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Polarization Dynamics under Algorithmic Recommendations in LLM-based Online Social Networks

Ali Safarpoor Dehkordi, Mohammad Shirzadi, Mehwish Nasim, Ahad N. Zehmakan

arXiv:2610.13351v1cs.SI

TL;DR

Real-platform data and numerical opinion models make it difficult to isolate recommendation effects while capturing natural-language interaction, and the ER-versus-CR comparison remains underexplored. This paper compares both mechanisms in a controlled LLM-based OSN simulation and finds higher polarization and extremization than without recommendations, with differences smaller when exposure counts are controlled.

  • Problem

    A controlled comparison of Edge Recommendation and Content-Exposure Recommendation using the same strategies to study opinion dynamics in LLM-based OSN simulations remains underexplored.

    Source: §2.4 · p. 3

  • Method

    The study compares edge-adding and post-exposure recommendation mechanisms in a controlled LLM-based OSN simulation.

    Source: §1 · p. 2, §6 · p. 12

  • Results

    Both mechanisms generally produce higher mean polarization and extremization than the no-recommendation baseline, while polarization differences shrink when exposure counts are controlled.

    Source: §6 · p. 12

  • Takeaways & Limitations

    The smaller differences under exposure-count control suggest that higher exposure volume under recommendation may partly explain the observed differences.

    Source: §6 · p. 12

    The simulation assumes recommended connections are accepted and recommended posts are viewed.

    Source: §6.1 · p. 12

Abstract

from arXiv · show

How do recommendation algorithms contribute to the formation of polarized opinions in online social networks? This question has been studied through empirical analyses of real platforms and mathematical models of opinion dynamics. Empirical studies capture user behavior but are often limited by noisy, incomplete, or inaccessible platform data, while mathematical models offer control and interpretability but usually rely on simplified opinion update rules. More recently, large language model (LLM)-based social simulations have provided an alternative for studying recommendation and opinion dynamics through natural-language interactions. However, how different ways of applying recommendations shape opinion dynamics remains underexplored. In this work, we provide a controlled comparison of two different recommendation mechanisms in an LLM-based online social network simulation. Edge Recommendation (ER) introduces new connections in the network, while Content-Exposure Recommendation (CR) exposes additional users to individual posts without modifying the underlying graph. Our framework represents users as LLM-based agents who interact in natural language while maintaining evolving opinion states. We measure polarization as opinion dispersion, extremization as the average distance of opinions from the neutral midpoint, and reinforcement as interactions that amplify already aligned opinions. Our results show higher mean polarization and extremization across recommendation conditions compared with the no-recommendation baseline, with absolute differences of up to $0.12$ in our main experiments.

1 Introduction

The paper asks how recommendation algorithms contribute to polarization, a question that is difficult to isolate in real platforms and simplified mathematical models. It compares two recommendation mechanisms in a controlled LLM-based social-network simulation and reports higher polarization, extremization, and reinforcement than without recommendations.

1 Introduction

  • Isolating recommendation effects is difficult because platform data can be costly or incomplete and user choices, design, and network structure are hard to control independently.Real-platform experiments can also raise costs and ethical concerns.Source: §1 · p. 2
  • Numerical opinion models offer control but often use predefined update rules that may miss how message content, tone, user traits, and network structure shape opinion change.The paper notes that such formulations may not capture differences between neutral and aggressive messages expressing the same stance.Source: §1 · p. 2
  • Edge Recommendation adds user connections, whereas Content-Exposure Recommendation expands who sees posts without changing the network structure.The comparison asks whether these mechanisms yield different dynamics when the recommendation strategy is held fixed.Source: §1 · p. 2
  • Both recommendation mechanisms produce generally higher mean polarization, extremization, and reinforcement than the no-recommendation baseline in a controlled LLM-based OSN simulation.The study tests these dynamics across different synthetic network structures.Source: §1 · p. 2

2 Related Work

Related work spans empirical studies, numerical opinion models, recommendation modeling, and LLM-based simulations. The paper positions its contribution as a controlled comparison of edge and content-exposure recommendation using the same strategies in LLM-based OSNs.

