When information (about products, ideas, etc.) spreads through a population by word of mouth, one might hope that the population would eventually aggregate the opinions of its individual members. However, it is also possible for a majority opinion to be lost or suppressed; for example, if a very influential individual holds a minority view. In this talk we will study the outcomes of information aggregation in social networks. We will show that networks with certain realistic structural properties avoid information cascades and enable a population to effectively learn information from individual noisy signals.

In our model, each individual in a network holds a private, independent opinion about a product or idea. Individuals declare their opinions asynchronously, can observe the declarations 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 majority opinion. 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 minority opinion with positive probability. On the other hand, we show that individual opinions will be aggregated successfully with high probability in expansive bounded-degree networks.