In the last few years two fundamentally different measurement approaches have been developed to model multiattribute preferences. The first is based on expected utility theory, which uses risky preferences among gambles to construct a utility function over multiattribute outcomes. The second is founded in difference measurement, which asks for riskless judgments about strength of preferences to derive a value function. This paper presents conditions under which both representations are related by closed form functional relationships. We reduce functional equations which relate the two representations to basic Cauchy type equations, and show that these functional relationships are very simple, if the value function and the utility function is either additive or multiplicative. The functional relationships are then used to predict empirical relationships between value functions and utility functions in an experimental evaluation of hypothetical job offers. The results indicate that predictions based on the theoretical relationship are equal or better than a simple linear prediction for nine subjects out of ten. Implications for the interpretation and application of value functions and utility functions are discussed.
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