Normative And Descriptive Decision Theory
"Decision Theory"WikipediaDecision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying thevalues, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision.It is very closely related to the field of game theory.Normative and descriptive decision theoryMost of decision theory is normative or prescriptive, i.e., it is concerned with identifying the best decision to take,assuming an ideal decision maker who is fully informed, able to compute with perfect accuracy, and fully rational.The practical application of this prescriptive approach (how people actually make decisions) is called decisionanalysis, and aimed at finding tools, methodologies and software to help people make better decisions. The mostsystematic and comprehensive software tools developed in this way are called decision support systems.Since people usually do not behave in ways consistent with axiomatic rules, often their own, leading to violations ofoptimality, there is a related area of study, called a positive or descriptive discipline, attempting to describe whatpeople will actually do. Since the normative, optimal decision often creates hypotheses for testing against actualbehaviour, the two fields are closely linked. Furthermore it is possible to relax the assumptions of perfectinformation, rationality and so forth in various ways, and produce a series of different prescriptions or predictionsabout behaviour, allowing for further tests of the kind of decision-making that occurs in practice.In recent decades, there has been increasing interest in what is sometimes called 'behavioral decision theory' and thishas contributed to a re-evaluation of what rational decision-making requires (see for instance Anand, 1993).What kinds of decisions need a theory?Choice under uncertaintyThis area represents the heart of decision theory. The procedure now referred to as expected value was known fromthe 17th century. Blaise Pascal invoked it in his famous wager (see below), 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 giverise to more than one possible outcome with different probabilities, the rational procedure is to identify all possibleoutcomes, determine their values (positive or negative) and the probabilities that will result from each course ofaction, and multiply the two to give an expected value. The action to be chosen should be the one that gives rise tothe highest total expected value. In 1738, Daniel Bernoulli published an influential paper entitled Exposition of aNew Theory on the Measurement of Risk, in which he uses the St. Petersburg paradox to show that expected valuetheory must be normatively wrong. He also gives an example in which a Dutch merchant is trying to decide whetherto insure a cargo being sent from Amsterdam to St Petersburg in winter, when it is known that there is a 5% chancethat the ship and cargo will be lost. In his solution, he defines a utility function and computes expected utility ratherthan expected financial value (see[1] for a review).In the 20th century, interest was reignited by Abraham Wald's 1939 paper[2] pointing out that the two centralprocedures of sampling–distribution based statistical-theory, namely hypothesis testing and parameter estimation, arespecial cases of the general decision problem. Wald's paper renewed and synthesized many concepts of statisticaltheory, including loss functions, risk functions, admissible decision rules, antecedent distributions, Bayesianprocedures, and minimax procedures. The phrase "decision theory" itself was used in 1950 by E. L. Lehmann.[3]The revival of subjective probability theory, from the work of Frank Ramsey, Bruno de Finetti, Leonard Savage andothers, extended the scope of expected utility theory to situations where subjective probabilities can be used. At thistime, von Neumann's theory of expected utility proved that expected utility maximization followed from basicpostulates about rational behavior.Source URL: http://www.en.wikipedia.org/wiki/Decision theorySaylor URL: http://www.saylor.org/courses/cs408Attributed to [Wikipedia]Saylor.orgPage 1 of 6
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has systematic and sometimesimportant departures from expected-utility maximization. The prospect theory of Daniel Kahneman and AmosTversky renewed the empirical study of economic behavior with less emphasis on rationality presuppositions.Kahneman and Tversky found three regularities — in actual human decision-making, "losses loom larger thangains"; persons focus more on changes in their utility–states than they focus on absolute utilities; and the estimationof subjective probabilities is severely biased by anchoring.Castagnoli and LiCalzi (1996), Bordley and LiCalzi (2000) recently showed that maximizing expected utility ismathematically equivalent to maximizing the probability that the uncertain consequences of a decision are preferableto an uncertain benchmark (e.g., the probability that a mutual fund strategy outperforms the S&P 500 or that a firmoutperforms the uncertain future performance of