Sequential decision aggregation with social pressure

Abstract

This paper proposes and characterizes a sequential decision aggregation system consisting of agents performing binary sequential hypothesis testing and a fusion center which collects the individual decisions and reaches the global decision according to some threshold rule. Individual decision makers’ behaviors in the system are influenced by other decision makers, through a model for social pressure; our notion of social pressure is proportional to the ratio of individual decision makers who have already made the decisions. For our proposed model, we obtain the following results: First, we derive a recursive expression for the probabilities of making the correct and wrong global decisions as a function of time, system size, and the global decision threshold. The expression is based on the individual decision makers’ decision probabilities and does not rely on the specific individual decision-making policy. Second, we discuss two specific threshold rules: the fastest rule and the majority rule. By means of a mean-field analysis, we relate the asymptotic performance of the fusion center, as the system size tends to infinity, to the individual decision makers’ decision probability sequence. In addition to theoretical analysis, simulation work is conducted to discuss the speed/accuracy tradeoffs for different threshold rules.