Editing Expected utility hypothesis (section)

=== Savage's subjective expected utility representation ===
In the 1950s, [[Leonard Jimmie Savage]], an American statistician, derived a framework for comprehending expected utility. Savage's framework involved proving that expected utility could be used to make an optimal choice among several acts through seven axioms.<ref name = "Savage_1951">{{cite journal| vauthors = Savage LJ |date= March 1951 |title=The Theory of Statistical Decision |journal=Journal of the American Statistical Association|volume=46|issue=253|pages=55–67|doi=10.1080/01621459.1951.10500768|issn=0162-1459}}</ref> In his book, ''The Foundations of Statistics'', Savage integrated a normative account of decision making under risk (when probabilities are known) and under uncertainty (when probabilities are not objectively known). Savage concluded that people have neutral attitudes towards uncertainty and that observation is enough to predict the probabilities of uncertain events.<ref>{{cite journal| vauthors = Lindley DV |date= September 1973 |title=The foundations of statistics (second edition), by Leonard J. Savage. Pp xv, 310. £1·75. 1972 (Dover/Constable) |journal=The Mathematical Gazette|volume=57|issue=401|pages=220–221|doi=10.1017/s0025557200132589|s2cid= 164842618 |issn=0025-5572}}</ref> A crucial methodological aspect of Savage's framework is its focus on observable choices—cognitive processes and other psychological aspects of decision-making matter only to the extent that they directly impact choice.

The theory of subjective expected utility combines two concepts: first, a personal utility function, and second, a personal [[probability distribution]] (usually based on [[Bayesian probability theory]]). This theoretical model has been known for its clear and elegant structure and is considered by some researchers to be "the most brilliant axiomatic theory of utility ever developed."<ref>{{Citation|title=1. Foundations of probability theory|date=2009-01-21|doi = 10.1515/9783110213195.1 |work=Interpretations of Probability|pages=1–36 |place=Berlin, New York|publisher=Walter de Gruyter|isbn=978-3-11-021319-5 }}</ref> Instead of assuming the probability of an event, Savage defines it in terms of preferences over acts. Savage used the states (something a person doesn't control) to calculate the probability of an event. On the other hand, he used utility and intrinsic preferences to predict the event's outcome. Savage assumed that each act and state were sufficient to determine an outcome uniquely. However, this assumption breaks in cases where an individual does not have enough information about the event.

Additionally, he believed that outcomes must have the same utility regardless of state. Therefore, it is essential to identify which statement is an outcome correctly. For example, if someone says, "I got the job," this affirmation is not considered an outcome since the utility of the statement will be different for each person depending on intrinsic factors such as financial necessity or judgment about the company. Therefore, no state can rule out the performance of an act. Only when the state and the act are evaluated simultaneously is it possible to determine an outcome with certainty.<ref name = "Li_2017">{{cite journal| vauthors = Li Z, Loomes G, Pogrebna G |date=2017-05-01|title=Attitudes to Uncertainty in a Strategic Setting |journal=The Economic Journal|language=en|volume=127|issue=601|pages=809–826|doi=10.1111/ecoj.12486|issn=0013-0133|doi-access=free}}</ref>

==== Savage's representation theorem ====
[[Savage's subjective expected utility model|Savage's representation theorem]] (Savage, 1954): A preference < satisfies P1–P7 if and only if there is a finitely additive probability measure P and a function u : C → R such that for every pair of acts ''f'' and ''g''.<ref name="Li_2017" />
''f'' < ''g'' ⇐⇒ Z Ω ''u''(''f''(''ω'')) ''dP'' ≥ Z Ω ''u''(''g''(''ω'')) ''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.