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 $i \in V$ is associated with an innate opinion $s_i \in [0,1]$ , and a susceptibility to persuasion parameter $\alpha_i \in (0,1]$ . We assume that each node $i$ updates its opinion according to the following dynamics: $x_i(t+1) = \alpha_i s_i + (1-\alpha_i) \frac{ \sum\limits_{j \in N(i)} x_j(t) }{\deg(i)}$ . 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 $\{\alpha_i\}_{i \in V}$ .

Contributions

Model. We formalize and study the following questions. Given a positive integer $k$ , find a set of nodes $S \subseteq V, |S| \leq k$ , and set the resistance parameters $\alpha_i \in [\ell, u]$ for each $i \in S$ , in order to maximize /minimize the total sum of opinions at equilibrium. We refer to the case $k \geq n$ as the unbudgeted opinion maximization problem and the case $k < n$ 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.