Decision Sciences Journal
Volume 31, Number 2
Spring 2000
Distribution of Aggregate Utility Using Stochastic Elements
of Additive Multiattribute Utility Models
Herbert Moskowitz and Jen Tang
Krannert Graduate School of Management, Purdue University, West
Lafayette, IN 47907-1310, email: herbm@mgmt.purdue.edu, jtang@mgmt.purdue.edu
Peter Lam
PAREXEL International Corporation, 195 West Street, Waltham,
MA 02451
ABSTRACT. Conventionally, elements of a multiattribute
utility model characterizing a decision maker’s preferences,
such as attribute weights and attribute utilities, are treated
as deterministic, which may be unrealistic because assessment
of such elements can be imprecise and erroneous, or differ among
a group of individuals. Moreover, attempting to make precise
assessments can be time consuming and cognitively demanding.
We propose to treat such elements as stochastic variables to
account for inconsistency and imprecision in such assessments.
Under these assumptions, we develop procedures for computing
the probability distribution of aggregate utility for an additive
multiattribute utility function (MAUF), based on the Edgeworth
expansion. When the distributions of aggregate utility for all
alternatives in a decision problem are known, stochastic dominance
can then be invoked to filter inferior alternatives. We show
that, under certain mild conditions, the aggregate utility distribution
approaches normality as the number of attributes increases. Thus,
only a few terms from the Edgeworth expansion with a standard
normal density as the base function will be sufficient for approximating
an aggregate utility distribution in practice. Moreover, the
more symmetric the attribute utility distributions, the fewer
the attributes to achieve normality. The Edgeworth expansion
thus can provide a basis for a computationally viable approach
for representing an aggregate utility distribution with imprecisely
specified attribute weights and utilities assessments (or differing
weights and utilities across individuals). Practical guidelines
for using the Edgeworth approximation are given. The proposed
methodology is illustrated using a vendor selection problem.
Subject Areas: Decision Analysis, Edgeworth Expansion,
Imprecise Assessments, Multiattribute Utility Function, Stochastic
Dominance, and Weights. |