Editing Decision theory (section)

==Types of decisions==

===Choice under uncertainty=== <!-- This section is linked from [[Risk]] -->
{{Details|Expected utility hypothesis}}
The area of choice under uncertainty represents the heart of decision theory. Known from the 17th century ([[Blaise Pascal]] invoked it in his [[Pascal's Wager|famous wager]], which is contained in his ''[[Pensées]]'', published in 1670), the idea of [[expected value]] is that, when faced with a number of actions, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that will result from each course of action, and multiply the two to give an "expected value", or the average expectation for an outcome; the action to be chosen should be the one that gives rise to the highest total expected value. In 1738, [[Daniel Bernoulli]] published an influential paper entitled ''Exposition of a New Theory on the Measurement of Risk'', in which he uses the [[St. Petersburg paradox]] to show that expected value theory must be [[Norm (philosophy)|normatively]] wrong. He gives an example in which a Dutch merchant is trying to decide whether to insure a cargo being sent from Amsterdam to St. Petersburg in winter. In his solution, he defines a [[utility function]] and computes [[expected utility]] rather than expected financial value.<ref>For a review see {{cite journal |last=Schoemaker |first=P. J. |title=The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations|journal=Journal of Economic Literature|volume=20|year=1982|issue=2 |pages=529–563 |jstor=2724488}}</ref>

In the 20th century, interest was reignited by [[Abraham Wald|Abraham Wald's]] 1939 paper pointing out that the two central procedures of [[frequentist statistics|sampling-distribution-based]] statistical-theory, namely [[statistical hypothesis testing|hypothesis testing]] and [[estimation theory|parameter estimation]], are special cases of the general decision problem.<ref>{{cite journal | title = Contributions to the Theory of Statistical Estimation and Testing Hypotheses | last = Wald | first = Abraham | author-link = Abraham Wald | journal = [[Annals of Mathematical Statistics]] | volume = 10 | issue = 4 | pages = 299–326 | year = 1939 | doi = 10.1214/aoms/1177732144 | mr = 932 | doi-access = free }}</ref> Wald's paper renewed and synthesized many concepts of statistical theory, including [[loss function]]s, [[risk function]]s, [[admissible decision rule]]s, [[prior probability|antecedent distributions]], [[admissible decision rule#Bayes rules|Bayesian procedures]], and [[minimax]] procedures. The phrase "decision theory" itself was used in 1950 by [[E. L. Lehmann]].<ref>{{cite journal |vauthors=Lehmann EL |author-link=E. L. Lehmann |title=Some Principles of the Theory of Testing Hypotheses |journal=[[Annals of Mathematical Statistics]] |year=1950 |volume=21 |issue=1 |pages=1–26 |jstor=2236552 |doi=10.1214/aoms/1177729884 |doi-access=free}}</ref>

The revival of [[subjective probability]] theory, from the work of [[Frank P. Ramsey|Frank Ramsey]], [[Bruno de Finetti]], [[L. J. Savage|Leonard Savage]] and others, extended the scope of expected utility theory to situations where subjective probabilities can be used. At the time, von Neumann and Morgenstern's theory of [[expected utility]]<ref>{{Cite book|title=Theory of Games and Economic Behavior | edition = third |last1=Neumann|first1=John von|last2=Morgenstern|first2=Oskar | name-list-style = vanc |publisher=Princeton University Press|year=1953 |orig-year=1944|location=Princeton, NJ}}</ref> proved that expected utility maximization followed from basic postulates about rational behavior.

