A Few Results about Averaging Models: Sometimes An Individual Performs Better Than A Crowd

Given a collection of computational models that all estimate values of the same process, we compare the performance of the average of the collection to the individual member whose estimates are best. We define performance as the ability of a model, or average, to reproduce a sequence of observations of the process. We identify a condition that determines if a single model performs better than the average. That result also yields a necessary condition for when the average performs better than any individual model. We give sharp bounds for the performance of the average, and we conclude with some comments on model selection.