Recent news about Russian propaganda bots influencing elections n the US and Europe has created a need for social media counter-measures. One approach is to deploy agents in a social network to counter the influence campaign.  These can be viewed as “stubborn” agents whose goal is to shift the opinions of non-stubborn people by sharing relevant content. In this talk we show how to deploy stubborn agents in a social network in order to accomplish this.  We begin by proposing an opinion dynamics model for interacting individuals in a social network.  Our model differs from previous models by allowing individuals to grow more stubborn with time.  Despite the time varying nature of our model, we are able to provide a precise characterization of the conditions under which the opinions convergence to an equilibrium.  We find that the equilibrium opinions are given by a linear system which has a form similar to Ohm’s Law from circuit theory. 

To validate this opinion model, we use it to predict the opinions of hundreds of thousands of Twitter users discussing varying polarized topics.  We use the content of these users tweets as a measure of their true opinions.   We develop a neural network to extract the user’s opinions from their tweet text.  We find that our opinion model accurately predicts the mean opinion of the populations and has a high correlation with their tweet based opinions.

Using state of the art detection algorithms, we are able to identify bots in our datasets and use our opinion model to measure the effect they have on the population opinions.  We also show how to place stubborn agents in a network to have maximal impact on the population opinion.  We formulate this as a discrete optimization problem.  We show that the problem is submodular, which allows us to find an accurate and fast solution using a greedy algorithm.  We find that a relatively small number of stubborn agents can have a strong effect on the population opinion in several real social networks.