Minimizing the time to a decision

TL;DR

This paper introduces an optimal strategy for quickly determining the majority boundary decision among three independent diffusions with absorbing states, minimizing total decision time.

Contribution

It proposes a novel stopping rule that efficiently identifies the majority boundary in a trio of diffusions, optimizing decision speed.

Findings

The strategy always runs the diffusion with a median value among the three.

It minimizes the expected total time to reach a majority decision.

The approach is proven optimal within the model's framework.

Abstract

Suppose we have three independent copies of a regular diffusion on $[0,1]$ with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimizing the total time spent running the processes.