Group Decision-Making Models for Sequential Tasks

The sequential probability ratio test (SPRT) and related drift-diffusion model (DDM) are optimal for choosing between two hypotheses using the minimal (average) number of samples and relevant for modeling the decision-making process in human observers. This work extends these models to group decision making. Previous works have focused almost exclusively on group accuracy; here, we explicitly address group decision time. First, we derive explicit solutions for the error rate and probability distribution function of decision times for a group of independent, (possibly) nonidentical decision makers using one of three simple rules: Race, Majority Total, and Majority First. We illustrate our solutions with a group of N i.i.d. decision makers who each make an individual decision using the SPRTbased DDM, then compare the performance of each group rule under different constraints. We then generalize these group rules to the η-Total and η-First schemes, to demonstrate the flexibility and power of our approach in characterizing the performance of a group, given the performance of its individual members.