Accounting for noise in the microfoundations of information aggregation

This paper shows that the basic unit of information aggregation described by the Geanakoplos and Polemarchakis (1982) posterior revision process does not always produce public statistics that are closer to the full information posterior than the common prior. I study this process of back and forth communication between two individuals with private signals by introducing white noise into payoff computations, defining the evolution of common knowledge, and providing conjectures on the resulting public statistics. I then develop a computational method to ex-ante rank information structures on their tolerance to noise. Subjects' behavior in a laboratory experiment is consistent with the model's prediction: though the posterior revision process do move reports towards each other and towards the full information posterior, noise persists and aggregation is incomplete. As predicted, aggregation attempts in the two least noise-tolerant information structures result in public statistics that perform worse than the common prior.