Structural changes steer group opinions beyond target thresholds
Rewiring the Majority: Structural Median Opinion Control in the Friedkin-Johnsen Model
Social and Information Networks
Summary
Changing how people are connected in a social network can shift the overall group opinion in a desired direction. The paper studies how adding new connections between individuals affects the median opinion at equilibrium in a network model. The authors find that deciding the best connections to add is computationally hard, but they develop approximate methods to identify helpful links. Their experiments show success depends on network shape, where positive opinions are placed, and how open individuals are to influence. Structural interventions can be more cost-effective than directly changing individuals once realistic costs are considered.
What this means in practice
- •For social media platform designers: Design network changes like suggested friend links to guide collective opinions toward healthy or desired outcomes.
- •For marketing campaign teams: Improve message spread by adding social ties in influencer networks to steer target group opinions more efficiently.
Authors
Elisabetta Biondi, Chiara Boldrini, Andrea Passarella, Marco Conti
Abstract
Opinion control under the Friedkin-Johnsen (FJ) model has traditionally focused on modifying individual users, for example by changing their opinions or susceptibility to social influence. We study a complementary problem: can collective outcomes be steered by modifying the interaction network instead? We formulate structural median control as an edge-addition problem aimed at moving the equilibrium median beyond a target threshold. We show that the problem is NP-hard even under highly restricted settings and propose both continuous optimization methods and computationally lighter opinion-aware heuristics for selecting edge additions. Experiments on synthetic and real-world networks reveal that intervention success depends jointly on network topology, the placement of favorable opinions, and user susceptibility. Structural interventions produce the largest shifts when opinion placement and network structure allow added edges to create useful influence pathways toward the target outcome. Finally, under a homogeneous reference setting, we compare structural and node-level interventions using normalized budgets and a degree-weighted cost model. We show that, although node interventions often appear stronger under normalized budgets, structural interventions become competitive and frequently more cost-effective once the higher cost of targeting high-reach users is taken into account.