  It is well understood that the structure of a social network is critical to
whether or not agents can aggregate information correctly. In this paper, we
study social networks that support information aggregation when rational agents
act sequentially and irrevocably. Whether or not information is aggregated
depends, inter alia, on the order in which agents decide. Thus, to decouple the
order and the topology, our model studies a random arrival order.
  Unlike the case of a fixed arrival order, in our model, the decision of an
agent is unlikely to be affected by those who are far from him in the network.
This observation allows us to identify a local learning requirement, a natural
condition on the agent's neighborhood that guarantees that this agent makes the
correct decision (with high probability) no matter how well other agents
perform. Roughly speaking, the agent should belong to a multitude of mutually
exclusive social circles.
  We illustrate the power of the local learning requirement by constructing a
family of social networks that guarantee information aggregation despite that
no agent is a social hub (in other words, there are no opinion leaders).
Although the common wisdom of the social learning literature suggests that
information aggregation is very fragile, another application of the local
learning requirement demonstrates the existence of networks where learning
prevails even if a substantial fraction of the agents are not involved in the
learning process. On a technical level, the networks we construct rely on the
theory of expander graphs, i.e., highly connected sparse graphs with a wide
range of applications from pure mathematics to error-correcting codes.
