Optimizing Opinions with Stubborn Agents

• 成果类型: Article
• 署名作者: Hunter, David Scott; Zaman, Tauhid
• 署名单位: Massachusetts Institute of Technology (MIT); Yale University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2291
• 发表日期: 2022
• 关键词: Social networks; opinion dynamics; stubborn agents; submodular optimization

摘要

We consider the problem of optimizing the placement of stubborn agents in a social network in order to maximally influence the population. We assume the network contains stubborn users whose opinions do not change, and nonstubborn users who can be persuaded. We further assume that the opinions in the network are in an equilibrium that is common to many opinion dynamics models, including the well-known DeGroot model. We develop a discrete optimization formulation for the problem of maximally shifting the equilibrium opinions in a network by targeting users with stubborn agents. The opinion objective functions that we consider are the opinion mean, the opinion variance, and the number of individuals whose opinion exceeds a fixed threshold. We show that the mean opinion is a monotone sub modular 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 nontrivially influence the equilibrium opinions. Furthermore, we show that our greedy algorithm outperforms several common benchmarks. We then propose an opinion dynamics model where users communicate noisy versions of their opinions, communications are random, users grow more stubborn with time, and there is heterogeneity in how users' stubbornness increases. We prove that, under fairly general conditions on the stubbornness rates of the individuals, the opinions in this model converge to the same equilibrium as the DeGroot model, despite the randomness and user heterogeneity in the model.