Adversarial Perturbations of Opinion Dynamics in Networks Jason - PowerPoint PPT Presentation

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Adversarial Perturbations of Opinion Dynamics in Networks Jason Gaitonde (Cornell University) EC 2020 Joint work with Jon Kleinberg (Cornell) and va Tardos (Cornell) Problem Setup Peoples opinions evolve via their interactions with

Adversarial Perturbations of Opinion Dynamics in Networks Jason Gaitonde (Cornell University) EC 2020 Joint work with Jon Kleinberg (Cornell) and Éva Tardos (Cornell)
Problem Setup • People’s opinions evolve via their interactions with others • We study the ability of an adversary to induce discord in a network with the Friedkin-Johnsen model of opinion dynamics Main Question: what is the relationship between graph structure, opinion dynamics, and an adversary’s ability to sow discord?
Main Results • For some forms of discord, entire spectral structure of network can control adversary’s power; for others, only extreme parts of spectrum matter • Network Defense: optimal node weights to minimize adversary’s power solvable via convex programming • Generalize to setting where opinion dynamics and disagreement graphs are decoupled and quantify how adversary’s power changes
Proof Techniques & Details • Write formulations of discord as quadratic forms in graph Laplacian • Courant-Fischer min-max theorem implies adversary’s power/strategy controlled by largest eigenvalue/corresponding eigenvector of quadratic form • As balance between innate opinions and network interactions changes in FJ model, adversary maximizing disagreement moves through all eigenvectors à interpolate between sparse and large cuts • For other formulations, no matter balance, uses fixed eigenvectors • With two graphs, adversary power typically increases; dictated by spectral similarity between Laplacians

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