  We study the outcomes of information aggregation in online social networks.
Our main result is that networks with certain realistic structural properties
avoid information cascades and enable a population to effectively aggregate
information. In our model, each individual in a network holds a private,
independent opinion about a product or idea, biased toward a ground truth.
Individuals declare their opinions asynchronously, can observe the stated
opinions of their neighbors, and are free to update their declarations over
time. Supposing that individuals conform with the majority report of their
neighbors, we ask whether the population will eventually arrive at consensus on
the ground truth. We show that the answer depends on the network structure:
there exist networks for which consensus is unlikely, or for which declarations
converge on the incorrect opinion with positive probability. On the other hand,
we prove that for networks that are sparse and expansive, the population will
converge to the correct opinion with high probability.
