Phase Transition in the Social Impact Model of Opinion Formation in Scale-Free Networks: The Social Power Effect

Human interactions and opinion exchanges lead to social opinion dynamics, which is well described by opinion formation models. In these models, a random parameter is usually considered as the system noise, indicating the individual's inexplicable opinion changes. This noise could be an indicator of any other influential factors, such as public media, affects, and emotions. We study phase transitions, changes from one social phase to another, for various noise levels in a discrete opinion formation model based on the social impact theory with a scale-free random network as its interaction network topology. We also generate another similar model using the concept of social power based on the agents' node degrees in the interaction network as an estimation for their persuasiveness and supportiveness strengths and compare both models from phase transition viewpoint. We show by agent-based simulation and analytical considerations how opinion phases, including majority and non-majority, are formed in terms of the initial population of agents in opinion groups and noise levels. Two factors affect the system phase in equilibrium when the noise level increases: breaking up more segregated groups and dominance of stochastic behavior of the agents on their deterministic behavior. In the high enough noise levels, the system reaches a non-majority phase in equilibrium, regardless of the initial combination of opinion groups. In relatively low noise levels, the original model and the model whose agents' strengths are proportional to their centrality have different behaviors. The presence of a few high-connected influential leaders in the latter model consequences a different behavior in reaching equilibrium phase and different thresholds of noise levels for phase transitions.