Optimal team and individual decision rules in uncertain dichotomous situations

In this paper, we consider the problem of determining the optimalteam decision rules in uncertain, binary (dichotomous) choice situations. We show that the Relative (Receiver) Operating Characteristic (ROC) curve plays a pivotal role in characterizing these rules. Specifically, the problem of finding the optimal aggregation rule involves finding a set ofcoupled operating points on the individual ROCs. Introducing the concept of a “team ROC curve”, we extend the method of characterizing decision capabilities of an individual decisionmaker (DM) to a team of DMs. Given the operating points of the individual DMs on their ROC curves, we show that the best aggregation rule is a likelihood ratio test. When the individual opinions are conditionally independent, the aggregation rule is a weighted majority rule, but with different asymmetric weights for the ‘yes’ and ‘no’ decisions. We show that the widely studied weighted majority rule with symmetric weights is a special case of the asymmetric weighted majority rule, wherein the competence level of each DM corresponds to the intersection of the main diagonal and the DM's ROC curve. Finally, we demonstrate that the performance of the team can be improved by jointly optimizing the aggregation rule and the individual decision rules, the latter possibly requiring a shift from the isolated (non-team) optimal operating point of each DM.