  When learning from others, people tend to focus their attention on those with
similar views. This is often attributed to flawed reasoning, and thought to
slow learning and polarize beliefs. However, we show that echo chambers are a
rational response to uncertainty about the accuracy of information sources, and
can improve learning and reduce disagreement. Furthermore, overextending the
range of views someone is exposed to can backfire, slowing their learning by
making them less responsive to information from others. We model a Bayesian
decision maker who chooses a set of information sources and then observes a
signal from one. With uncertainty about which sources are accurate, focusing
attention on signals close to one's own expectation can be beneficial, as their
expected accuracy is higher. The optimal echo chamber balances the credibility
of views similar to one's own against the usefulness of those further away.
