  Social media platforms are known to optimize user engagement with the help of
algorithms. It is widely understood that this practice gives rise to echo
chambers\emdash users are mainly exposed to opinions that are similar to their
own. In this paper, we ask whether echo chambers are an inevitable result of
high engagement; we address this question in a novel model. Our main
theoretical results establish bounds on the maximum engagement achievable under
a diversity constraint, for suitable measures of engagement and diversity; we
can therefore quantify the worst-case tradeoff between these two objectives.
Our empirical results, based on real data from Twitter, chart the Pareto
frontier of the engagement-diversity tradeoff.
