ON THE RELEVANCE OF NONSTANDARD THEORIES OF UNCERTAINTY IN MODELING AND POOLING EXPERT OPINIONS

Wu, Apostolakis and Okrent1 have recently analyzed the current status of emerging alternatives to classical probabilistic methods in the modeling and pooling of expert opinions in safety analysis of engineering systems. They have pointed out some difficulties faced by these theories, due to their relative lack of maturity. This paper pursues the investigation so as to clarify some aspects of belief functions and possibility theories, and also to point out the need for further research. A comparison between the mathematical models of expert opinion pooling offered by Bayesian probabilities, belief functions and possibility theory is carried out. It is proved that the Bayesian approach that these authors advocate suffers from the same numerical stability problems as possibilistic and evidential rules of combination in the presence of strongly conflicting information due to their strong structural similarities. The problem of dependence between experts is briefly addressed. The other main point of this paper is that a single combination rule cannot reasonably address all situations where expert opinions must be pooled. It is suggested that the framework of possibility and evidence theories offers a more flexible framework for representing and combining subjective uncertain judgments than the one of subjective probability alone although some progress is required to reach the maturity of the Bayesian theory.