[论文解读] Opinion Dynamics with Stubborn Agents.

David Scott Hunter, Tauhid Zaman|arXiv (Cornell University)|Jun 29, 2018

Opinion Dynamics and Social Influence参考文献 24被引用 8

一句话总结

本文提出一种具有时变固执度的动态意见模型，表明在一般条件下，意见会收敛到线性均衡。该研究引入了调和影响中心性，并将固执代理人的布局问题形式化为单调子模优化问题，通过贪心算法实现仅用少量代理人的有效影响。

ABSTRACT

We consider the problem of optimizing the placement of stubborn agents in a social network in order to maximally impact population opinions. 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. Each individual updates his opinion using a time-varying update rule that has him become more stubborn with time and be less affected by new posts. The dynamic update rule is a novel component of our model and reflects realistic behaviors observed in many psychological studies. We show that in the presence of stubborn agents with immutable opinions and under fairly general conditions on the stubbornness rate of the individuals, the opinions converge to an equilibrium determined by a linear system. We give an interesting electrical network interpretation of the equilibrium. We also use this equilibrium to present a simple closed form expression for harmonic influence centrality, which is a function that quantifies how much a node can affect the mean opinion in a network. We develop a discrete optimization formulation for the problem of maximally shifting opinions in a network by targeting nodes with stubborn agents. We show that this is an optimization problem with a monotone and submodular objective, allowing us to utilize a greedy algorithm. Finally, we show that a small number of stubborn agents can non-trivially influence a large population using simulated networks.

研究动机与目标

• 建立一个有向社交网络中个体固执度随时间变化的模型，以描述意见的演化过程。
• 理解不可变的固执代理人对均衡意见分布的影响。
• 开发一个可处理的优化框架，用于放置固执代理人以最大化意见改变。
• 通过电网络类比表征均衡意见状态。
• 推导出调和影响中心性的闭式表达式，作为节点影响力的度量。

提出的方法

• 将个体建模为具有潜在意见，通过与邻居的噪声性、时变通信进行更新。
• 引入一种时变更新规则，个体随时间变得更加固执，对新信息的敏感度降低。
• 在固执度变化率的一般条件下，证明系统收敛到线性均衡。
• 建立均衡状态的电网络解释，将网络结构与意见结果联系起来。
• 将固执代理人布局问题形式化为具有单调且子模目标函数的离散优化任务。
• 由于子模性，应用贪心算法高效求解该优化问题。

实验结果

研究问题

• RQ1 时变固执度如何影响社交网络中的意见收敛？
• RQ2 当引入具有固定意见的固执代理人时，均衡意见分布是什么？
• RQ3 均衡状态能否通过电网络类比进行解释？
• RQ4 如何为网络中的节点推导出调和影响中心性的闭式表达式？
• RQ5 如何最优地放置固执代理人以最大化意见改变？其有效性如何？

主要发现

• 在一般条件下，即使存在噪声通信，意见仍会收敛到线性均衡。
• 均衡状态可用电网络类比解释，将网络拓扑与意见结果联系起来。
• 推导出调和影响中心性的闭式表达式，量化了节点影响平均意见的潜力。
• 意见改变优化问题具有单调性和子模性，可通过贪心算法高效求解。
• 模拟结果表明，通过战略性地放置少量固执代理人，可显著影响整体人群的意见。