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

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