  Understanding information exchange and aggregation on networks is a central
problem in theoretical economics, probability and statistics. We study a
standard model of economic agents on the nodes of a social network graph who
learn a binary "state of the world" S, from initial signals, by repeatedly
observing each other's best guesses.
  Asymptotic learning is said to occur on a family of graphs G_n = (V_n, E_n),
with |V_n| tending to infinity, if with probability tending to 1 as n tends to
infinity all agents in G_n eventually estimate S correctly. We identify
sufficient conditions for asymptotic learning and contruct examples where
learning does not occur when the conditions do not hold.
