Optimizing Opinions with Stubborn Agents Under Time-Varying Dynamics
Year: 2018
Type: preprint
Abstract: We consider optimizing the placement of stubborn agents in a social network in order to maximally influence the population. We assume individuals in a directed social network each have a latent opinion that evolves over time in response to social media posts by their neighbors. The individuals randomly communicate noisy versions of their latent opinion to their neighbors, causing them to update their opinions using a time-varying update rule that has them become more stubborn with time and be less affected by new posts. The noisy communicated opinion and dynamic update rule are novel components of our model and they reflect realistic behaviors observed in many psychological studies.
We prove that under fairly general conditions, the opinions converge to an equilibrium in the presence of stubborn agents. What is surprising about this result is that the equilibrium condition depends only upon the network structure and the identity of the stubborn agents. The time-varying opinion update rules, which are heterogeneous across individuals, do not affect the equilibrium. We also prove bounds on the rate of convergence to this equilibrium.
We then use this model to develop a discrete optimization formulation for the problem of maximally shifting the equilibrium opinions in a network by targeting users with stubborn agents. We consider maximizing the mean opinion and also maximizing the number of individuals whose opinion exceeds a fixed threshold. We show that the mean opinion is a monotone submodular function, allowing us to find a good solution using a greedy algorithm. We find that on real social networks in Twitter consisting of tens of thousands of individuals, a small number of stubborn agents can non-trivially influence the equilibrium opinions. Furthermore, we show that our greedy algorithm outperforms several common benchmarks.
Source: arXiv (Cornell University)
Authors: David Scott Hunter, Tauhid Zaman
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2998350422