Decision Analysis Working Paper Abstract
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WP030023
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Title: Utility Transversality: A Value-Based Approach
Authors:
James E. Matheson Chairman, SmartOrg, Inc. and Stanford University
and Ali Abbas
Stanford University
Date: October 2003
Status: Working Paper
We examine multiattribute decision problems where a value function is specified
over the attributes of a decision problem, as is typically done in the
deterministic phase of a decision analysis. When uncertainty is present,
a utility function is then assigned over the value function to represent
the risk attitude of the decision maker towards value. With this structure,
we derive a “chain rule” for deriving the risk attitude towards any attribute
from the risk attitude of the utility function towards value combined with
a “risk attitude” induced by the value function. This shows that
the value function plays a major role in determining risk attitude towards
an attribute.
We then define utility transversality equations, and show how the risk
attitude of one attribute may be derived from the risk attitude of another
through knowledge of the value function. In this sense there is only
one dimension of risk attitude once the value function is determined. Specification
of the risk attitude on one attribute thus determines the risk attitude
of all other attributes, through transversality. Value functions that do
not induce risk attitude are defined as risk neutral. This important class
of value functions includes the multilinear family. We present several
examples to illustrate how this approach unifies the derivation of several
classical results.
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