Editing Expected utility hypothesis (section)

{{Short description|Concept in economics}}
The '''expected utility hypothesis''' is a foundational assumption in [[mathematical economics]] concerning [[decision theory|decision making]] under [[uncertainty]]. It postulates that [[rational agent]]s maximize utility, meaning the subjective desirability of their actions. [[Rational choice theory]], a cornerstone of [[microeconomics]], builds this postulate to model aggregate social behaviour.

The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is <math>U(p)=\sum u(x_k)p_k </math> where <math>p_k</math> is the probability that outcome indexed by <math>k</math> with payoff <math>x_k</math> is realized, and function ''u'' expresses the utility of each respective payoff.<ref>{{Cite web|title=Expected Utility Theory {{!}} Encyclopedia.com|url=https://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/expected-utility-theory|access-date=2021-04-28|website=www.encyclopedia.com}}</ref> Graphically the curvature of the u function captures the agent's risk attitude.

For example, imagine you’re offered a choice between receiving $50 for sure, or flipping a coin to win $100 if heads, and nothing if tails. Although both options have the same average payoff ($50), many people choose the guaranteed $50 because they value the certainty of the smaller reward more than the possibility of a larger one, reflecting [[Risk aversion|risk-averse]] preferences.

Standard utility functions represent [[ordinal utility|ordinal]] preferences. The expected utility hypothesis imposes limitations on the utility function and makes utility [[cardinal number|cardinal]] (though still not comparable across individuals).

Although the expected utility hypothesis is standard in economic modeling, it is violated in psychological experiments. Psychologists and economic theorists have been developing new theories to explain these deficiencies for many years.<ref>{{Cite journal|date=2011-05-01|title=Mixture models of choice under risk|url=https://hal.archives-ouvertes.fr/hal-00631676/file/PEER_stage2_10.1016%252Fj.jeconom.2009.10.011.pdf|journal=Journal of Econometrics|language=en|volume=162|issue=1|pages=79–88|doi=10.1016/j.jeconom.2009.10.011|issn=0304-4076|last1=Conte|first1=Anna|last2=Hey|first2=John D.|last3=Moffatt|first3=Peter G.|s2cid=33410487 }}</ref> These include [[prospect theory]], [[rank-dependent expected utility]] and [[cumulative prospect theory]], and [[bounded rationality]].