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

Timeline algorithms are key parts of online social networks, but during recent years they have been blamed for increasing polarization and disagreement in our society. Opinion-dynamics models have been used to study a variety of phenomena in online social networks, but an open question remains on how these models can be augmented to take into account the fine-grained impact of user-level timeline algorithms. We make progress on this question by providing a way to model the impact of timeline algorithms on opinion dynamics. Specifically, we show how the popular Friedkin--Johnsen opinion-formation model can be augmented based on aggregate information, extracted from timeline data. We use our model to study the problem of minimizing the polarization and disagreement; we assume that we are allowed to make small changes to the users' timeline compositions by strengthening some topics of discussion and penalizing some others. We present a gradient descent-based algorithm for this problem, and show that under realistic parameter settings, our algorithm computes a $(1+\varepsilon)$-approximate solution in time $\tilde{O}(m\sqrt{n} \lg(1/\varepsilon))$, where $m$ is the number of edges in the graph and $n$ is the number of vertices. We also present an algorithm that provably computes an $\varepsilon$-approximation of our model in near-linear time. We evaluate our method on real-world data and show that it effectively reduces the polarization and disagreement in the network. Finally, we release an anonymized graph dataset with ground-truth opinions and more than 27\,000 nodes (the previously largest publicly available dataset contains less than 550 nodes).