Convolution of individual and group identity: self-reliance increases polarisation in basic opinion model

Human opinion formation is a dynamic process deeply influenced by social interactions. While many individual decisions are insignificant, collective opinion formation significantly impacts societal outcomes, as seen in elections and market trends. Research into social influence, stemming from Asch's conformity studies, has illuminated mechanisms of opinion polarization. The escalating political polarization in numerous countries, exacerbated by crises like the COVID-19 pandemic, and its impact on climate mitigation policies, underscores the urgent need for a better understanding of these mechanisms. Existing agent-based models (ABMs) often rely on homophily (the tendency to associate with like-minded individuals) or bounded confidence (limiting influence to similar opinions). This study proposes a minimalist ABM to explore whether the inherent human desires for both group belonging and individual distinctiveness drive opinion polarization. This competition, first proposed by Brewer (1991), forms the basis of optimal distinctiveness theory. While similar approaches exist in the literature, this model differs by focusing on self-reliance (the degree of independence in opinion formation) as the primary driver, eliminating homophily and bounded confidence assumptions. The model analyzes both the continuous opinion distribution and final binary decisions (e.g., voting), and introduces a social cohesion measure (opinion spread) representing the distance between extreme opinions, which is a proxy for societal identification and agreement on common goals. The study aims to show a trade-off between social cohesion and individual alignment with intrinsic beliefs at both individual and societal levels.

Agent-based modeling (ABM) has proven valuable in exploring opinion formation and polarization. Many ABMs incorporate homophily, demonstrating its role in amplifying affinities between lifestyle and ideology, shaping group formation, and explaining social structures. Concepts like biased assimilation (where individuals cling to inherent beliefs despite inconclusive information) have also been integrated into ABMs to study polarization. This study differs by focusing on self-reliance rather than homophily and biased assimilation. It contrasts with the model of Mäs et al. (2010), which uses an adaptive white-noise term for individualization, by employing a constant self-reliance parameter. Furthermore, unlike Mäs et al. (2010) and Mäs and Flache (2013), this model does not rely on homophily or an exchange of arguments. Other ABMs incorporate repulsion effects, where agents distance themselves from dissimilar opinions, investigating polarization's effects on tolerance and responsiveness. This research distinguishes itself by focusing on the interplay between conformity and adherence to intrinsic beliefs, using self-reliance as a measure of the inherent desire for individual expression. This approach explores a different underlying mechanism driving polarization than those considered in previous models.

This agent-based model (ABM) explores opinion polarization using a simple framework that considers two key factors: the tendency to conform to social norms and the desire to maintain intrinsic beliefs. Each agent is assigned a self-reliance parameter (γ) ranging from 0 (highly dependent) to 1 (highly self-reliant) and an initial conviction (A) representing their intrinsic opinion (0-1). Agents are placed on a periodic grid, interacting with their Moore neighbors. At each time step, each agent updates its attitude (A) based on the weighted influence of its neighbors (1-γ) and the difference between its current attitude and its initial conviction (γ). The dynamics are given by equation (1): ΔAᵢ/Δt = r((1-γᵢ)Nᵢ(t) + γᵢ(Aᵢ - Aᵢ(t-1))), where Nᵢ represents the weighted average attitude difference from the neighbors. The model runs until convergence, after which each agent makes a binary decision (dᵢ = 1 if Aᵢ > 0.5, 0 otherwise). To measure self-fulfillment, decision alignment (δᵢ = dᵢ - dᵢ) quantifies the agreement between initial and final decisions. Societal self-fulfillment (Δ) is the average decision alignment. Social cohesion is measured by opinion spread (w), the difference between the 90th and 10th percentiles of final attitudes. A larger opinion spread indicates lower social cohesion. The model uses a mean-field approximation to analytically estimate average decision alignment, facilitating comparison with simulation results. Various scenarios are simulated, including uniform and normal distributions for self-reliance and initial conviction, varying neighborhood radii, and grid population densities. The simulations are averaged over multiple runs with varied initial conditions.

Simulations consistently revealed the emergence of stable, polarized opinion clusters from random initial conditions. In scenarios with uniform distributions of self-reliance and initial attitude, distinct clusters of agents with strongly diverging final attitudes formed, surrounded by agents with moderate opinions. The final decisions showed clear, separated clusters, indicating a significant level of polarization. When varying the distribution of self-reliance (using normal distributions with different means), the results showed that a higher average self-reliance led to increased opinion spread and greater polarization. Agents with high self-reliance populated the tails of the final attitude distribution, significantly driving the overall polarization of the society. This observation held true even when relaxing the assumption that initial attitude equals inherent conviction and when varying neighborhood radii and grid population densities. Analysis of decision alignment revealed a trade-off between self-fulfillment (agents aligning with their initial convictions) and social cohesion (measured by opinion spread). Societies with more self-reliant agents exhibited higher decision alignment but also greater opinion spread and thus lower social cohesion. This trade-off was consistently observed across different scenarios, indicating a robust relationship between individual independence and societal unity. Analytical estimations using mean-field approximations confirmed the simulation results, demonstrating a strong correlation between average societal self-reliance and the level of decision alignment.

The findings highlight the significance of self-reliance as a driver of opinion polarization. The model's simplicity allows focusing on the interplay between the drive for individual expression and the influence of group dynamics. The emergence of stable, polarized clusters even under simple rules suggests this interplay is a crucial mechanism for societal polarization. The observed increase in opinion spread with higher self-reliance aligns with empirical observations of increasing political polarization, supporting the model's relevance to real-world phenomena. The trade-off between self-fulfillment and social cohesion implies that promoting individual autonomy could lead to a more fragmented society. This complements existing research on polarization mechanisms by emphasizing the role of individual convictions and the strength of those convictions in the face of social pressure. This study is distinct from previous work by not explicitly modeling repulsion from differing opinions; instead, polarization emerges from a stronger drive toward one's personal beliefs. The minimal model, despite its simplicity, reproduces key observations from more complex models and offers a novel perspective on polarization mechanisms.

This study introduces a minimalist agent-based model demonstrating the emergence of opinion polarization from the interplay between individual self-reliance and social influence. The model reveals a robust trade-off between individual fulfillment and societal cohesion, with increased self-reliance leading to greater polarization. Future research could explore the model's sensitivity to different network structures, the introduction of external information sources, or the impact of diverse self-reliance distributions on polarization dynamics.

The model's simplicity, while offering clarity, also presents limitations. The assumptions of a regular grid and uniform interactions might not fully capture the complexity of real-world social networks. The model omits other factors influencing opinion formation, such as media influence, persuasive communication strategies, and the role of leaders. Despite these limitations, the model provides valuable insights into the fundamental mechanisms driving polarization.