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

TL;DR

This work addresses how online timeline algorithms influence opinion dynamics by augmenting the Friedkin-Johnsen model with aggregate timeline information. It introduces a low-rank timeline-informed graph update that couples user-topic and influence-topic interactions to the network dynamics, and develops GDPM, a gradient-descent method with provable convergence that runs in near-linear time. A key contribution is an efficient approximation scheme for expressed opinions using a Woodbury-based decomposition and a Laplacian solver, enabling scalable optimization on large graphs, along with baselines for comparison. Empirical results on 27 real-world datasets show that the proposed approach substantially reduces the polarization-disagreement index and scales to graphs with tens of thousands of nodes, while releasing anonymized data for reproducibility. The work provides a principled framework to study and potentially mitigate polarization by adjusting aggregate information in timeline algorithms, with implications for the design of recommender systems in social networks.

Abstract

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).

Figures (13)

• Figure 1: Reduction of the disagreement--polarization index on two datasets for all of our algorithms ($L=10$). The $y$-axis shows the reduction ratio ${f(\mathbf{X}\xspace_{ \operatorname \text{ALG}\xspace })}/{f(\mathbf{X}\xspace)}$. In (a)-(b) we set $C=0.1$ and vary $\theta\in\{0.05,0.1,0.15,0.2\}$. In (c)-(d) we set $\theta=0.1$ and vary $C \in\{0.1,0.2,0.3,0.4\}$.
• Figure 2: Behavior of GDPM on $\mathbb{X}$-Large ($\theta=0.1$, $C=0.1$, $L=10$). We report the change of topic importance ($y$-axis) and the weighted average of the opinions of influential users for each topic ($x$-axis): (a) weighted innate opinions $\tau_{j,\mathbf{s}\xspace}$; (b) weighted expressed opinions before optimization $\tau_j$; (c) weighted expressed opinions after optimization $\tau_j$. (d)---(f) repeat the same plots when the algorithm must not change interest in political topics. For reference, the results are fitted with a quadratic function.
• Figure 3: Compute an approximation $\widetilde{\mathbf{z}\xspace}_{\mathbf{X}\xspace}$ of $\mathbf{z}\xspace_{\mathbf{X}\xspace}$
• Figure 4: GDPM
• Figure 5: Baselines BL-1 and BL-2

Theorems & Definitions (15)

• Lemma 1
• Proposition 3
• Corollary 4
• Proposition 5
• Theorem 6
• Lemma 7
• Lemma 8
• Lemma 9
• Lemma 10
• Claim 12