Shifting Opinions in a Social Network Through Leader Selection

TL;DR

This paper investigates how to strategically select leaders in a social network to influence the overall opinion, using a mathematical model and algorithms, with validation on real and synthetic networks.

Contribution

It formulates the leader selection problem for opinion shifting as an NP-hard optimization, and proposes a greedy approximation algorithm with theoretical and experimental validation.

Findings

The problem of selecting leaders is NP-hard.

A greedy algorithm effectively approximates the optimal solution.

Experiments demonstrate the algorithm's effectiveness on real and synthetic networks.

Abstract

We study the French-DeGroot opinion dynamics in a social network with two polarizing parties. We consider a network in which the leaders of one party are given, and we pose the problem of selecting the leader set of the opposing party so as to shift the average opinion to a desired value. When each party has only one leader, we express the average opinion in terms of the transition matrix and the stationary distribution of random walks in the network. The analysis shows balance of influence between the two leader nodes. We show that the problem of selecting at most $k$ absolute leaders to shift the average opinion is $\mathbf{NP}$-hard. Then, we reduce the problem to a problem of submodular maximization with a submodular knapsack constraint and an additional cardinality constraint and propose a greedy algorithm with upper bound search to approximate the optimum solution. We also conduct experiments in random networks and real-world networks to show the effectiveness of the algorithm.