We study a model of information aggregation and social learning recently
proposed by Jadbabaie, Sandroni, and Tahbaz-Salehi, in which individual agents
try to learn a correct state of the world by iteratively updating their beliefs
using private observations and beliefs of their neighbors. No individual
agent's private signal might be informative enough to reveal the unknown state.
As a result, agents share their beliefs with others in their social
neighborhood to learn from each other. At every time step each agent receives a
private signal, and computes a Bayesian posterior as an intermediate belief.
The intermediate belief is then averaged with the belief of neighbors to form
the individual's belief at next time step. We find a set of minimal sufficient
conditions under which the agents will learn the unknown state and reach
consensus on their beliefs without any assumption on the private signal
structure. The key enabler is a result that shows that using this update,
agents will eventually forecast the indefinite future correctly