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Expected utility hypothesis
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==Criticism== In the early days of the calculus of probability, classic utilitarians believed that the option with the greatest utility would produce more pleasure or happiness for the agent and, therefore, must be chosen.<ref name=":1">{{cite journal| vauthors = Oberhelman DD |date=June 2001|title=Stanford Encyclopedia of Philosophy | veditors = Zalta EN |journal=Reference Reviews|volume=15|issue=6|pages=9|doi=10.1108/rr.2001.15.6.9.311 }}</ref> The main problem with the [[Expected value|expected value theory]] is that there might not be a unique correct way to quantify utility or to identify the best trade-offs. For example, some of the trade-offs may be intangible or qualitative. Rather than [[Incentive|monetary incentives]], other desirable ends can also be included in utility, such as pleasure, knowledge, friendship, etc. Originally, the consumer's total utility was the sum of independent utilities of the goods. However, the expected value theory was dropped as it was considered too static and deterministic.<ref name=":2">{{cite book |title=Expected Utility Hypotheses and the Allais Paradox|date=1979|publisher=Springer Netherlands|isbn=978-90-481-8354-8| veditors = Allais M, Hagen O | location= Dordrecht|language=en|doi=10.1007/978-94-015-7629-1 }}</ref> The classic counter example to the expected value theory (where everyone makes the same "correct" choice) is the [[St. Petersburg paradox|St. Petersburg Paradox]].<ref name=":2" /> In empirical applications, several violations of expected utility theory are systematic, and these falsifications have deepened our understanding of how people decide. [[Daniel Kahneman]] and [[Amos Tversky]] in 1979 presented their [[prospect theory]] which showed empirically how preferences of individuals are inconsistent among the same choices, depending on the [[Framing (social sciences)|framing]] of the choices, i.e., how they are presented.<ref>{{cite journal | vauthors = Kahneman D, Tversky A | title = Prospect Theory: An Analysis of Decision under Risk. | journal = Econometrica | year = 1979 | volume = 47 | issue = 2 | pages = 263–292 | doi = 10.2307/1914185 | jstor = 1914185 | url = http://www.dklevine.com/archive/refs47656.pdf }}</ref> Like any [[mathematical model]], expected utility theory simplifies reality. The mathematical correctness of expected utility theory and the salience of its primitive concepts do not guarantee that expected utility theory is a reliable guide to human behavior or optimal practice. The mathematical clarity of expected utility theory has helped scientists design experiments to test its adequacy and to distinguish systematic departures from its predictions. This has led to the [[behavioral finance]] field, which has produced deviations from the expected utility theory to account for the empirical facts. Other critics argue that applying expected utility to economic and policy decisions has engendered inappropriate valuations, particularly when monetary units are used to scale the utility of nonmonetary outcomes, such as deaths.<ref>{{Cite web|title=Expected utility {{!}} decision theory|url=https://www.britannica.com/topic/expected-utility|access-date=2021-04-28|website=Encyclopedia Britannica|language=en}}</ref> ===Conservatism in updating beliefs=== Psychologists have discovered systematic violations of probability calculations and behavior by humans. This has been evidenced by examples such as the [[Monty Hall problem]], where it was demonstrated that people do not revise their degrees on belief in line with experimented probabilities and that probabilities cannot be applied to single cases. On the other hand, in updating probability distributions using evidence, a standard method uses [[conditional probability]], namely the [[Bayes's rule|rule of Bayes]]. An experiment on [[belief revision]] has suggested that humans change their beliefs faster when using Bayesian methods than when using informal judgment.<ref>Subjects changed their beliefs faster by conditioning on evidence (Bayes's theorem) than by using informal reasoning, according to a classic study by the psychologist Ward Edwards:<br /> * {{cite book| vauthors = Edwards W | chapter=Conservatism in Human Information Processing|editor=Kleinmuntz, B| title=Formal Representation of Human Judgment|publisher=Wiley|year=1968}} * {{cite book| vauthors = Edwards W | chapter=Conservatism in Human Information Processing (excerpted)|editor=[[Daniel Kahneman]], [[Paul Slovic]] and [[Amos Tversky]]| title=Judgment under uncertainty: Heuristics and biases|publisher=Cambridge University Press|year=1982}} * {{cite book | vauthors = Phillips LD, Edwards W |chapter=Chapter 6: Conservatism in a simple probability inference task (''Journal of Experimental Psychology'' (1966) 72: 346-354) |title=A Science of Decision Making:The Legacy of Ward Edwards | veditors = Weiss JW, Weiss DJ |isbn=978-0-19-532298-9 |page=536 |date=October 2008 |publisher= Oxford University Press}}</ref> According to the empirical results, there has been almost no recognition in decision theory of the distinction between the problem of justifying its theoretical claims regarding the properties of rational belief and desire. One of the main reasons is that people's basic tastes and preferences for losses cannot be represented with utility as they change under different scenarios.