Functional Relationships Between Risky and Riskless Multiattribute Utility Functions.
Abstract
Expected utility theory and conjoint measurement theory form two major classes of models and assessment procedures to construct multi-attribute utility functions. In conjoint measurement theory a value function v is constructed which preserves preferences among riskless multi-attributed outcomes. The risky utility function u, constructed in the framework of expected utility theory, also preserves such riskless preferences. In addition, u is an appropriate guide for decisions under uncertainty since its expectation preserves risky preferences among gambles. Since both u and v are order preserving functions, they must be related by a strictly increasing transformation. However, u and v need not coincide or be related through any special functional forms, unless some simple decomposition forms are assumed. More restricted functional relationships obtain, if u and v are assumed to be either additive or multiplicative. In particular, u can be shown to be linearily, logarithmically, or exponentially related to v, depending on which function is additive and which is multiplicative. The paper proves such functional relationships based on the theory of functional equations, and techniques are described to assess the parameters of these functions. The results are discussed from a behavioral standpoint of interpretating the form and shape of multi-attribute utility functions and from a practical standpoint of simplifying multi-attribute utility assessment.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1979
- Accession Number
- ADA182908
Entities
People
- Detlof Von Winterfeldt
Organizations
- University of Southern California