Accuracy and decision time for decentralized implementations of the sequential probability ratio test

Abstract

This paper focuses on decentralized decision making in a population of individuals each implementing the sequential probability ratio test. The individual decisions are combined by a fusion center into a collective decision via an aggregation rule. For distinct aggregation rules, we study how the population size affects the performance of the collective decision making, i.e., the decision accuracy and time. We analyze two aggregation rules, the fastest rule and the majority rule. In the fastest rule, the group decision is equal to the first decision made by any individual. In the majority rule, the group decision is equal to the majority of the decisions. Under the assumption of measurement independence among individuals, we introduce a novel numerical representation of the performance of decentralized decision making. We study our settings analytically as well as numerically. Our numerical results and simulations characterize the tradeoff between accuracy and decision time as a function of the population size.