2 Related Work

  • Research on OSN polarization includes empirical studies, classical opinion dynamics, recommendation models, and LLM-based simulations.These approaches provide complementary ways to examine how polarization emerges.Source: §2 · p. 2

2.1 Empirical Studies

  • Empirical studies document real-world exposure and polarization patterns, but separating recommendation effects from user choices and network structure remains challenging.Exposure to opposing views can increase polarization in some settings.Source: §2.1 · p. 2

2.2 Numerical Opinion Dynamics Models

  • Numerical models such as Friedkin–Johnsen and bounded-confidence approaches use predefined rules and typically do not represent opinion formation through natural-language interactions [8].Extensions can include individual differences such as stubbornness [20] [21].Source: §2.2 · pp. 2–3

2.3 Modeling Recommendation Algorithms

  • Recommendation models have studied effects including user choices, content diversity, preference reinforcement, and separation between groups.Prior edge-recommendation work found that adding edges can reduce opinion conflict or the perception gap [24] [25].Source: §2.3 · p. 3

2.4 LLM-Based Simulations

  • LLM-based OSN simulations model text interactions, and prior work has added recommendation systems, evolving connections, or exposure controls [11] [12] [14] [30] [31].A controlled ER-versus-CR comparison using the same recommendation strategies to study opinion dynamics remains underexplored.Source: §2.4 · p. 3

3 Preliminaries

The preliminaries define the network, user attributes, outcome measures, and simulation process. The setup combines LLM-generated natural-language interactions with simulator-controlled activation, exposure, recommendations, and state updates.

3.1 Network and Opinion Notation

  • The OSN is an undirected graph whose nodes represent users and edges represent connections; each user has a dynamic opinion and static stubbornness and activeness traits.Stubbornness captures resistance to opinion change, while activeness represents the likelihood of initiating activities.Source: §3.1 · p. 3

3.2 Opinion Dynamics Measures

  • Polarization is opinion variance, extremization is average absolute opinion, and reinforcement counts interactions that keep the recipient aligned with the sender while making the recipient’s opinion more extreme.Polarization and extremization describe the network’s opinion state; reinforcement is measured at the interaction level.Source: §3.2 · p. 4

3.3 Simulation Model and LLM-Based Agents

  • At each step, an active user creates an LLM-generated post, recipients receive it, and the LLM returns updated stance descriptors that are mapped back to numerical opinions.Opinion and stubbornness values are represented to the LLM through qualitative descriptors; stubbornness affects resistance without prescribing the direction of change.Source: §3.3 · p. 4
  • ER modifies the graph before simulation, while CR dynamically adds recipients to individual posts; the interaction model excludes resharing, reply chains, and repeated engagement.This stateless design isolates recommendation effects from additional multi-step diffusion dynamics.Source: §3.3 · pp. 4–5

4 Recommendation Algorithms

The section separates recommendation strategy—how users are selected—from mechanism—how recommendations are applied. It compares two scoring strategies under edge additions and post-level exposure.

4 Recommendation Algorithms

  • The framework distinguishes which users are selected from whether recommendations add connections or expose posts, and evaluates both mechanisms under a fixed strategy.The four conditions pair Jaccard or APPR with ER or CR; no recommendation is the baseline.Source: §4 · p. 5, §4.1 · p. 5

4.2 Scoring Functions

  • Jaccard ranks users by overlap between their local neighborhoods, a symmetric similarity corresponding to shared-connection recommendations.The Jaccard score is unchanged when the two users’ order is reversed.Source: §4.2 · p. 5
  • APPR combines network structure with opinion similarity by weighting random-walk transitions according to opinion distance.Its source-dependent scores can be symmetrized for ER by taking the maximum of the two directional scores.Source: §4.2 · pp. 5–6

