Computational Agent-based Models in Opinion Dynamics: A Survey on Social Simulations and Empirical Studies

The study of opinion formation has evolved from early models like DeGroot (1974), which used weighted averages to explain consensus, to more complex models like Hegselmann-Krause (2002), emphasizing bounded confidence and opinion polarization. Recent interdisciplinary efforts integrate psychological theories—such as confirmation bias, cognitive dissonance—and network science, leading to diverse ABMs that simulate macro phenomena like extremism, echo chambers, and societal polarization. Despite progress, existing models often lack a unified theoretical foundation, making cross-comparison and systematic analysis difficult. The increasing availability of social media data and computational power motivates the development of comprehensive frameworks that can incorporate multiple influence mechanisms, multi-dimensional attitudes, and dynamic network effects, aiming to improve predictive accuracy and interpretability.

The core challenge is to accurately model how individuals update their attitudes under social influence, considering multiple sources, influence types, and psychological biases. Existing models tend to focus on single mechanisms or lack a systematic structure, limiting their ability to generalize across different social contexts. Moreover, parameters are often calibrated empirically without a unifying theoretical basis, reducing interpretability and robustness. Capturing the complex interplay between influence strength, source credibility, and attitude extremity remains unresolved. Addressing these issues requires a comprehensive, formalized framework that can unify diverse models, incorporate psychological insights, and support multi-scale simulations.

This work introduces a unified mathematical framework for ABMs, decomposing attitude change into three core functions—update, select, and message—each parameterized to include influence strength, trust, and bias factors. It systematically formalizes four influence components—assimilation, reinforcement, similarity bias, and repulsion—grounded in psychological theories, enabling nuanced modeling of opinion dynamics. The framework supports multi-dimensional attitudes, complex network topologies, and dynamic influence parameters, facilitating scalable and interpretable simulations. It bridges the gap between theory-driven and empirical models, offering a versatile platform for analyzing macro social phenomena from micro-level rules, thus advancing both theoretical understanding and practical applications.

• �� Define attitude variables a_i,t as real numbers within a bounded or unbounded space.
• �� Construct attitude update function f_update, integrating influence via g, which combines four components: assimilation (pulling attitudes closer), reinforcement (amplifying messages), similarity bias (favoring similar opinions), and repulsion (pushing away dissimilar opinions).
• �� Model influence strength α and trust s as parameters, with α possibly dynamic based on network or context.
• �� Design selection function f_select to determine influence sources based on network topology, similarity, or randomness.
• �� Define message function f_message, typically transmitting the agent’s current attitude, with options for stochastic or biased messaging.
• �� Calibrate parameters using empirical data, enabling simulation of phenomena like opinion polarization, extremism, and consensus.
• �� Run simulations across different network structures and parameter sets to analyze macro-level opinion distributions.

The models are validated against social media datasets and survey data, focusing on polarization and consensus metrics. Parameters such as influence strength (α), confidence bounds, and network topology are varied systematically. Baseline comparisons include DeGroot, Hegselmann-Krause, and physics-inspired models. Metrics like opinion deviation, polarization index, and opinion extremity are used. Sensitivity analyses reveal the impact of influence components and network effects. Experiments demonstrate the model’s robustness across random, small-world, and real social network structures, confirming its applicability for diverse social contexts. Calibration results show parameter ranges that best fit empirical data, guiding future real-world applications.

The unified framework successfully reproduces key social phenomena: polarization indices exceeding 0.7 in high-influence scenarios, consensus formation with less than 5% deviation from empirical data, and opinion extremization under certain influence parameter configurations. Incorporating the four influence components allows nuanced control over opinion dynamics, with influence strength α being the most sensitive parameter. Simulations across network types show consistent macro-level patterns, validating the model’s generality. The results confirm that targeted adjustments of influence parameters can effectively mitigate polarization or promote consensus, providing actionable insights for social policy and online platform design.

The models can inform social media moderation strategies, political campaigning, and public health messaging by predicting opinion shifts and identifying influential nodes. They support scenario testing for intervention policies aimed at reducing societal polarization or misinformation spread. In industry, they can guide marketing campaigns by modeling consumer opinion dynamics. Policymakers can leverage these models to design more effective communication strategies, optimize information dissemination, and foster social cohesion, especially in polarized environments. The framework’s scalability enables real-time social monitoring and adaptive intervention planning.

Current models primarily focus on single-dimensional attitudes, limiting their capacity to simulate complex, multi-faceted opinions. Parameter calibration depends on extensive empirical data, which may not be available in all contexts. The static nature of influence parameters and source trustworthiness reduces realism in dynamic social environments. Additionally, the computational complexity increases with network size and attitude dimensions, posing scalability challenges. Future work should address multi-dimensional attitudes, adaptive influence mechanisms, and integration with big data for real-time social analysis.