Fitting in and breaking up: A nonlinear version of coevolving voter models

Area of Science:

• Complex Systems
• Network Science
• Sociophysics

Background:

• Coevolving voter models simulate opinion dynamics and network structure changes.
• Existing models primarily use linear update rules for rewiring and adoption probabilities.
• Limited exploration of nonlinear dynamics where local agreement influences network evolution.

Purpose of the Study:

• To investigate a nonlinear version of coevolving voter models.
• To analyze how local opinion agreement influences node state and network structure updates.
• To compare the nonlinear model's dynamics against established linear coevolving voter models.

Main Methods:

• Developed a nonlinear update rule where rewiring/adoption probability depends on the fraction of neighbors sharing the node's opinion (local-survey parameter σᵢ).
• Incorporated a nonlinearity parameter (q) to control the influence of local agreement on update probabilities.
• Studied three rewiring schemes: rewiring-to-random, rewiring-to-same, and rewiring-to-none (unfriending).

Main Results:

• Initial network topology plays a more significant role in dynamics compared to linear models.
• The choice of rewiring mechanism has a less pronounced effect on the overall dynamics.
• A minority opinion can spread extensively if minority nodes perceive themselves as the majority, demonstrating a 'majority illusion'.

Conclusions:

• Nonlinear coevolving voter models offer a richer dynamic landscape influenced by local agreement.
• The findings highlight the importance of initial network structure and local social perception in opinion spread.
• Results connect to the 'majority illusion' phenomenon observed in real-world social networks.