  We study the utility of social learning in a distributed detection model with
agents sharing the same goal: a collective decision that optimizes an agreed
upon criterion. We show that social learning is helpful in some cases but is
provably futile (and thus essentially a distraction) in other cases.
Specifically, we consider Bayesian binary hypothesis testing performed by a
distributed detection and fusion system, where all decision-making agents have
binary votes that carry equal weight. Decision-making agents in the team
sequentially make local decisions based on their own private signals and all
precedent local decisions. It is shown that the optimal decision rule is not
affected by precedent local decisions when all agents observe conditionally
independent and identically distributed private signals. Perfect Bayesian
reasoning will cancel out all effects of social learning. When the agents
observe private signals with different signal-to-noise ratios, social learning
is again futile if the team decision is only approved by unanimity. Otherwise,
social learning can strictly improve the team performance. Furthermore, the
order in which agents make their decisions affects the team decision.
