Soft Triangles for Expert Aggregation

We consider the problem of eliciting expert assessments of an uncertain parameter. The context is risk control, where there are, in fact, three uncertain parameters to be estimates. Two of these are probabilities, requiring the that the experts be guided in the concept of "uncertainty about uncertainty." We propose a novel formulation for expert estimates, which relies on the range and the median, rather than the variance and the mean. We discuss the process of elicitation, and provide precise formulas for these new distributions.