Optimal Decision Fusion Under Order Effects

This paper studies an optimal decision fusion problem with a group of human decision makers when an order effect is present. The order effect refers to situations wherein the process of decision making by a human is affected by the order of decisions. In our set-up, all human decision makers, called observers, receive the same data which is generated by a common but unknown hypothesis. Then, each observer independently generates a sequence of decisions which are modeled by employing noncommutative probabilistic models of the data and their relation to the unknown hypothesis. The use of non-commutative probability models is motivated by recent psychological studies which indicate that these non-commutative probability models are more suitable for capturing the order effect in human decision making, compared with the classical probability model. A central decision maker (CDM) receives (possibly a subset of) the observers’ decisions and decides on the true hypothesis. The considered problem becomes an optimal decision fusion problem with observations modeled using a non-commutative (Von Neumann) probability model. The structure of the optimal decision rule at the CDM is studied under two scenarios. In the first scenario, the CDM receives the entire history of the observers’ decisions whereas in the second scenario, the CDM receives only the last decision of each observer. The perfromance of the optimal fusion rule is numerically evaluated and compared with the optimal fusion rule derived when using a classical probability model.