  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.
