The Sound of Silence in Social Networks

2024-10-25

arXiv.org

AI Summary

Classical DeGroot opinion dynamics assume continuous opinion exchange, neglecting social silence—where individuals suppress expression upon perceiving themselves as minorities, a phenomenon formalized by the “spiral of silence” theory in communication studies. Method: We formally integrate this theory into the DeGroot model via two silence-update mechanisms: memoryless (SOM⁻) and memory-augmented (SOM⁺), capturing context-dependent silencing behavior. Contribution/Results: Theoretical analysis reveals that silence fundamentally disrupts consensus convergence: SOM⁻ guarantees convergence on clique graphs but fails to ensure it on strongly connected aperiodic graphs; SOM⁺ may diverge even on cliques. Numerical simulations reproduce hallmark spiral-of-silence phenomena—including accelerated opinion polarization, self-reinforcement of majority views, and marginalization of minority opinions. Our work exposes structural limitations to consensus formation in social networks and establishes a novel nonlinear framework for modeling asymmetric opinion dynamics and emergent imbalance in public discourse.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

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

Abstract

We generalize the classic multi-agent DeGroot model for opinion dynamics to incorporate the Spiral of Silence theory from political science. This theory states that individuals may withhold their opinions when they perceive them to be in the minority. As in the DeGroot model, a community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. However, agents whose current opinions are in the minority become silent (i.e., they do not express their opinion). Two models for opinion update are then introduced. In the memoryless opinion model ($mbox{SOM}^-$), agents update their opinion by taking the weighted average of their non-silent neighbors' opinions. In the memory based opinion model ($mbox{SOM}^+$), agents update their opinions by taking the weighted average of the opinions of all their neighbors, but for silent neighbors, their most recent opinion is considered. We show that for $mbox{SOM}^-$ convergence to consensus is guaranteed for clique graphs but, unlike for the classic DeGroot, not guaranteed for strongly-connected aperiodic graphs. In contrast, we show that for $mbox{SOM}^+$ convergence to consensus is not guaranteed even for clique graphs. We showcase our models through simulations offering experimental insights that align with key aspects of the Spiral of Silence theory. These findings reveal the impact of silence dynamics on opinion formation and highlight the limitations of consensus in more nuanced social models.

Problem

• Modeling opinion dynamics with Spiral of Silence theory
• Analyzing consensus convergence under silence mechanisms
• Investigating minority opinion suppression in social networks

Innovation

• Incorporated Spiral of Silence theory
• Introduced memoryless and memory-based models
• Analyzed convergence in different graph structures