Targeting interventions for displacement minimization in opinion dynamics

TL;DR

This paper addresses how to optimally intervene in social networks to minimize opinion displacement caused by adversarial influence, proposing a min-max framework with distinct strategies based on budget size.

Contribution

It introduces a novel min-max optimization model for targeted interventions in opinion dynamics, revealing different optimal strategies depending on budget constraints.

Findings

Optimal intervention acts on all nodes proportionally at high budgets.

At low budgets, intervention targets specific individuals.

The model provides a new network centrality measure for intervention planning.

Abstract

Social influence is largely recognized as a key factor in opinion formation processes. Recently, the role of external forces in inducing opinion displacement and polarization in social networks has attracted significant attention. This is in particular motivated by the necessity to understand and possibly prevent interference phenomena during political campaigns and elections. In this paper, we formulate and solve a targeted intervention problem for opinion displacement minimization on a social network. Specifically, we consider a min-max problem whereby a social planner (the defender) aims at selecting the optimal network intervention within her given budget constraint in order to minimize the opinion displacement in the system that an adversary (the attacker) is instead trying to maximize. Our results show that the optimal intervention of the defender has two regimes. For large enough budget, the optimal intervention of the social planner acts on all nodes proportionally to a new notion of network centrality. For lower budget values, such optimal intervention has a more delicate structure and is rather concentrated on a few target individuals.