# Opinion Dynamics with

Varying Susceptibility to Persuasion

In this work we study a social influence problem using a popular opinion dynamics model. Specifically, we ask the following question.

Given an opinion dynamics model, and a set of agents, each of whom has an innate opinion that reflects her core value on a topic and a susceptibility to persuasion parameter measuring her propensity for changing her opinion, how should we alter the agents’ susceptibility in order to maximize/minimize the total sum of opinions at equilibrium?

Specifically, each agent is associated with an innate opinion , and a susceptibility to persuasion parameter . We assume that each node updates its opinion according to the following dynamics: . It is well known that it converges to an equilibrium. Our goal is to optimize an objective of the equilibrium over the set of parameters .

## Contributions

**Model**. We formalize and study the following questions. Given a positive integer , find a set of nodes , and set the resistance parameters for each , in order to*maximize*/*minimize*the total sum of opinions at equilibrium. We refer to the case as the unbudgeted opinion maximization problem and the case as the budgeted opinion maximization problem.**Algorithms**. We prove that both the*maximization*and*minimization*versions of the unbudgeted opinion optimization are solvable in polynomial time using convex optimization. On the contrary, the budgeted problem is NP-hard. Furthermore, in contrast to prior work that studies opinion maximization at the innate opinion level, the objective is neither sub- nor super-modular. For this problem, we propose a greedy heuristic.**Experiments**. We evaluate our proposed methods on several real-world datasets, including a Twitter network where users express their opinions on the Delhi legislative assembly elections.