Opinion Dynamics and the Evolution of Social Power in Social Networks (Springer Theses)

This book uses rigorous mathematical analysis to advance opinion dynamics models for social networks in three major directions. First, a novel model is proposed to capture how a discrepancy between an individual’s private and expressed opinions can develop due to social pressures that arise in group situations or through extremists deliberately shaping public opinion. Detailed theoretical analysis of the final opinion distribution is followed by use of the model to study Asch’s seminal experiments on conformity, and the phenomenon of pluralistic ignorance. Second, the DeGroot-Friedkin model for evolution of an individual’s social power (self-confidence) is developed in a number of directions. The key result establishes that an individual’s initial social power is forgotten exponentially fast, even when the network changes over time; eventually, an individual’s social power depends only on the (changing) network structure. Last, a model for the simultaneous discussion of multiple logically interdependent topics is proposed. To ensure that a consensus across the opinions of all individuals is achieved, it turns out that the interpersonal interactions must be weaker than an individual’s introspective cognitive process for establishing logical consistency among the topics. Otherwise, the individual may experience cognitive overload and the opinion system becomes unstable. Conclusions of interest to control engineers, social scientists, and researchers from other relevant disciplines are discussed throughout the thesis with support from both social science and control literature. "This book uses rigorous mathematical analysis to advance opinion dynamics models for social networks in three major directions. First, a novel model is proposed to capture how a discrepancy between an individual's private and expressed opinions can develop due to social pressures that arise in group situations or through extremists deliberately shaping public opinion. Detailed theoretical analysis of the final opinion distribution is followed by use of the model to study Asch's seminal experiments on conformity, and the phenomenon of pluralistic ignorance. Second, the DeGroot-Friedkin model for evolution of an individual's social power (self-confidence) is developed in a number of directions. The key result establishes that an individual's initial social power is forgotten exponentially fast, even when the network changes over time; eventually, en individual's social power depends only on the (chaing) network structure. Last, a model for the simultaneous discussion of multiple logically interdependent topics is proposed. To ensure that a consensus across the opinions of all individuals is achieved, it turns out that the interpersonal interactions must be weaker than an individual's introspective cognitive process for establishing logical consistency among the topics. Otherwise, the individual may experience cognitive overload and the opinion system becomes unstable. Conclusions of interest to control engineers, social scientists, and researchers from other relevant disciplines are discussed throughout the thesis with support from both social science and control literature"--Back cover Front Matter ....Pages i-xxiii Introduction (Mengbin Ye)....Pages 1-14 Preliminaries (Mengbin Ye)....Pages 15-23 Front Matter ....Pages 25-25 A Novel Model for Opinion Dynamics Under Pressure to Conform (Mengbin Ye)....Pages 27-54 The EPO Model’s Connections with Social Psychology Concepts (Mengbin Ye)....Pages 55-82 Front Matter ....Pages 83-83 Evolution of Social Power in Networks with Constant Topology (Mengbin Ye)....Pages 85-104 Dynamic Social Networks: Exponential Forgetting of Perceived Social Power (Mengbin Ye)....Pages 105-123 Modification of Social Dominance in Autocratic Networks (Mengbin Ye)....Pages 125-145 Nonlinear Mapping Convergence and Application to Social Power Analysis (Mengbin Ye)....Pages 147-159 Front Matter ....Pages 161-161 Continuous-Time Opinion Dynamics with Interdependent Topics (Mengbin Ye)....Pages 163-189 Conclusions and Future Work (Mengbin Ye)....Pages 191-199 Back Matter ....Pages 201-209