a major competitor.). This reinterpretation relates to psychologicalwork suggesting that individuals have fuzzy aspiration levels (Lopes & Oden), which may vary from choice contextto choice context. Hence it shifts the focus from utility to the individual's uncertain reference point.Pascal's Wager is a classic example of a choice under uncertainty. The uncertainty, according to Pascal, is whether ornot God exists. Belief or non-belief in God is the choice to be made. However, the reward for belief in God if Godactually does exist is infinite. Therefore, however small the probability of God's existence, the expected value ofbelief exceeds that of non-belief, so it is better to believe in God. (There are several criticisms of the argument.)Intertemporal choiceThis area is concerned with the kind of choice where different actions lead to outcomes that are realised at differentpoints in time. If someone received a windfall of several thousand dollars, they could spend it on an expensiveholiday, giving them immediate pleasure, or they could invest it in a pension scheme, giving them an income at sometime in the future. What is the optimal thing to do? The answer depends partly on factors such as the expected ratesof interest and inflation, the person's life expectancy, and their confidence in the pensions industry. However evenwith all those factors taken into account, human behavior again deviates greatly from the predictions of prescriptivedecision theory, leading to alternative models in which, for example, objective interest rates are replaced bysubjective discount rates.Competing decision makersSome decisions are difficult because of the need to take into account how other people in the situation will respondto the decision that is taken. The analysis of such social decisions is more often treated under the label of gametheory, rather than decision theory, though it involves the same mathematical methods. From the standpoint of gametheory most of the problems treated in decision theory are one-player games (or the one player is viewed as playingagainst an impersonal background situation). In the emerging socio-cognitive engineering the research is especiallyfocused on the different types of distributed decision-making in human organizations, in normal andabnormal/emergency/crisis situations.The signal detection theory is based on the Decision theory.Complex decisionsOther areas of decision theory are concerned with decisions that are difficult simply because of their complexity, orthe complexity of the organization that has to make them. In such cases the issue is not the deviation between realand optimal behaviour, but the difficulty of determining the optimal behaviour in the first place. The Club of Rome,for example, developed a model of economic growth and resource usage that helps politicians make real-lifedecisions in complex situations.Source URL: http://www.en.wikipedia.org/wiki/Decision theorySaylor URL: http://www.saylor.org/courses/cs408Attributed to [Wikipedia]Saylor.orgPage 2 of 6
Paradox of choiceObserved in many cases is the paradox that more choices may lead to a poorer decision or a failure to make adecision at all. It is sometimes theorized to be caused by analysis paralysis, real or perceived, or perhaps fromrational ignorance. A number of researchers including Sheena S. Iyengar and Mark R. Lepper have published studieson this phenomenon.[4] This analysis was popularized by Barry Schwartz in his 2004 book, The Paradox of Choice.Statistical decision theorySeveral statistical tools and methods are available to organize evidence, evaluate risks, and aid in decision making.The risks of Type I and type II errors can be quantified (estimated probability, cost, expected value, etc.) and rationaldecision making is improved.One example shows a structure for deciding guilt in a criminal trial:Actual conditionDecisionGuiltyNot guiltyVerdict of'guilty'True PositiveFalse Positive(i.e. guiltreportedunfairly)Type I errorVerdict of'not guilty'FalseNegative(i.e. guiltnot detected)Type II errorTrue Negative Alternatives to decision theoryA highly controversial issue is whether one can replace the use of probability in decision theory by other alternatives.Probability theoryThe Advocates of probability theory point to: the work of Richard Threlkeld Cox for justification of the probability axioms, the Dutch book paradoxes of Bruno de Finetti as illustrative of the theoretical difficulties that can arise fromdepartures from the probability axioms, and the complete class theorems, which show that all admissible decision rules are equivalent to the Bayesian decisionrule for some utility function and some prior distribution (or for the limit of a sequence of prior distributions).Thus, for every decision rule, either the rule may be reformulated as a Bayesian procedure, or there is a (perhapslimiting) Bayesian rule that is sometimes better and never worse.Alternatives to probability theoryThe proponents of fuzzy logic, possibility theory, Dempster-Shafer theory and info-gap decision theory maintain thatprobability is only one of many alternatives and point to many examples where non-standard alternatives have beenimplemented with apparent success; notably, probabilistic decision theory is sensitive to assumptions about theprobabilities of various events, while non-probabilistic rules such as minimax are robust, in that they do not makesuch assumptions.Source URL: http://www.en.wikipedia.org/wiki/Decision theorySaylor URL: http://www.saylor.org/courses/cs408Attributed to [Wikipedia]Saylor.orgPage 3 of 6
