Mathematical Modeling of Individual Behavior Based on Viewpoint Dynamics: Analyzing Group Cohesion Effects Induced by Individual Potential Power Differences

The group cohesion effect refers to individuals' identification with the group's viewpoint, resulting from behavioral and cognitive changes during interactions, and is crucial for group development. However, individual differences in intrinsic characteristics lead to varied group behaviors and cohesion. This paper uses a mathematical model based on viewpoint dynamics to explore how these differences shape group cohesion. The primary consideration is the potential power inherent in individual characteristics, which can be understood as symmetry-breaking concepts. In the model, individuals are classified into two types, each supporting one of two viewpoints. The potential power reflects the individuals' degree of firmness regarding their viewpoint and their perceptual range. Differences in the potential power, both within and between types, drive shifts in viewpoints and behaviors, generating diverse cohesion effects. Additionally, the model also incorporates the influence of group size and external factors, such as individuals with no viewpoints and those holding public opinion viewpoints. The results indicate that group size has no significant effect on group cohesion, while individuals with no viewpoints contribute to stabilizing it, whereas individuals with public opinions weaken it. These findings highlight the complex relationship between individual differences in potential power and group cohesion, suggesting that symmetry-breaking dynamics can effectively explain group cohesion effects.