<ref name=":7">{{cite journal| vauthors = Vind K |date= February 2000 |title=von Neumann Morgenstern preferences |journal=Journal of Mathematical Economics|volume=33|issue=1|pages=109–122|doi=10.1016/s0304-4068(99)00004-x|issn=0304-4068}}</ref> ===Irrational deviations=== [[Behavioral finance]] has produced several [[generalized expected utility]] theories to account for instances where people's choices deviate from those predicted by expected utility theory. These deviations are described as "[[Rational choice theory|irrational]]" because they can depend on the way the problem is presented, not on the actual costs, rewards, or probabilities involved. Particular theories, including [[prospect theory]], [[rank-dependent expected utility]], and [[cumulative prospect theory]], are considered insufficient to predict preferences and the expected utility.<ref>{{cite journal | vauthors = Baratgin J | title = Rationality, the Bayesian standpoint, and the Monty-Hall problem | journal = Frontiers in Psychology | volume = 6 | pages = 1168 | date = 2015-08-11 | pmid = 26321986 | pmc = 4531217 | doi = 10.3389/fpsyg.2015.01168 | doi-access = free }}</ref> Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von Neumann–Morgenstern. This is because preferences and utility functions constructed under different contexts differ significantly. This is demonstrated in the contrast of individual preferences under the insurance and lottery context, which shows the degree of indeterminacy of the expected utility theory. Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von Neumann–Morgenstern. In practice, there will be many situations where the probabilities are unknown, and one operates under [[uncertainty]]. In economics, [[Knightian uncertainty]] or [[ambiguity aversion|ambiguity]] may occur. Thus, one must make assumptions about the probabilities, but the expected values of various decisions can be very [[sensitivity analysis|sensitive]] to the assumptions. This is particularly problematic when the expectation is dominated by rare extreme events, as in a [[long-tailed distribution]]. Alternative decision techniques are [[Robust decision|robust]] to the uncertainty of probability of outcomes, either not depending on probabilities of outcomes and only requiring [[scenario analysis]] (as in [[minimax]] or [[minimax regret]]), or being less sensitive to assumptions. [[Bayesian probability|Bayesian]] approaches to probability treat it as a degree of belief. Thus, they do not distinguish between risk and a wider concept of uncertainty: they deny the existence of Knightian uncertainty. They would model uncertain probabilities with [[multilevel model|hierarchical model]]s, i.e., as distributions whose parameters are drawn from a higher-level distribution ([[hyperprior]]s). ===Preference reversals over uncertain outcomes=== Starting with studies such as Lichtenstein & Slovic (1971), it was discovered that subjects sometimes exhibit signs of preference reversals about their certainty equivalents of different lotteries. Specifically, when eliciting [[certainty equivalent]]s, subjects tend to value "p bets" (lotteries with a high chance of winning a low prize) lower than "$ bets" (lotteries with a small chance of winning a large prize). When subjects are asked which lotteries they prefer in direct comparison, however, they frequently prefer the "p bets" over "$ bets".<ref>{{cite journal | vauthors = Lichtenstein S, Slovic P |year=1971|title=Reversals of preference between bids and choices in gambling decisions|journal=Journal of Experimental Psychology|volume=89|issue=1|pages=46–55|doi=10.1037/h0031207|hdl=1794/22312 |hdl-access=free}}</ref> Many studies have examined this "preference reversal", from both an experimental (e.g., Plott & Grether, 1979)<ref>{{cite journal | vauthors = Grether DM, Plott CR |year=1979|title=Economic Theory of Choice and the Preference Reversal Phenomenon|journal=[[American Economic Review]]|volume=69|issue=4|pages=623–638|jstor=1808708}}</ref> and theoretical (e.g., Holt, 1986)<ref>{{cite journal| vauthors = Holt C |year=1986|title=Preference Reversals and the Independence Axiom |journal=[[American Economic Review]]|volume=76|issue=3|pages=508–515|jstor=1813367}}</ref> standpoint, indicating that this behavior can be brought into accordance with neoclassical economic theory under specific assumptions.
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