Decision Analysis Working Paper Abstract
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WP030008
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Title: Uncertainty Aversion With Second-Order Utilities and Probabilities
Authors: Robert
F. Nau,
Duke University
Date: December 2002
Status: working paper
Aversion to uncertainty or ambiguity, as demonstrated by the Ellsberg paradox,
is most commonly explained by the hypothesis of kinked indifference curves
(i.e., non-smooth preferences) induced by the combination of a unique non-additive
probability measure with a state-independent cardinal utility function,
as in the Choquet and maxmin expected utility models. This paper
shows that uncertainty aversion can arise even when the decision maker
has smooth preferences and state-dependent utility, in which case probabilities
and utilities cannot be uniquely separated. Starting from the state-preference
framework of choice under uncertainty (rather than Savage’s or Anscombe-Aumann’s
frameworks), uncertainty aversion is defined and measured in direct behavioral
terms without reference to probabilistic beliefs or consequences with state-independent
utility. A simple axiomatic model of “partially separable” non-expected
utility preferences is presented, in which the decision maker satisfies
the independence axiom selectively within partitions of the state space
whose elements have similar degrees of uncertainty. As such, she
may behave like an expected-utility maximizer with respect to assets in
the same uncertainty class, while exhibiting higher degrees of risk aversion
toward assets that are more uncertain. An alternative interpretation
of the same model is that the decision maker may be uncertain about her
credal state (represented by second-order probabilities for her first-order
probabilities and utilities), and she may be averse to that uncertainty
(represented by a second-order utility function). The model is shown
to be able to account for both the Ellsberg and Allais paradoxes
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