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Utility functions are an important component of normative decision analysis. They also serve to characterize the nature of people's risk-taking attitudes. In this paper we examine various factors that make it difficult to speak of the utility function for a given person. Similarly we show that it is questionable to pool data across studies (for descriptive purposes) that differ in the elicitation methods employed. The following five sources of indeterminacy are specifically discussed. First, the certainty equivalence method generally yields more risk-seeking preferences than the probability equivalence method. Second, the probability and outcome levels used in reference lotteries induce systematic bias. Third, combining gain and loss domains yields different utility measures than separate examinations of the two domains. Fourth, whether a risk is assumed or transferred away exerts a significant influence on people's preferences in ways counter to expected utility theory. Finally, context or framing differences strongly affect choice in a non-normative manner. The above five factors are first discussed as essential choices to be made by the decision scientist in constructing Von Neumann-Morgenstern utility functions. Next, each is examined separately in view of existing literature, and demonstrated via experiments. The emerging picture is that basic preferences under uncertainty exhibit serious incompatibilities with traditional expected utility theory. An important implication of this paper is to commence development of a systematic theory of utility encoding which incorporates the many information processing effects that influence people's expressed risk preferences.