Modeling the Impact of Timeline Algorithms on Opinion Dynamics Using Low-rank Updates

Timeline algorithms are key parts of online social networks, but duringrecent years they have been blamed for increasing polarization and disagreementin our society. Opinion-dynamics models have been used to study a variety ofphenomena in online social networks, but an open question remains on how thesemodels can be augmented to take into account the fine-grained impact ofuser-level timeline algorithms. We make progress on this question by providinga way to model the impact of timeline algorithms on opinion dynamics.Specifically, we show how the popular Friedkin–Johnsen opinion-formation modelcan be augmented based on aggregate information, extracted from timeline data.We use our model to study the problem of minimizing the polarization anddisagreement; we assume that we are allowed to make small changes to the users'timeline compositions by strengthening some topics of discussion and penalizingsome others. We present a gradient descent-based algorithm for this problem,and show that under realistic parameter settings, our algorithm computes a(1+ε)-approximate solution in time Õ(m√(n)(1/ε)), where m is the number of edges in the graph and n isthe number of vertices. We also present an algorithm that provably computes anε-approximation of our model in near-linear time. We evaluate ourmethod on real-world data and show that it effectively reduces the polarizationand disagreement in the network. Finally, we release an anonymized graphdataset with ground-truth opinions and more than 27 000 nodes (the previouslylargest publicly available dataset contains less than 550 nodes).