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Expected utility hypothesis
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==== Savage's representation theorem ==== [[Savage's subjective expected utility model|Savage's representation theorem]] (Savage, 1954): A preference < satisfies P1βP7 if and only if there is a finitely additive probability measure P and a function u : C β R such that for every pair of acts ''f'' and ''g''.<ref name="Li_2017" /> ''f'' < ''g'' ββ Z Ξ© ''u''(''f''(''Ο'')) ''dP'' β₯ Z Ξ© ''u''(''g''(''Ο'')) ''dP'' <ref name="Li_2017" /> <nowiki>*</nowiki>If and only if all the axioms are satisfied, one can use the information to reduce the uncertainty about the events that are out of their control. Additionally, the theorem ranks the outcome according to a utility function that reflects personal preferences. The key ingredients in Savage's theory are: * ''States:'' The specification of every aspect of the decision problem at hand or "A description of the world leaving no relevant aspect undescribed."<ref name = "Savage_1951" /> * ''Events:'' A set of states identified by someone * ''Consequences:'' A consequence describes everything relevant to the decision maker's utility (e.g., monetary rewards, psychological factors, etc.) * '''''Acts:''''' An act is a finite-valued function that maps states to consequences.
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