the legend, from Strongly Disagree (dark red) to Strongly Agree (dark green). sycophantic behavior documented in prior work [10, 64, 26, 32]. Sycophancy is the tendency of an LLM to align with a userโs explicitly stated belief (regardless of truth or epistemic consistency) in order to maximise perceived helpfulness/social approval. Agreement drift, by contrast, is a directional susceptibility in which positions expressing endorsement of the discussion statement exert systemat- ically greater persuasive pull than positions expressing rejection. In other words, when agents holding opposing views interact, movement toward the pro-position is more likely than toward the contra-position, regardless of who initially holds the majority, and without any external reward for compliance. The second main result concerns the role of structural and contextual constraints in modulating this intrinsic ten- dency. Homophily regulates the reach of the directional bias by controlling the frequency of cross-opinion encounters. At low and moderate levels of homophily, heterogeneous exposure enables the asymmetric persuasive mechanism to propagate through the population, leading to rapid conver- gence toward agreement even in the absence of a numerical advantage. At high homophily, by contrast, the same bias becomes trapped within segregated clusters, leading the sys- tem to stabilize in polarized configurations. Class imbalance acts as an additional gatekeeper: large disagreeing majorities can prevent the diffusion of agreement drift by reducing the probability of encounters with pro-position agents, while small minorities disappear quickly when exposure is high. Providing agents with information about their local neigh- borhood introduces a further layer of mediation. Rather than simply accelerating convergence, neighborhood awareness reshapes the outcome by favouring moderate agreement and by making opinion change contingent on local alignment, thereby revealing a mechanism analogous to peer-pressure effects in classical opinion-dynamics models. Implications. Our findings have direct methodological im- plications for the use of LLM agents as proxies for human behavior in computational social science. In many empir- ical and theoretical models of human opinion dynamics, persuasive influence is assumed to be directionally neutral and collective outcomes are primarily attributed to network topology, initial conditions, and exposure patterns [60, 61, 48, 42]. In the LLM populations studied here, by contrast, the micro-level persuasive interaction is intrinsically asym- metric due to agreement drift. This shows that convergence in LLM-based social simulations cannot be interpreted as evidence of consensus dynamics without first characterising the modelโs intrinsic persuasion tendency. This means that simulations employing LLM agents may systematically overestimate the emergence of consensus whenever cross- opinion encounters are sufficiently frequent, and conversely, attribute persistent disagreement to segregation even when a directional persuasive tendency is present at the interaction level. For the growing literature that treats LLM populations as behavioral surrogates for human groups, this result high- lights the need to disentangle structural effects from model- intrinsic interaction biases before drawing substantive con- clusions about social processes. Limitations and Future Directions. Several limitations should be acknowledged. First, the results are obtained for a specific interaction protocol and a single non-factual Erica Cau et al.: Preprint submitted to ElsevierPage 9 of 13 Network Effects and Agreement Drift discussion topic; although the agreement drift is likely not a consequence of our interaction procedure because it emerges even under different configurations [9, 39], different prompting strategies or semantically grounded statements may alter its strength. Second, we consider networks of fixed size and a specific generative model; larger pop- ulations and/or alternative topologies may introduce ad- ditional mesoscopic effects. Third, the strong differences observed between LLM families call for a systematic anal- ysis across models. Addressing these aspects is essential to determine which behavioral patterns are model-specific and which represent general properties of LLM societies. Future work should therefore investigate how heterogeneous agent profiles, memory, and repeated interactions affect the persistence of minority opinions, and calibrate LLM- based dynamics against empirical human data to assess their behavioral realism. Understanding how intrinsic agreement biases interact with algorithmic mediation and recommender systems is also crucial for evaluating the risk of artificial consensus formation in humanโAI hybrid environments. A. Networks with Controlled Homophily and Group Size To address our research questions, we need to generate networks with controlled group sizes (i.e., node attribute fre- quencies) and mixing biases (i.e., nodesโ preferences for con- necting with similar/dissimilar peers). To do so, we leverage the BA-homophily model introduced in [31], which extends the classical BarabรกsiโAlbert (BA) preferential attachment model [31] by incorporating a homophily parameter. The classic BA model [3] is a foundational generative model for scale-free networks. It captures two key mechanisms un- derlying many real-world complex systems: network growth and preferential attachment. The model starts with a small connected network of ํ 0 nodes. At each time step, a new node is added to the network and forms ํ โค ํ 0 links to existing nodes. The probability ฮ ํ that the new node connects to an existing node ํ is proportional to the degree ํ ํ of that node: ฮ ํ = ํ ํ โ ํ ํ ํ This rule encodes preferential attachment, where well- connected nodes are more likely to attract additional links, a โrich-get-richerโ dynamic. Over time, this process generates networks with a power-law degree distribution, ํ(ํ) โ ํ โํพ , with ํพ โ 3. The BA-homophily enriches this framework in two ways. First, each node belongs to one of two groups,ํ (minority) or ํ (majority), with group sizes defined by relative proportions ํ ํ and ํ ํ = 1 โ ํ ํ , where ํ ํ โค ํ ํ . Second, when a new node ํ arrives, it selects ํ existing