Accuracy and Decision Time for Sequential Decision Aggregation

TL;DR

This paper analyzes how groups of identical agents can efficiently aggregate sequential binary decisions using threshold rules, optimizing for accuracy and decision time, with scalable computational methods and insights into large-group behavior.

Contribution

It provides a comprehensive analysis of sequential decision aggregation strategies, characterizing accuracy and timing, and explores scalability and tradeoffs for different decision rules.

Findings

Decision time for fastest rule converges to earliest individual time in large groups.

Majority rule exponentially improves accuracy over individual decisions.

Scalability of the approach is linear in group size.

Abstract

This paper studies prototypical strategies to sequentially aggregate independent decisions. We consider a collection of agents, each performing binary hypothesis testing and each obtaining a decision over time. We assume the agents are identical and receive independent information. Individual decisions are sequentially aggregated via a threshold-based rule. In other words, a collective decision is taken as soon as a specified number of agents report a concordant decision (simultaneous discordant decisions and no-decision outcomes are also handled). We obtain the following results. First, we characterize the probabilities of correct and wrong decisions as a function of time, group size and decision threshold. The computational requirements of our approach are linear in the group size. Second, we consider the so-called fastest and majority rules, corresponding to specific decision thresholds. For these rules, we provide a comprehensive scalability analysis of both accuracy and decision time. In the limit of large group sizes, we show that the decision time for the fastest rule converges to the earliest possible individual time, and that the decision accuracy for the majority rule shows an exponential improvement over the individual accuracy. Additionally, via a theoretical and numerical analysis, we characterize various speed/accuracy tradeoffs. Finally, we relate our results to some recent observations reported in the cognitive information processing literature.