Approximations of Two-Attribute Utility Functions

Abstract
This report 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) = f(1)(x)g(1)(y) +...+ f(m)(x)g(m)(y) where the f(i) and/or g(i) 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.

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