nodes to connect to, choosing targets based on both their degree and group similarity. Formally, the probabilityฮ ํํ that nodeํ connects to node ํ is given by: ฮ ํํ = โ ํํ โ ํ ํ โ ํ โ ํํ โ ํ ํ , where ํ ํ is the degree of node ํ and โ ํํ encodes ho- mophilic preference. In the symmetric case where node groups show equal homophilic preferences, we have that โ ํ = โ ํ = โ, โ ํํ = โ ํํ = 1 โ โ Via this mechanism, the model can generate networks with complete heterophily (nodes only connect to the opposite group,โ = 0), neutral mixing (no group preference, classical BA, โ = 0.5), up to complete homophily (nodes only connect within their group, โ = 1). As shown in [31], in heterophilic networks (โ < 0.5), minority nodes become structural hubs, attracting a disproportionate number of links from the majority. Conversely, in homophilic settings (โ > 0.5), they become increasingly segregated. B. Opinion Transition Probabilities and Validation To uncover the mechanisms underlying the observed opinion dynamics, we analyze micro-level interaction pat- terns between Discussant and Opponent agents. Specifically, we construct transition probability matrices that quantify the likelihood that a Discussant shifts its opinion toward that of the Opponent following an interaction, conditional on the Discussantโs and Opponentโs initial opinion class. Formally, we estimate: ํ ( ํํํ ํโ ํํ โฃ ํ ํํํ ํ ,ํ ํํ ) , where ํํํ ํโ ํํ denotes a change in the Discussantโs opinion toward the Opponentโs position, ํ ํํํ ํ is the Discus- santโs initial opinion, and ํ ํํ is the Opponentโs opinion. By doing so, we aim to estimate the rate of successful (as in persuasive) interactions. For the simulations in which agents are equipped with information on their neighborsโ opinion distribution, we additionally condition this probability on the Discussantโs local neighborhood configuration, distinguishing whether its neighbors are aligned, misaligned, or mixed, with respect to the direction of change. This extension isolates the effect of peer agreement on opinion shifts. Formally: ํ ( ํํํ ํโ ํํ โฃ ํ ํํํ ํ ,ํ ํํ ,ํ ) , where ํ โ aligned, misaligned, mixed denotes the con- figuration of the Discussantโs neighborhood relative to the direction of the potential opinion shift, that is, whether the majority of the Discussantโs neighbors hold opinions that are closer to the Opponentโs position (aligned), closer to the Discussantโs initial position (misaligned), or are evenly split between the two (mixed). Erica Cau et al.: Preprint submitted to ElsevierPage 10 of 13 Network Effects and Agreement Drift To identify statistically significant transitions, we adopt a permutation-based null model that tests whether the ob- served association between opinion pairs and the direction of change exceeds what would be expected by chance. For each interaction, we keep the pair (ํ ํํํ ํ ,ํ ํํ ) (resp. (ํ ํํํ ํ ,ํ ํํ ,ํ) for the extension) fixed and randomly shuffle the observed opinion variations across interactions. This procedure preserves the empirical distribution of opinion changes as well as the frequency of each opinion pair, while removing any systematic relationship between them. For ev- ery permutation, we recompute the transition probabilities, thereby obtaining a null distribution for each conditioning configuration. The statistical significance of the observed probability is then assessed using a two-tailed test, defined as the fraction of null values that are at least as extreme as the empirical estimate. CRediT authorship contribution statement Erica Cau: Conceptualization, Methodology, Investi- gation, Formal analysis, Visualization, Writing - Original Draft. Andrea Failla: Conceptualization, Methodology, Formal analysis, Validation, Visualization, Writing - Orig- inal Draft. Giulio Rossetti: Conceptualization, Methodol- ogy, Software, Writing - Review & Editing, Supervision, Funding acquisition. References [1] AI@Meta, 2024. Llama 3 model card. N.A. 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Erica Cau et al.: Preprint submitted to ElsevierPage 13 of 13 Network Effects and Agreement Drift (a) ํํํ=0.5 (b) ํํํ=0.3 (c) ํํํ=0.1 (d) Reverse with ํํํ=0.3 (e) Reverse with ํํํ=0.1 Figure 6: Opinion trends under neighborhood awareness across homophily levels. Panels (aโc) show the base scenario (strongly agreeing majority) for minority fractions ํ = 0.5, ํ = 0.3, and ํ = 0.1, respectively; panels (dโe) show the reversed scenario (strongly disagreeing majority) for ํ = 0.3 and ํ = 0.1. Each panel reports the proportion of agents in each opinion state over 100 iterations. colors map the 7-point scale from Strongly Disagree (dark red) to Strongly Agree (dark green). Erica Cau et al.: Preprint submitted to ElsevierPage 14 of 13 Network Effects and Agreement Drift Figure 7: Conditional probabilities of persuasion in pairwise interactions between LLM agents. Each matrix reports ํ ( ํํํ ํโ ํํ โฃ ํ ํํํ ํ ,ํ ํํ ) for balanced populations (min = 0.5), with the 7-point scale collapsed into low- and high-opinion macrostates. Rows correspond to the discussantโs initial opinion and columns to the opponentโs. Panels compare homophily levels (โ) and interaction settings (base vs. neighborhood-aware). Only statistically significant probabilities are shown. Figure 8: Facet plots of statistically significant opinion shifts for Llama agents under different neighborhood conditions. Each panel reports ํ ( ํํํ ํโ ํํ โฃ ํ ํํํ ํ ,ํ ํํ ,ํ ) , where ํ โ aligned, misaligned, mixed denotes the discussantโs local neighborhood configuration. Rows correspond to aligned, misaligned, and mixed neighborhoods, while columns vary the homophily level โ. Only statistically significant transitions are shown. Erica Cau et al.: Preprint submitted to ElsevierPage 15 of 13 Network Effects and Agreement Drift Figure 9: Facet plots of statistically significant opinion shifts for Llama agents under different neighborhood conditions. Each panel reports ํ ( ํํํ ํโ ํํ โฃ ํ ํํํ ํ ,ํ ํํ ,ํ ) , where ํ โ aligned, misaligned, mixed denotes the discussantโs local neighborhood configuration. Rows correspond to aligned, misaligned, and mixed neighborhoods, while columns vary the homophily level โ. Only statistically significant transitions are shown. Erica Cau et al.: Preprint submitted to ElsevierPage 16 of 13