Paper ID: 2410.19685 • Published Oct 25, 2024
The Sound of Silence in Social Networks
Jesús Aranda, Juan Francisco Díaz, David Gaona, Frank Valencia
TL;DR
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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.