Reconciliation of Probability Distributions

Several people each express their opinion of an uncertain quantity by providing their mean and standard deviation of it. In this paper we discuss the problem of incorporating all these opinions into a single, reconciled, probability distribution for the quantity. The usual procedure is least squares, based on normality. The paper illustrates the advantages of using t-distributions, instead, and clarifies the role of the information provided by the standard deviations. Suitable approximations are provided for many cases.