Distributed decision making by categorically-thinking agents

Human decision makers think categorically when facing a great variety of objects due to their limited information processing capacities. The categorical thinking by Bayesian decision makers is modeled as classifying objects into a small number of categories with respect to their prior probabilities. The classification follows a quantization rule for the prior probabilities. The categorical thinking enables decision makers to handle infinitely many objects but simultaneously causes them to lose precision of prior probabilities and, consequently, of decisions. This chapter considers group decision making by imperfect agents that only knowquantized prior probabilities for use in Bayesian likelihood ratio tests. Global decisions are made by information fusion of local decisions, but information sharing among agents before local decision making is forbidden. The quantization rule of the agents is investigated so as to achieve the minimum mean Bayes risk; optimal quantizers are designed by a novel extension to the Lloyd-Max algorithm. It is proven that agents using identical quantizers are not optimal. Thus diversity in the individual agents' quantizers leads to optimal performance. In addition, for comparison, it is shown how much their performance gets better when information sharing and collaboration among agents before local decision making is allowed.