The role of prior in optimal team decisions for pattern recognition

Optimal team decision making subject to error-prone team members with different capabilities has been studied extensively—particularly in the context of binary classification. The over-arching goal is to correctly classify an object as either being a True or a False Target. Each team member with known Type I and II error rates is asked whether or not he determines the object to be a True Target. Based on the members’ responses, a group decision is made about the identity of the object. We are interested in the optimal team decision rule that results in the least error rate or probability of misclassification. This is a widely researched topic, having applications in pattern recognition, organizational decision making, social (dichotomous) choice situations, reliability studies etc.; however, the obvious connection to information theory is missing. In this work, we establish the optimal team decision rules by direct application of Bayes decision theory. In doing so, we bring out the key role played by the parameter $\alpha$ that represents the known a priori probability that the object is a True Target. In particular, for a homogeneous team composition, we establish the criteria whence a majority voting scheme is optimal. Whereupon, it immediately follows that the higher the prior, α, the fewer the number of affirmative votes needed to classify the object as a True Target.

Keywords

pattern recognition, maximum $\textit{a posteriori}$ estimate, majority voting, dichotomous choice

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Published 12 August 2016