  Many people rely on online social networks as sources of news and
information, and the spread of media content with ideologies across the
political spectrum influences online discussions and impacts actions offline.
To examine the impact of media in online social networks, we generalize
bounded-confidence models of opinion dynamics by incorporating media accounts
as influencers in a network. We quantify partisanship of content with a
continuous parameter on an interval, and we formulate higher-dimensional
generalizations to incorporate content quality and increasingly nuanced
political positions. We simulate our model with one and two ideological
dimensions, and we use the results of our simulations to quantify the
"entrainment" of content from non-media accounts to the ideologies of media
accounts in a network. We maximize media impact in a social network by tuning
the number of media accounts that promote the content and the number of
followers of the accounts. Using numerical computations, we find that the
entrainment of the ideology of content spread by non-media accounts to media
ideology depends on a network's structural features, including its size, the
mean number of followers of its nodes, and the receptiveness of its nodes to
different opinions. We then introduce content quality --- a key novel
contribution of our work --- into our model. We incorporate multiple media
sources with ideological biases and quality-level estimates that we draw from
real media sources and demonstrate that our model can produce distinct
communities ("echo chambers") that are polarized in both ideology and quality.
Our model provides a step toward understanding content quality and ideology in
spreading dynamics, with ramifications for how to mitigate the spread of
undesired content and promote the spread of desired content.