4.3 Recommendation Mechanisms

  • In the baseline, a post is delivered only to the activated user’s existing neighbors.Figure 1 contrasts this local delivery with recommendation-driven exposure and added edges.Source: §4.3 · p. 6, Figure 1 · p. 6
  • ER adds selected non-adjacent edges before the simulation and uses the resulting graph throughout; all recommended edges are assumed accepted.Jaccard ranks non-adjacent pairs globally, while APPR uses the maximum of the two directional scores.Source: §4.3 · p. 6
  • CR selects additional non-neighbors for each post at each time step, changing information flow without modifying the network structure.Eligible users are sampled without replacement in proportion to their Jaccard or APPR scores; APPR scores can evolve as opinions change.Source: §4.3 · p. 6

5 Experiments

The experiments examine whether LLM-based opinion updates respond to network structure, message tone, and user attributes in ways not represented by the numerical formulations considered. Across these tests, network connectivity, tone, stubbornness, opinion distance, and model identity relate to different update patterns.

5.1 Motivation: Limitations of Numerical Opinion Dynamics Models

  • The motivation is that numerical models use predefined rules and do not directly represent how network structure, message content, or linguistic framing shape updates.The experiments examine these dependencies without assuming LLM responses are completely realistic.Source: §5.1 · p. 7

5.1.1 Sensitivity to Network Structure

  • With cross-block connectivity fixed, changing within-community connectivity produces different polarization trajectories in the LLM simulation, unlike the considered numerical-model formulations.The comparison uses three fixed two-block SBM graphs and averages 10 independent GPT-4.1-mini runs over 100 time steps.Source: §5.1.1 · p. 7, Figure 2 · p. 7

5.1.2 Sensitivity to Tone and Message Content

  • Aggressive wording lowers the average update toward the sender from +0.23 to +0.06 and the share moving toward the sender from 53% to 27%.The pooled opinion-change difference is significant (two-sided Mann–Whitney U test, p < 0.05), although the expressed stance is unchanged.Source: §5.1.2 · pp. 7–8

5.1.3 Characterizing LLM Opinion Updates

  • Across DeepSeek, GPT-4o-mini, and GPT-4.1-mini, higher stubbornness reduces both the probability and average magnitude of opinion change.From lowest to highest stubbornness, change probabilities fall from 0.64 to 0.33, 0.78 to 0.51, and 0.72 to 0.37, respectively.Source: §5.1.3 · p. 8
  • Update probability rises with opinion distance to a peak at 0.4–0.6, then declines for highly opposed opinions.At maximum distance 2.0, change probabilities are 0.17 for DeepSeek, 0.24 for GPT-4o-mini, and 0.08 for GPT-4.1-mini.Source: §5.1.3 · p. 8
  • Mean signed updates differ by model: DeepSeek is negative, GPT-4.1-mini positive, and GPT-4o-mini has no detectable directional bias.The reported means are −0.029, +0.022, and −0.001, respectively.Source: §5.1.3 · p. 8
  • Recipients sometimes become more extreme even when movement toward the sender would not increase extremity, including after opposite-side messages.The reported opposite-side backfire-type response rates are 27% for DeepSeek, 40% for GPT-4o-mini, and 31% for GPT-4.1-mini.Source: §5.1.3 · p. 8

5.2 Experimental Setup

The experiments use synthetic networks and repeated LLM simulations, with shared graphs and initial attributes enabling paired comparisons across recommendation conditions.

