Minimizing Polarization from Partially to Fully Observable Initial Opinions
Abstract: This paper investigates the problem of minimizing polarization within a network, operating under the foundational assumption that the evolution of underlying opinions adheres to the most prevalent model, the Friedkin-Johnson (FJ) model. Although the objective function is non-convex, we show that for this problem, every local minimum is a global minimum. We extend this characterization to encompass a comprehensive class of matrix functions, including those pertinent to polarization and multiperiod polarization, even when addressing scenarios involving stubborn actors. Leveraging the geometry of the function, we propose a novel non-convex framework for this class of matrix functions and demonstrate its practical efficacy for minimizing polarization. Through empirical assessments conducted in real-world network scenarios, our proposed approach consistently outperforms existing state-of-the-art methodologies. Moreover, we extend our work to encompass a novel problem setting that has not been previously studied, wherein the observer possesses access solely to a subset of initial opinions. Within this agnostic framework, we introduce a nonconvex relaxation methodology with similar theoretical guarantees to mitigate polarization.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: The updated draft (version 2.0) incorporates the reviewers' suggestions. All new changes specific to version 2.0 are highlighted in orange, while revisions from the earlier version, addressing the initial reviewer comments, are marked in blue for clarity and ease of reference.
Assigned Action Editor: ~Jacek_Cyranka1
Submission Number: 3861
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