  Normative models are often used to describe how humans and animals make
decisions. These models treat deliberation as the accumulation of uncertain
evidence that terminates with a commitment to a choice. When extended to social
groups, such models often assume that individuals make independent
observations. However, individuals typically gather evidence from common
sources, and their observations are rarely independent. Here we ask: For a
group of ideal observers who do not exchange information, what is the impact of
correlated evidence on decision accuracy? We show that even when agents are
identical, correlated evidence causes decision accuracy to depend on temporal
decision order. Surprisingly, the first decider is less accurate than a lone
observer. Early deciders are less accurate than late deciders. These phenomena
occur despite the fact that the rational observers use the same decision
criterion, so they are equally confident in their decisions. We analyze
discrete and continuum evidence-gathering models to explain why the first
decider is less accurate than a lone observer when evidence is correlated.
Pooling the decisions of early deciders using a majority rule does not rescue
accuracy in the sense that such pooling results in only modest accuracy gain.
Although we analyze an idealized model, we believe that our analysis offers
insights that do not depend on exactly how groups integrate evidence and form
decisions.
