The impact of bias on the accuracy of early and late deciders in groups*

How does a decision made quickly differ from a more deliberate one? In this talk, we answer this question for a large heterogeneous population of independent agents and show how initial bias influences the accuracy of early and late deciders. In particular, we consider a population of agents who stochastically accumulative evidence until crossing a threshold, triggering a decision. Remarkably, we are able to determine the exact order statistics of this passage process in the asymptotic limit of not merely the first and last decider but of all early and late deciders. In the extreme decider case, we find that the first agent to decide almost always holds the strongest initial bias and decides accordingly. Slow agents, conversely, decide as if they held no initial bias. Hence, we conclude that in large groups an early decision reflects the initial bias of an agent, while a late decision is made as if the agent had no initial bias at all.