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Abstract-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-tonoise 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.

Abstract-This paper studies the quantization of prior probabilities, drawn from an ensemble, in distributed detection with data fusion by combination of binary local decisions. Design and performance equivalences between a team of agents and a more powerful single agent are obtained. Effects of identical quantization and diverse quantization on mean Bayes risk are compared. It is shown that when agents using diverse quantizers interact to agree on a perceived common risk, the effective number quantization levels is increased. With this collaboration, optimal diverse regular quantization with cells per quantizer performs as well as optimal identical quantization with cells per quantizer. Similar results are obtained for the maximum Bayes risk error criterion.

The effect of quantization of prior probabilities in a collection of distributed Bayesian binary hypothesis testing problems over which the priors themselves vary is studied, with focus on conflicting agents. Conflict arises from differences in Bayes costs, even when all agents desire correct decisions and agree on the meaning of correct. In a setting with fusion of local binary decisions by majority rule, Nash equilibrium local decision strategies are found. Assuming that agents follow Nash equilibrium decision strategies, designing quantizers for prior probabilities becomes a strategic form game; we discuss its Nash equilibria. We also propose two different constrained quantizer design games, find Nash equilibrium quantizer designs, and compare performance. The system has deadweight loss: equilibrium decisions are not Pareto optimal.

Abstract-Choosing among alternatives is a basic decision problem faced by people in all aspects of life, whether individually or collectively. Results in cognitive science suggest that people perform approximately Bayes-optimal decision making but that cognitive limitations require the coarse categorization of ensembles of problems rather than the application of optimal decision rules on a problem-by-problem basis. These observations motivate the development of a mathematical theory for Bayesian hypothesis testing with quantized prior information.This paper reviews recent results in minimum Bayes risk quantizer design and its economic implications. In the context of individual decision making, the theory explains differentials in false alarm and missed detection error rates for majority and minority subpopulations without appealing to a taste for discrimination. In group decision making by majority vote, quantizer design becomes a strategic form game. Nash equilibria are guaranteed to exist but often are not Pareto optimal. The analysis reveals precise senses in which a team of agents performs best when it is diverse and shares common goals. Finally, the implications of the theory for crowdsourcing are discussed.