Measuring the vague meanings of probability terms.

Abstract

Can the vague meanings of probability terms such as doubtful probable or likely be expressed as membership functions over the [0 1] probability interval? A function for a given term would assign a membership value of zero to probabilities not at all in the vague concept represented by the term a membership value of one to probabilities definitely in the concept and intermediate membership values to probabilities represented by the term to some degree. A modified pair-comparison procedure was used in two experiments to empirically establish and assess membership functions for several probability terms. Subjects performed two tasks in both experiments: They judged (a) to what degree one probability rather than another was better described by a given probability term and (b) to what degree one term rather than another better described a specified probability. Probabilities were displayed as relative areas on spinners. Task a data were analyzed from the perspective of conjoint-measurement theory and membership function values were obtained for each term according to various scaling models. The conjoint-measurement axioms were well satisfied and goodness-of-fit measures for the scaling procedures were high. Individual differences were large but stable. Furthermore the derived membership function values satisfactorily predicted the judgments independently obtained in task b. The results support the claim that the scaled values represented the vague meanings of the terms to the individual subjects in the present experimental context. Methodological implications are discussed as are substantive issues raised by the data regarding the vague meanings of probability terms. (authors)