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Abstract In this article nonexpected utility theories are reviewed, which focuses on four controversial axioms underlying Savage's subjective expected utility theory. For each axiom, we present practical concerns raised by each axiom along with Savage's defense of that axiom. We then discuss efforts to address these problems that are consistent with Savage's axioms (which we refer to as paradigm preserving ) as well as efforts to address these problems that relax or violate Savage's axioms (which we refer to as paradigm shifting. ) We conclude that this tension between paradigm‐preserving versus paradigm‐shifting approaches to address problems in Savage's formulation has been invaluable.
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