Minimizing Polarization and Disagreement in the Friedkin-Johnsen Model with Unknown Innate Opinions
Federico Cinus, Atsushi Miyauchi, Yuko Kuroki, Francesco Bonchi
TL;DR
This work tackles opinion optimization under the Friedkin–Johnsen model when innate opinions are unknown by introducing a budgeted, three-step framework: select a small set of nodes to query, reconstruct the remaining innate opinions, and optimize a chosen objective using the reconstructed data. It provides a theoretical error-propagation bound linking reconstruction accuracy to optimization quality, and derives explicit Lipschitz constants for six objective functions (P-Dir, D-Dir, PD-Dir; P-Undir, D-Undir, PD-Undir). The framework combines node-selection heuristics, reconstruction methods (Label Propagation, Graph Neural Networks, Graph Signal Processing), and optimization approaches (gradient-based for directed graphs, SDP for the undirected PD-Undir) and demonstrates effectiveness on real and synthetic networks, achieving polarization/disagreement reductions with limited innate-information. These results offer practical pathways for mitigating echo chambers in large-scale social networks under information constraints and suggest directions for scalable, robust, and ethics-conscious extensions.
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.