The effect of a toroidal opinion space on opinion bi-polarisation

Large language models (LLMs) increasingly interact with one another in multi-agent systems, from simulations of human discourse to influence operations and fully LLM-driven social platforms. These interactions give rise to new regimes of opinion propagation that are not yet well understood. We investigate whether classical opinion dynamics models, which have long been used to explain how interactions shape collective beliefs in human societies, can capture the behavior of LLM networks. Specifically, we quantify the relative contributions of classical opinion-dynamics mechanisms, including neighbor influence, stubbornness, homophily, and bias, to the evolution of LLM opinions. Among the mechanisms considered, a bias term capturing regression toward a model- and topic-dependent opinion emerges as a significant explanatory component, with its inclusion reducing cumulative estimated mean opinion error by up to $88\%$. We additionally observe similar trends across the evaluated model families, discussion topics, and network structures.

The study of opinion dynamics in social networks is one of the key challenges in computational social science with direct relevance to understanding political polarization, misinformation, and health responses. Current approaches focus on simplified mathematical models that ignore linguistic and contextual factors related to belief updates or use Large Language Model (LLM)-based simulations that have not been validated against real data. We present a framework based on the concept of a digital twin to simulate opinion dynamics in social networks. The approach fills the gap by cloning a real-world Twitter network, assigns a set of attributes for agents (such as persona, emotions, centrality, stubbornness, and influence), and employs Mistral-7B to perform opinion update based on memory and social exposure. To evaluate the proposed approach, we validate it against two real Twitter datasets (COVID-19 discourse and U.S elections 2020). The results show that the capability of the proposed framework reproduces opinion trajectories and reduces individual prediction error by more than 50% compared to the best-performing classical baseline (Mistral-7B achieves Mean Absolute Error (MAE) = 0.150 and 0.121 on the COVID-19 and US Election 2020 datasets, respectively). We observe similar improvements in structural alignment (Delta_r = 0.120 and 0.180) and polarization dynamics (Delta_Var = 0.106 and 0.115) on the two datasets, respectively. Additionally, the ablation studies confirm that agent attributes, memory, and social exposure all contribute to the framework's predictive fidelity in reproducing opinion trajectories, with agent attributes being the most critical contributor. Overall, our results demonstrate that grounding Mistral-7B within empirically cloned interaction networks produces a realistic simulation framework capable of reproducing complex social dynamics.

LLM agents in social simulation revise their opinions implicitly, in context: how open an agent is to persuasion can neither be specified nor verified, and collective outcomes inherit the model's training prior. We introduce Bayesian Chronicle Agents (BCA), a minimal belief layer separating what an agent believes from how it speaks. Each stance is a probability, updated by one Bayesian step per utterance heard. A single prior-strength parameter $κ$ encodes stubbornness, modeled after its role in Friedkin--Johnsen (FJ) opinion dynamics. We then sweep this parameter to yield three canonical regimes of opinion dynamics on demand (consensus, persistent disagreement, committed-minority influence), with persistent disagreement matching the FJ closed-form fixed points at $R^2\!=\!0.93$--$0.99$. We further show that prescribed $κ$ remains recoverable after the language round-trip, with perfect rank-order recovery across all four models. Explicit belief also makes simulation auditable: the layer surfaces systematic per-model stance biases that end-to-end simulation would silently absorb.