5.2 Experimental Setup

  • Main experiments use hyperbolic random graphs, while five-block stochastic block-model networks provide a structurally different robustness setting.The HRGs have 100 nodes and average degree 5; the SBM has five 20-node blocks with within- and cross-block probabilities 0.2 and 0.0025.Source: §5.2 · pp. 8–9
  • Simulations run for 200 time steps and 10 repetitions, sharing each run’s graph and initial user attributes across recommendation conditions.Remote Work is the default topic; robustness analyses also vary recommendation budgets, LLMs, and topics.Source: §5.2 · p. 9
  • Unless otherwise stated, budgets are kE = 200 edges for ER and kC = 4 additional users for CR, approximately calibrated for comparable expected exposure.All recommended ER edges are added, and APPR uses restart probability 0.15.Source: §5.2 · p. 9
  • Main-condition comparisons use paired final-time differences, with 95% t-based confidence intervals and Holm-adjusted exact two-sided paired permutation tests.Adjustment is across the four recommendation conditions within each graph and metric; confidence intervals are unadjusted.Source: §5.2 · p. 9
  • User opinions are initialized around sampled community means, then mean-centered, rescaled to [−1, 1], and mapped to ordinal stance levels.Stubbornness is sampled and clipped to [0, 1], while activeness follows a truncated power-law distribution.Source: §5.2 · p. 9
  • Experiments primarily use GPT-4.1-mini and GPT-4o-mini, with additional runs using DeepSeek-V4.1-Flash.User sessions are isolated, prompt templates are fixed across conditions, and inference uses external APIs.Source: §5.2 · p. 9

5.3 Effects of ER and CR

ER and CR increase mean polarization, extremization, and cumulative reinforcement relative to the no-recommendation baseline. Matching exposure counts reduces these differences, but they remain.

5.3 Effects of ER and CR

  • 0.05 to 0.12 higher mean polarization under all four recommendation conditions than baseline, with every increase significant after Holm correction.The paired differences range from 0.05 for ER-Jaccard to 0.12 for CR-APPR.Source: §5.3 · p. 9, Figure 4 · p. 9, Table 1 · p. 10
  • With exposure counts matched to baseline, differences in polarization, extremization, and cumulative reinforcement become smaller but remain.Recommendation conditions reached the baseline's total exposure count after 113 ± 29 steps on average.Source: §5.3 · pp. 9–10, Table 2 · p. 10
  • 0.100 to 0.118 higher extremization and 53.4 to 102.2 more cumulative reinforcement interactions under recommendation, with all four comparisons significant.Higher reinforcement accompanies greater extremization across both mechanisms; increased interaction volume partly contributes to the differences.Source: §5.3 · p. 10, Figure 5 · p. 10

5.4 Impact of Recommendation Budget

Larger recommendation budgets generally accelerate polarization, although very large budgets do not always produce higher final polarization. The main patterns also generally persist across SBM graphs, discussion topics, and LLMs, with varying magnitudes.

5.4 Impact of Recommendation Budget

  • Higher budgets do not always produce higher final polarization, although larger budgets generally accelerate polarization under both ER and CR.ER adds persistent edges and repeated interactions, whereas CR exposes more users to recommended content at each step.Source: §5.4 · pp. 10–11, Figure 6 · p. 11
  • Both mechanisms show qualitatively similar trends across budgets, despite ER's persistent structural changes and CR's per-post exposure.Both can alter polarization and extremization dynamics.Source: §5.4 · p. 11

5.5 Sensitivity Analyses

  • On SBM graphs, all recommendation conditions have 0.072 to 0.144 higher mean polarization than baseline; extremization and reinforcement increase in most conditions.The magnitudes vary across recommendation strategies.Source: §5.5 · p. 11, Table 3 · p. 11
  • Across discussion topics and LLMs, recommendation generally produces higher polarization than baseline in most settings, with varying effect magnitudes.The main patterns generally persist across these settings.Source: §5.5 · p. 11, Figure 7 · p. 12

6 Conclusion and Future Work

In controlled LLM-based OSN simulations, both recommendation mechanisms generally increase polarization and extremization relative to no recommendation, while their effects are partly associated with higher exposure volume. The conclusion also notes that the findings are bounded by simplified interaction and agent-memory assumptions, and that alignment with human behavior remains open.

