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Binary Opinion Dynamics with Stubborn Agents

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TLDR
It is shown that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations.
Abstract
We study binary opinion dynamics in a social network with stubborn agents who influence others but do not change their opinions. We focus on a generalization of the classical voter model by introducing nodes (stubborn agents) that have a fixed state. We show that the presence of stubborn agents with opposing opinions precludes convergence to consensus; instead, opinions converge in distribution with disagreement and fluctuations. In addition to the first moment of this distribution typically studied in the literature, we study the behavior of the second moment in terms of network properties and the opinions and locations of stubborn agents. We also study the problem of optimal placement of stubborn agents where the location of a fixed number of stubborn agents is chosen to have the maximum impact on the long-run expected opinions of agents.

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Citations
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References
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Journal ArticleDOI

A model for spatial conflict

TL;DR: In this paper, a simple stochastic model for this process is described and rules are given for the calculation, as a function of time, of the probabilities that individual territories and groups of territories are held by a single species.
Journal ArticleDOI

Bayesian learning in social networks

TL;DR: This work introduces a social network and assumes that agents can only observe the actions of agents to whom they are connected by this network, and allows agents to choose a different action at each date.
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Bayesian Learning in Social Networks

TL;DR: The main theorem shows that when the probability that each individual observes some other individual from the recent past converges to one as the social network becomes large, unbounded private beliefs are sufficient to ensure asymptotic learning.
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