Investigating Utility and Value Functions with an “Assessment Cube”

Abstract

Recent studies (McCord, 1986; McCord and de Neufville, 1986) indicate that new methods can reduce some of the difficulties encountered when assessing von Neumann-Morgenstern utility functions over single dimensional outcomes (McCord and de Neufville, 1985, 1983; Hershey et al., 1982; Allais, 1979). But the outcomes of realistic decision problems are characterized by more than one dimension or attribute. And although “multi-attribute” utility functions have been used in such problems for some time (Keeney and Raiffa, 1976), there is no data indicating the validity of these functions. Experience with utility functions over one attribute implies that empirical investigations must be performed before any confidence can be placed in an assessed multi-attribute utility function. In this paper we develop a new research instrument, the three-dimensional “assessment cube,” to investigate the sensitivity of two-dimensional utility functions to the parameters used in their assessment. The cube can also be used to determine the validity of the “pricing out” concept (Keeney and Raiffa, 1976) when constructing value functions under certainty. We also present empirical results obtained with this instrument which indicate that the utility functions do, indeed, depend on the values of the assessment parameters and that the “pricing out” method can lead to invalid results.