Marketing Papers

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Working Paper

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Management Science





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Von Neumann-Morgenstern (vN-M) utility theory is the dominant theoretical model of risk preference. Recently, market researchers have adapted vN-M theory to model consumer risk preference. But, most applications assess utility functions by asking just n questions to specify n parameters. However, any questioning format, especially under market research conditions, introduces measurement error. This paper explores the implications of measurement error on the estimation of the unknown parameters in vN-M utility functions and provides procedures to deal with measurement error.

We assume that the functional form of the utility function, but not its parameters, can be determined a priori through qualitative questioning. We then model measurement error as if question format and other influences cause the consumer to choose the unknown “risk parameter” from a probability distribution and to make his decisions accordingly. We provide procedures to estimate the unknown parameters when the measurement error is either (a) Normal or (b) Exponential.

Uncertainty in risk parameters induces uncertainty in utility and expected utility, and hence uncertainty in choice outcomes. Thus, we derive the induced probability distributions of the consumer's utility and the estimators for the implied probability that an alternative is chosen.

Results are obtained for both the standard decision analysis “preference indifference” question format and for a “revealed preference” format in which the consumer is asked simply to choose between two risky alternatives.

Since uniattribute functions illustrate the essential risk preference properties of vN-M functions, we emphasize uniattribute results. We also provide multiattribute estimation procedures. Numerical examples illustrate the analytical results.

Copyright/Permission Statement

Originally published in Management Science © 1985 INFORMS

This is a pre-publication version. The final version is available at


marketing, utility theory, risk modeling



Date Posted: 15 June 2018

This document has been peer reviewed.