A Laplacian Approach to Stubborn Agents and their Role in Opinion Formation on Influence Networks

Abstract

Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased towards a certain opinion and have a major effect on the collective opinion formation process. Based on a modified version of the network Laplacian we derive quantities capturing the transient dynamics of the system and the emerging stationary opinion states. In the case of a single stubborn agent we characterize his/her ability to coherently change a prevailing consensus. For two antagonistic stubborn agents we investigate the opinion heterogeneity of the emerging non-consensus states and describe their statistical properties using a graph metric similar to the resistance distance in electrical networks. Applying the model to synthetic and empirical networks we find while opinion diversity is decreased by small-worldness and favored in the case of a pronounced community structure the opposite is true for the coherence of opinions during a consensus change.

arXiv commentPreprint accepted in Physica A 29 pages, 8 figures

References in corpus (19)

• Emergence of scaling in random networks
• Statistical physics of social dynamics
• A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part I
• Biased Assimilation, Homophily and the Dynamics of Polarization
• Social consensus through the influence of committed minorities
• Does a Single Zealot Affect an Infinite Group of Voters ?
• On the Role of Zealotry in the Voter Model
• The Emergence of Consensus: A Primer
• Starling flock networks manage uncertainty in consensus at low cost
• Opinion Polarization by Learning from Social Feedback
• The Key Player Problem in Complex Oscillator Networks and Electric Power Grids: Resistance Centralities Identify Local Vulnerabilities
• Opinion control in complex networks
• Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices
• Dynamics of opinion formation in a small-world network
• Optimal Network Topology for Effective Collective Response
• Committed activists and the reshaping of status-quo social consensus
• Zealotry Effects on Opinion Dynamics in the Adaptive Voter Model
• Global Robustness vs. Local Vulnerabilities in Complex Synchronous Networks
• Tipping Diffusivity in Information Accumulation Systems: More Links, Less Consensus

Cited by in corpus (5)

• Persistent individual bias in a voter model with quenched disorder
• Assessing the impact of Byzantine attacks on coupled phase oscillators
• How zealots affect the energy cost for controlling complex social networks
• Learning particle swarming models from data with Gaussian processes
• Evolution of robustness in growing random networks