A Statistical Model for Combining Biased Expert Opinions

A statistical model is developed to combine subjective estimates of an unknown parameter. The maximum likelihood estimator is a weighted geometric mean of adjusted estimates, each being adjusted to remove certain s-biases. The mean-square error of this estimator is compared to that of an unweighted geometric mean of unadjusted estimates; under the assumed model, this unweighted estimator is inferior except when there is no s-bias and when all estimates have the same uncertainty. An s-unbiased version of the maximum likelihood estimator has even smaller mean-square error in an example problem. A simple s-confidence interval estimator is derived.