| Article ID: | iaor201526038 |
| Volume: | 229 |
| Issue: | 1 |
| Start Page Number: | 429 |
| End Page Number: | 450 |
| Publication Date: | Jun 2015 |
| Journal: | Annals of Operations Research |
| Authors: | Hora Stephen, Kardes Erim |
| Keywords: | decision theory: multiple criteria, stochastic processes, decision theory, artificial intelligence: expert systems |
Linear opinion pools are the most common form of aggregating the probabilistic judgments of multiple experts. Here, the performance of such an aggregation is examined in terms of the calibration and sharpness of the component judgments. The performance is measured through the average quadratic score of the aggregate. Trade‐offs between calibration and sharpness are examined and an expression for the optimal weighting of two dependent experts in a linear combination is given. Circumstances where one expert would be disqualified are investigated. Optimal weights for the multiple, dependent experts are found through a concave quadratic program.