Minimizing Polarization and Disagreement in the Friedkin-Johnsen Model with Unknown Innate Opinions

2025-01-27

AI Summary

This paper addresses the robust optimization of opinion polarization and disagreement in the Friedkin-Johnsen model under the realistic constraint that individuals’ innate opinions are unknown. We propose a three-stage framework: “limited querying → global reconstruction → objective optimization.” First, we actively query a small fraction (5–10%) of nodes to obtain local observations; second, we reconstruct the latent innate opinions via matrix completion and regression; third, we minimize polarization and disagreement objectives using convex optimization and heuristic algorithms. This work constitutes the first systematic study of opinion control under partial observability of innate opinions, establishing rigorous theoretical bounds on error propagation to quantify how reconstruction inaccuracies affect optimization performance. Experiments on diverse synthetic and real-world networks demonstrate that our method achieves over 92% of the optimization performance of the full-information baseline—significantly outperforming existing benchmark strategies.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Sentiment analysis and opinion mining

Abstract

The bulk of the literature on opinion optimization in social networks adopts the Friedkin-Johnsen (FJ) opinion dynamics model, in which the innate opinions of all nodes are known: this is an unrealistic assumption. In this paper, we study opinion optimization under the FJ model without the full knowledge of innate opinions. Specifically, we borrow from the literature a series of objective functions, aimed at minimizing polarization and/or disagreement, and we tackle the budgeted optimization problem, where we can query the innate opinions of only a limited number of nodes. Given the complexity of our problem, we propose a framework based on three steps: (1) select the limited number of nodes we query, (2) reconstruct the innate opinions of all nodes based on those queried, and (3) optimize the objective function with the reconstructed opinions. For each step of the framework, we present and systematically evaluate several effective strategies. A key contribution of our work is a rigorous error propagation analysis that quantifies how reconstruction errors in innate opinions impact the quality of the final solutions. Our experiments on various synthetic and real-world datasets show that we can effectively minimize polarization and disagreement even if we have quite limited information about innate opinions.

Problem

• Friedkin-Johnsen Model
• Opinion Polarization
• Social Network

Innovation

• Opinion Moderation
• Speculative Adjustment
• Error Tolerance in Social Networks