Ratio-Scale Elicitation of Degrees of Support

Abstract

During the last decade, the computational paradigms known as inflzcence diagrams and belief networks have become to dominate the diagnostic expert systems field. Using elaborate collections of nodes and arcs, these representations describe how propositions of interest interact with each other through a variety of causal and predictive links. The links are parameterized with inexact degrees of support, typically expressed as subjective conditional probabilities or likelihood ratios. To date, most of the research in this area has focused on developing efficient belief-revision calculi to support decision making under uncertainty. Taking a different perspective, this paper focuses on the inputs of these calculi, i.e. on the human-supplied degrees of support which provide the currency of the belief revision process. Traditional methods for eliciting subjective probability functions are of little use in rule-based settings, where propositions of interest represent causally related and mostly discrete random variables. We describe ratio-scale and graphical methods for (i) eliciting degrees of support from human experts in a credible manner, and (ii) transforming them into the conditional probabilities and likelihood-ratios required by standard belief revision algorithms. As a secondary contribution, the paper offers a new graphical justification to eigenvector techniques for smoothing subjective answers to pair-wise elicitation questions.