  We show that it can be suboptimal for Bayesian decision-making agents
employing social learning to use correct prior probabilities as their initial
beliefs. We consider sequential Bayesian binary hypothesis testing where each
individual agent makes a binary decision based on an initial belief, a private
signal, and the decisions of all earlier-acting agents---with the actions of
precedent agents causing updates of the initial belief. Each agent acts to
minimize Bayes risk, with all agents sharing the same Bayes costs for Type I
(false alarm) and Type II (missed detection) errors. The effect of the set of
initial beliefs on the decision-making performance of the last agent is
studied. The last agent makes the best decision when the initial beliefs are
inaccurate. When the private signals are described by Gaussian likelihoods, the
optimal initial beliefs are not haphazard but rather follow a systematic
pattern: the earlier-acting agents should act as if the prior probability is
larger than it is in reality when the true prior probability is small, and vice
versa. We interpret this as being open minded toward the unlikely hypothesis.
The early-acting agents face a trade-off between making a correct decision and
being maximally informative to the later-acting agents.