The work of [[Maurice Allais]] and [[Daniel Ellsberg]] showed that human behavior has systematic and sometimes important departures from expected-utility maximization ([[Allais paradox]] and [[Ellsberg paradox]]).<ref>{{Cite book|title=Expected Utility Hypotheses and the Allais Paradox: Contemporary Discussions of the Decisions Under Uncertainty with Allais' Rejoinder|last1=Allais|first1=M.|last2=Hagen|first2=G. M.|date=2013|publisher=Springer Science & Business Media|isbn=9789048183548|location=Dordrecht|pages=333}}</ref> The [[prospect theory]] of [[Daniel Kahneman]] and [[Amos Tversky]] renewed the empirical study of [[behavioral economics|economic behavior]] with less emphasis on rationality presuppositions. It describes a way by which people make decisions when all of the outcomes carry a risk.<ref>{{Cite book|title=Judgment Under Uncertainty: Heuristics and Biases|last1=Morvan|first1=Camille|last2=Jenkins|first2=William J.|date=2017|publisher=Macat International Ltd.|isbn=9781912303687|location=London|pages=13}}</ref> Kahneman and Tversky found three regularities – in actual human decision-making, "losses loom larger than gains"; people focus more on ''changes'' in their utility-states than they focus on absolute utilities; and the estimation of subjective probabilities is severely biased by [[anchoring (cognitive bias)|anchoring]].

===Intertemporal choice===
{{Main|Intertemporal choice}}
Intertemporal choice is concerned with the kind of choice where different actions lead to outcomes that are realized at different stages over time.<ref>{{Cite book|title=Essays In Decision Making: A Volume in Honour of Stanley Zionts|last1=Karwan|first1=Mark|last2=Spronk|first2=Jaap|last3=Wallenius|first3=Jyrki|date=2012|publisher=Springer Science & Business Media|isbn=9783642644993|location=Berlin|pages=135}}</ref> It is also described as [[cost-benefit]] decision making since it involves the choices between rewards that vary according to magnitude and time of arrival.<ref>{{Cite book|title=Aging and Decision Making: Empirical and Applied Perspectives|last1=Hess|first1=Thomas M.|last2=Strough|first2=JoNell|last3=Löckenhoff|first3=Corinna|author3-link= Corinna Löckenhoff |date=2015|publisher=Elsevier|isbn=9780124171558|location=London|pages=21}}</ref> If someone received a windfall of several thousand dollars, they could spend it on an expensive holiday, giving them immediate pleasure, or they could invest it in a pension scheme, giving them an income at some time in the future. What is the optimal thing to do? The answer depends partly on factors such as the expected [[interest rate|rates of interest]] and [[inflation]], the person's [[life expectancy]], and their confidence in the pensions industry. However even with all those factors taken into account, human behavior again deviates greatly from the predictions of prescriptive decision theory, leading to alternative models in which, for example, objective interest rates are replaced by [[hyperbolic discounting|subjective discount rates]].{{cn|date=April 2025}}

===Interaction of decision makers===
[[File:NWC wargame 1958.jpg|alt=An electronic simulation room at the Naval War College during a 1958 wargame: against the far wall, a large map shows the outline of landmasses and some firing solutions.  Suited men sit at desks on the floor, papers in front of them, most staring up at the map.  Against the right wall, uniformed ensigns plot ship locations on (washed-out) screens.  |thumb|[[Military planners]] often conduct extensive [[Simulation|simulations]] to help predict the decision-making of relevant actors.  ]]
Some decisions are difficult because of the need to take into account how other people in the situation will respond to the decision that is taken. The analysis of such social decisions is often treated under decision theory, though it involves mathematical methods. In the emerging field of [[socio-cognitive]] engineering, the research is especially focused on the different types of distributed decision-making in human organizations, in normal and abnormal/emergency/crisis situations.<ref>Crozier, M. & Friedberg, E. (1995). "Organization and Collective Action. Our Contribution to Organizational Analysis" in Bacharach S.B, Gagliardi P. & Mundell P. (Eds). ''Research in the Sociology of Organizations''. Vol. XIII, Special Issue on European Perspectives of Organizational Theory, Greenwich, CT: JAI Press.</ref>

===Complex decisions===
Other areas of decision theory are concerned with decisions that are difficult simply because of their complexity, or the complexity of the organization that has to make them. Individuals making decisions are limited in resources (i.e. time and intelligence) and are therefore [[Bounded rationality|boundedly rational]]; the issue is thus, more than the deviation between real and optimal behavior, the difficulty of determining the optimal behavior in the first place. Decisions are also affected by whether options are framed together or separately; this is known as the [[distinction bias]].{{cn|date=April 2025}}