How Many Forecasters Do You Really Have? Mahalanobis Provides the Intuition for the Surprising Clemen and Winkler Result

The geometrical intuition behind the Clemen and Winkler result is provided and it is shown how the Cleman-Winkler formula breaks down i.e., gives bizarre results as the error covariance structure approaches singularity.

Abstract

How to combine expert opinions is an issue that has many aspects and even more “answers.” The problem addressed here is the incremental information an additional expert brings when he or she is correlated with the existing experts. R. T. Clemen and R. L. Winkler derive an algebraic formula that gives the surprising answer—usually very little. In this paper, we provide the geometrical intuition behind the Clemen and Winkler result. We also show how the Clemen and Winkler formula breaks down (i.e., gives bizarre results) as the error covariance structure approaches singularity.