  Randomness in scientific estimation is generally assumed to arise from
unmeasured or uncontrolled factors. However, when combining subjective
probability estimates, heterogeneity stemming from people's cognitive or
information diversity is often more important than measurement noise. This
paper presents a novel framework that models the heterogeneity arising from
experts that use partially overlapping information sources, and applies that
model to the task of aggregating the probabilities given by a group of experts
who forecast whether an event will occur or not. Our model describes the
distribution of information across experts in terms of easily interpretable
parameters and shows how the optimal amount of extremizing of the average
probability forecast (shifting it closer to its nearest extreme) varies as a
function of the experts' information overlap. Our model thus gives a more
principled understanding of the historically ad hoc practice of extremizing
average forecasts.