6 Conclusion and Future Work

  • Even without recommendations, local network interactions can sustain opinion variance and reduce the prevalence of moderate opinions.The conclusion suggests interaction structure alone can create conditions under which polarization emerges.Source: §6 · p. 12
  • Both ER and CR generally produce higher mean polarization and extremization than the no-recommendation baseline, with similar qualitative patterns despite different mechanisms.ER adds persistent connections; CR expands the audience of individual posts, and both increase interactions between aligned users and shift opinions away from moderate values.Source: §6 · p. 12
  • When exposure counts are controlled instead of simulation steps, polarization differences from the baseline become smaller, suggesting exposure volume partly explains them.The conclusion attributes only a partial explanation to higher exposure volume under recommendation.Source: §6 · p. 12
  • The observed patterns are broadly consistent across graph structures, discussion topics, recommendation budgets, and tested LLMs.Source: §6 · p. 12

6.1 Limitations and Future Work

  • The simulations assume recommended connections are accepted and posts are viewed, and model only single-step interactions without memory of earlier posts or interactions.These choices keep the mechanism comparison controlled; future work could add acceptance decisions, replies, resharing, repeated exposure, multi-step diffusion, interaction memory, and richer profiles.Source: §6.1 · p. 12
  • Whether LLM-based social simulations reflect human behavior remains an open question requiring further investigation.Source: §6.1 · p. 12
  • The study uses no real users or live-platform interventions and is intended to improve understanding of these dynamics.The authors note that the findings could also be misused to design strategies that amplify polarization or reinforce aligned views.Source: §6.1 · p. 13

A Calibration of ER and CR Budgets

The appendix calibrates ER and CR budgets by equating their expected numbers of recipients per post. For n = 100 and kC = 4, it uses kE = 200, while noting that expected exposure matching does not ensure identical exposure for each node or time step.

A Calibration of ER and CR Budgets

B Prompt Templates

The appendix describes how prompts translate internal agent attributes and opinions into natural-language inputs for post generation and opinion updating. LLM-selected stance descriptors are mapped back to numerical opinion states for subsequent computations.

B Prompt Templates

  • Numerical opinion and stubbornness values are hidden from the LLM and represented as natural-language descriptors in shared prompt templates.Placeholders vary with topic, the agent’s stance and stubbornness, interaction context, and the observed post.Source: B Prompt Templates · p. 15

B.1 Stance and Stubbornness Descriptors

  • Opinions use 11 ordinal stance levels from −5 to +5, with 0 denoting neutrality, mapped from continuous initialization to the nearest level.Each level has a distinct natural-language stance label, and normalized values are used in recommendation algorithms and opinion-dynamics measures.Source: §B.1 · p. 15
  • Continuous stubbornness values are mapped to five qualitative labels for prompting, while remaining continuous internally.The labels range from very open to changing one’s mind to very set in one’s view and rarely changing it.Source: §B.1 · p. 15

B.2 Post Generation Prompt

  • For post generation, the prompt conditions a 1–3 sentence expression on the topic and agent’s current stance, with tone matched to stance strength.The same prompt is used across evaluated LLMs.Source: §B.2 · p. 16

B.3 Opinion Update Prompt

  • For opinion updating, the LLM selects a resulting stance descriptor after seeing a post, the agent’s current stance and stubbornness, and connection status.The selected descriptor maps back to an ordinal level and normalized opinion for subsequent computations.Source: §B.3 · pp. 16–17
  • The update prompt allows reinforcement after agreement, persuasion toward a convincing post, or pushback against a strongly opposing or provocative post.These are possible rather than mandatory responses; higher stubbornness reduces the likelihood of change in either direction.Source: §B.3 · p. 16
  • The shared update prompt directs agents not to automatically move toward neutrality, compromise, or the poster’s view.It also says that unconvincing or irrelevant posts generally leave opinions unchanged and that higher stubbornness makes any change less likely.Source: §B.3 · pp. 16–17
  • The update prompt asks for a reaction to one post and requires the output to follow a fixed opinion format.The returned opinion is deterministically mapped to its corresponding ordinal level and normalized value.Source: §B.3 · p. 17

C Robustness Across Graph Structures

On SBM graphs, the reported recommendation effects follow patterns similar to those observed on HRGs. Varying the recommendation budget yields similar trends, suggesting the effects are not limited to a particular graph structure.

C Robustness Across Graph Structures

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