Group Decision-Making Models for Sequential Tasks
Margot Kimura, Jeff Moehlis · SIAM Review · 2012
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 SPRT-based DDM, then compare the performance of each group rule under different constraints. We then generalize these group rules to the $\eta$-Total and $\eta$-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.