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.
Uncertainly
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.
