Social teaching: Being informative vs. being right in sequential decision making

We consider sequential Bayesian binary hypothesis testing where each individual agent makes a binary decision motivated only by minimization of her own perception of the Bayes risk. The information available to each agent is an initial belief, a private signal, and decisions of all earlier-acting agents; it is follows that each agent should apply a standard Bayesian update of her belief as in social learning. The effect of the set of initial beliefs on the decision-making performance of the last agent is studied. In general, the optimal initial beliefs are not equal to the actual prior probability. When the private signals are described by Gaussian likelihoods, they also 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. Such open-mindedness increases but does not maximize the mutual information between the true hypothesis and a decision.