We examine how agents learn when information from original sources only reaches them after noisy relay. In the presence of random mutation of message content and transmission failures, there is a sharp threshold such that a receiver fully learns if and only if they have access to more chains...

We study learning and influence in a setting where agents communicate according to an arbitrary social network and naïvely update their beliefs by repeatedly taking weighted averages of their neighbors' opinions. A focus is on conditions under which beliefs of all agents in large societies...