Axiomatic Foundations of Expected Utility and Subjective Probability
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1.5.1 Expected Multi-Utility Representation Under Risk
Aumann (1962) was the first to model expected utility under risk without the com-
pleteness axiom.
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Invoking the algebraic approach, Shapley and Baucells (1998) char-
acterized in complete expected utility preferences over risky prospects whose domain
is lotteries. They showed that relaxing the completeness axiom while maintaining the
other aspects of the theory, one risky prospect, or lottery, is weakly preferred over
another only if its expected utility is greater for a set of von Neumann–Morgenstern
utility functions. ...
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