The Impact of External Sources on the Friedkin-Johnsen Model

2024-10-21

International Conference on Information and Knowledge Management

AI Summary

This paper investigates the impact of biased external media—such as false balance or selective reporting—on the Friedkin-Johnsen opinion dynamics model. We propose an extended model incorporating non-adaptive, systematically biased media sources to characterize opinion polarization and convergence under single- and dual-opposing-media regimes. Methodologically, we integrate graph-theoretic modeling, linear system analysis, and matrix perturbation theory, validating our framework on real-world networks (Twitter, Epinions) and synthetic data. Theoretically, we (i) derive the first rigorous characterization of steady-state solution structure under dual-opposing media; (ii) prove that non-adaptive media exert stronger and more robust opinion-shaping influence than adaptive media; and (iii) establish explicit, analytically tractable criteria for polarization onset and convergence time. Experiments align closely with theoretical predictions, accurately forecasting opinion distributions, polarization thresholds, and convergence rates.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Knowledge Representation and Reasoning: Preferences
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Web Mining and Content Analysis: Sentiment analysis and opinion mining
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

To obtain a foundational understanding of timeline algorithms and viral content in shaping public opinions, computer scientists started to study augmented versions of opinion formation models from sociology. In this paper, we generalize the popular Friedkin--Johnsen model to include the effects of external media sources on opinion formation. Our goal is to mathematically analyze the influence of biased media, arising from factors such as manipulated news reporting or the phenomenon of false balance. Within our framework, we examine the scenario of two opposing media sources, which do not adapt their opinions like ordinary nodes, and analyze the conditions and the number of periods required for radicalizing the opinions in the network. When both media sources possess equal influence, we theoretically characterize the final opinion configuration. In the special case where there is only a single media source present, we prove that media sources which do not adapt their opinions are significantly more powerful than those which do. Lastly, we conduct the experiments on real-world and synthetic datasets, showing that our theoretical guarantees closely align with experimental simulations.

Problem

• Analyzing external media influence on opinion formation dynamics
• Characterizing conditions for opinion radicalization in networks
• Comparing adaptive versus non-adaptive media source effectiveness

Innovation

• Augmented Friedkin-Johnsen model with external media
• Mathematical analysis of biased media influence conditions
• Theoretical characterization of final opinion configuration