From ordered beliefs to numbers: How to elicit numbers without asking for them (doable but computationally difficult)

One of the most important parts of designing an expert system is elicitation of the expert's knowledge. This knowledge usually consists of facts and rules. Eliciting these rules and facts is relatively easy: the more complicated task is assigning weights (numerical or interval-valued degrees of belief) to different statements from the knowledge base. Experts often cannot quantify their degrees of belief, but they can order them (by suggesting which statements are more reliable). It is, therefore, reasonable to try to reconstruct the degrees of belief from such an ordering.In this paper, we analyze when such a reconstruction is possible, whether it lead to unique values of degrees of belief, and how computationally complicated the corresponding reconstruction problem can be. © 1998 John Wiley & Sons, Inc.