Social Power Evolution Analysis for Friedkin-Johnsen Model With Oblivious Individuals.

Area of Science:

• Social sciences
• Network science
• Mathematical modeling

Background:

• Social power dynamics are complex, influenced by individual behavior and network structure.
• Existing models like DeGroot and Friedkin-Johnsen offer insights into opinion dynamics but require unified frameworks for social power evolution.

Purpose of the Study:

• To develop a unified framework for studying social power evolution.
• To analyze the impact of individual characteristics (oblivious vs. stubborn) and network topology on social power.
• To establish conditions for the convergence of social power dynamics.

Main Methods:

• Utilizing the DeGroot averaging model for oblivious individuals and the Friedkin-Johnsen model for stubborn individuals.
• Identifying a proper subset of the simplex for well-posedness and convergence of social power.
• Deriving a nonlinear mapping for social power evolution via the reflected appraisal mechanism.

Main Results:

• Social power dynamics converge when initial social power is restricted to a specific subset.
• Neither autocratic nor democratic social power is fully achieved; oblivious individuals gain higher average social power.
• Network topology significantly impacts social power more than individual stubbornness.

Conclusions:

• The study provides a robust framework for understanding social power evolution in diverse populations.
• Convergence of social power is achievable under specific conditions, with network structure playing a dominant role.
• Final social power rankings for oblivious individuals correlate with network centrality, while lower bounds for stubborn individuals are established.