🤖 AI Summary
This study investigates how social media platforms—when optimizing for user engagement—affect collective opinion dynamics, potentially leading to consensus or persistent polarization.
Method: We propose the first stochastic opinion dynamics model that explicitly incorporates the platform’s algorithmic objective, integrating social network structure (a two-community stochastic block model) with content distribution mechanisms. A novel two-agent approximation method is developed to enable analytically tractable analysis of high-dimensional systems.
Contribution/Results: We theoretically prove that the full opinion dynamics can be exactly reduced to a two-dimensional system, enabling precise characterization of phase transitions between consensus and disagreement. We quantify how platform strength and initial opinion polarization nonlinearly govern disagreement magnitude: weak platforms foster low-polarization consensus; strong platforms induce high-polarization disagreement; and intermediate strengths yield moderate polarization. Our framework bridges algorithmic design, network science, and opinion dynamics, offering rigorous insights into platform-driven societal fragmentation.
📝 Abstract
Individuals increasingly rely on social networking platforms to form opinions. However, these platforms typically aim to maximize engagement, which may not align with social good. In this paper, we introduce an opinion dynamics model where agents are connected in a social network, and update their opinions based on their neighbors' opinions and on the content shown to them by the platform. We focus on a stochastic block model with two blocks, where the initial opinions of the individuals in different blocks are different. We prove that for large and dense enough networks the trajectory of opinion dynamics in such networks can be approximated well by a simple two-agent system. The latter admits tractable analytical analysis, which we leverage to provide interesting insights into the platform's impact on the social learning outcome in our original two-block model. Specifically, by using our approximation result, we show that agents' opinions approximately converge to some limiting opinion, which is either: consensus, where all agents agree, or persistent disagreement, where agents' opinions differ. We find that when the platform is weak and there is a high number of connections between agents with different initial opinions, a consensus equilibrium is likely. In this case, even if a persistent disagreement equilibrium arises, the polarization in this equilibrium, i.e., the degree of disagreement, is low. When the platform is strong, a persistent disagreement equilibrium is likely and the equilibrium polarization is high. A moderate platform typically leads to a persistent disagreement equilibrium with moderate polarization. We analyze the effect of initial polarization on consensus and explore numerically various extensions including a three block stochastic model and a correlation between initial opinions and agents' connection probabilities.
