“Rational Social Learning with Random Sampling”, Sorensen and Smith
This paper explores rational social learning in which everyone only sees unordered random samples from the action history. In this model, herds need not occur when the distant past can be sampled. If private signal strengths are unbounded and the past is not over-sampled — not forever affected by any individual — there is complete learning and a correct proportionate herd. With recursive sampling, welfare almost surely converges under the new proviso that the recent past is not over-sampled. In this case, there is almost surely complete learning with unbounded beliefs and unit sample sizes. The sampling noise in this Polya urn model induces a path-dependent structure, so that re-running the model with identical signals generally produces different outcome.