A novel approach to probability distribution aggregation

Today’s business world is highly competitive and unpredictable, so effective decision-making is of primary importance. However, it is difficult to make effective decisions when sufficient information is not available, and decision-making in such situations involves a high risk of error. Conventional statistics based approaches to such problems are not effective, because in such situations decision-making is usually in the hands of a small panel of experts. However, the expert opinions can be represented by probability distribution functions. Thus, such a problem reduces to the aggregation of a set of probability distribution functions to an aggregated or consensus distribution. In this paper, we propose a new approach to address this problem. The novelties of the proposed approach include: (1) the problem is formulated as an optimization problem and (2) the overlapping area between an individual expert’s distribution and an aggregated distribution is taken to measure the expertise level of that expert and subsequently to determine the weight of the expert. The proposed approach in this paper is illustrated by an example reported in literature handled with the Delphi method, which also shows the effectiveness of our approach.