Proper efficiency and cardinal utilities in multicriteria decision making

The concept of proper efficiency has been characterized in several ways in the Multicriteria Decision Making (MCDM) literature. Geoffrion has optimized a positively weighted sum of the multicriteria value functions, and Choo and Atkins have used an extended form of the generalized Tchebycheff norm. This paper investigates proper efficiency in MCDM when it is possible to represent the decision maker's risk attitudes and preferences by cardinal (especially additive cardinal) utilities. Proper efficiency is characterized by optimizing associated utility-related scalar optimization problems. More detailed relationships among proper efficiency, measure of risk aversion and allocation strategies are discussed in an asset allocation context.