Opinion dynamics with varying susceptibility to persuasion

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates