Approximations of Two-Attribute Utility Functions

This paper considers the assessment of von Neumann-Morgenstern utility functions u defined on two attributes from the viewpoint of mathematical approximation theory. It focuses on approximations v of u that can be written as v(x, y) = f1(x)g1(y) + ⋯ + fm(x)gm(y) where the fi and/or gi are based on single-attribute conditional utility functions. The paper does not rely on independence axioms that enable u(x, y) to be expressed in simplified forms when they are valid.