Collaborative human decision making with random local thresholds

This paper considers a collaborative human decision making framework in which local decisions made at the individual agents are combined at a moderator to make the final decision. More specifically, we consider a binary hypothesis testing problem in which a group of n people makes individual decisions on which hypothesis is true based on a threshold based scheme and the thresholds are modeled as random variables. We assume that, in general, the decisions are not received by the moderator perfectly and the communication errors are modeled via a binary asymmetric channel. Assuming that the moderator does not have the knowledge of exact values of thresholds used by the individual decision makers but has probabilistic information, the performance in terms of the probability of error of the likelihood ratio based decision fusion scheme is derived when there are two agents in the decision making system. We show that the statistical parameters of the threshold distributions have optimal set of values which result in the minimum probability of error and we analytically derive these optimal values under certain conditions. We further provide detailed performance comparison to the case where the likelihood ratio based decision fusion is performed at the moderator with exact knowledge of the thresholds used by individual agents. For an arbitrary number of human agents n(> 2), we derive the performance of decision fusion with majority rule using certain approximations when the individual thresholds are modeled as random variables.