Abstract
We examine how well someone learns when information from original sources only
reaches them after repeated person-to-person noisy relay. We characterize how many
independent chains a learner needs to access in order to accurately learn, as these
chains grow long. In the presence of random mutation of message content and trans-
mission failures, there is a sharp threshold such that a receiver fully learns if they
have access to more chains than the threshold number, and learn nothing if they have
fewer. Moreover, we show that as the distance to primary sources grows, all learning
comes from either the frequency or content of received messages, so learning only from
the more informative dimension is equivalent to full Bayesian learning. However, even
slight uncertainty over the relative rates of mutations makes learning from long chains
impossible, no matter how many distinct sources information trickles down from. This
suggests that forces which lengthen chains of communication can severely disrupt social
learning, even if they increase the frequency of communication.