  In the age of information abundance, attention is a coveted resource. Social
media platforms vigorously compete for users' engagement, influencing the
evolution of their opinions on a variety of topics. With recommendation
algorithms often accused of creating "filter bubbles", where like-minded
individuals interact predominantly with one another, it's crucial to understand
the consequences of this unregulated attention market. To address this, we
present a model of opinion dynamics on a multiplex network. Each layer of the
network represents a distinct social media platform, each with its unique
characteristics. Users, as nodes in this network, share their opinions across
platforms and decide how much time to allocate in each platform depending on
its perceived quality. Our model reveals two key findings. i) When examining
two platforms - one with a neutral recommendation algorithm and another with a
homophily-based algorithm - we uncover that even if users spend the majority of
their time on the neutral platform, opinion polarization can persist. ii) By
allowing users to dynamically allocate their social energy across platforms in
accordance to their homophilic preferences, a further segregation of
individuals emerges. While network fragmentation is usually associated with
"echo chambers", the emergent multi-platform segregation leads to an increase
in users' satisfaction without the undesired increase in polarization. These
results underscore the significance of acknowledging how individuals gather
information from a multitude of sources. Furthermore, they emphasize that
policy interventions on a single social media platform may yield limited
impact.
