  This work studies sequential social learning (also known as Bayesian
observational learning), and how private communication can enable agents to
avoid herding to the wrong action/state. Starting from the seminal BHW
(Bikhchandani, Hirshleifer, and Welch, 1992) model where asymptotic learning
does not occur, we allow agents to ask private and finite questions to a
bounded subset of their predecessors. While retaining the publicly observed
history of the agents and their Bayes rationality from the BHW model, we
further assume that both the ability to ask questions and the questions
themselves are common knowledge. Then interpreting asking questions as
partitioning information sets, we study whether asymptotic learning can be
achieved with finite capacity questions. Restricting our attention to the
network where every agent is only allowed to query her immediate predecessor,
an explicit construction shows that a 1-bit question from each agent is enough
to enable asymptotic learning.