General criticismA general criticism of decision theory based on a fixed universe of possibilities is that it considers the "knownunknowns", not the "unknown unknowns": it focuses on expected variations, not on unforeseen events, which someargue (as in black swan theory) have outsized impact and must be considered – significant events may be "outsidemodel". This line of argument, called the ludic fallacy, is that there are inevitable imperfections in modeling the realworld by particular models, and that unquestioning reliance on models blinds one to their limits.For instance, a simple model of daily stock market returns may include extreme moves such as Black Monday(1987), but might not model the market breakdowns following the September 11 attacks.References[1] Schoemaker, P. J. H. (1982). "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations". Journal of EconomicLiterature 20: 529-563.[2] Wald, Abraham (1939). "Contributions to the Theory of Statistical Estimation and Testing Hypotheses". Annals of Mathematical Statistics 10(4): 299–326. doi:10.1214/aoms/1177732144. MR932.[3] Lehmann, E. L. (1950). "Some Principles of the Theory of Testing Hypotheses" (http:/ / www. jstor. org/ stable/ 2236552). Annals ofMathematical Statistics 21 (1): 1–26. . Retrieved 4 December 2010.[4] Iyengar, Sheena S. and Lepper, Mark R. When Choice is Demotivating: Can One Desire Too Much of a Good Thing? (http:/ / www.columbia. edu/ ss957/ whenchoice. html). Retrieved 2009-Feb-12.Further reading Akerlof, George A., Yellen, Janet L. (May 1987). Rational Models of Irrational Behavior. 77. pp. 137–142. Anand, Paul (1993). Foundations of Rational Choice Under Risk. Oxford: Oxford University Press.ISBN 0198233035. (an overview of the philosophical foundations of key mathematical axioms in subjectiveexpected utility theory - mainly normative) Arthur, W. Brian (May 1991). "Designing Economic Agents that Act like Human Agents: A Behavioral Approach to Bounded Rationality". The American Economic Review 81 (2): 353–9.Berger, James O. (1985). Statistical decision theory and Bayesian Analysis (2nd ed.). New York:Springer-Verlag. MR0804611. ISBN 0-387-96098-8.Bernardo, José M.; Smith, Adrian F. M. (1994). Bayesian Theory. Wiley. MR1274699. ISBN 0-471-92416-4.Clemen, Robert (1996). Making Hard Decisions: An Introduction to Decision Analysis (2nd ed.). Belmont CA:Duxbury Press. ISBN 0534260357. (covers normative decision theory)De Groot, Morris, Optimal Statistical Decisions. Wiley Classics Library. 2004. (Originally published 1970.)ISBN 0-471-68029-X.Goodwin, Paul and Wright, George (2004). Decision Analysis for Management Judgment (3rd ed.). Chichester:Wiley. ISBN 0-470-86108-8. (covers both normative and descriptive theory)Hansson, Sven Ove. "Decision Theory: A Brief Introduction" (http://www.infra.kth.se/ soh/decisiontheory.pdf) (PDF).Khemani , Karan, Ignorance is Bliss: A study on how and why humans depend on recognition heuristics in socialrelationships, the equity markets and the brand market-place, thereby making successful decisions, 2005.Miller L (1985). "Cognitive risk-taking after frontal or temporal lobectomy—I. The synthesis of fragmentedvisual information". Neuropsychologia 23 (3): 359–69. doi:10.1016/0028-3932(85)90022-3. PMID 4022303.Miller L, Milner B (1985). "Cognitive risk-taking after frontal or temporal lobectomy—II. The synthesis ofphonemic and semantic information". Neuropsychologia 23 (3): 371–9. doi:10.1016/0028-3932(85)90023-5.PMID 4022304.North, D.W. (1968). "A tutorial introduction to decision theory". IEEE Transactions on Systems Science andCybernetics 4 (3): 200–210. doi:10.1109/TSSC.1968.300114. Reprinted in Shafer & Pearl. (also about normativedecision theory)Source URL: http://www.en.wikipedia.org/wiki/Decision theorySaylor URL: http://www.saylor.org/courses/cs408Attributed to [Wikipedia]Saylor.orgPage 4 of 6
Peterson, Martin (2009). An Introduction to Decision Theory. Cambridge University Press.ISBN 9780521716543. Raiffa, Howard (1997). Decision Analysis: Introductory Readings on Choices Under Uncertainty. McGraw Hill.ISBN 0-07-052579-X. Robert, Christian (2007). The Bayesian Choice (2nd ed.). New York: Springer. doi:10.1007/0-387-71599-1.MR1835885. ISBN 0-387-95231-4. Shafer, Glenn and Pearl, Judea, ed (1990). Readings in uncertain reasoning. San Mateo, CA: Morgan Kaufmann. Smith, J.Q. (1988). Decision Analysis: A Bayesian Approach. Chapman and Hall. ISBN 0-412-27520-1. Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation" htm). Memoirs of the National Academy of Sciences 3: 73–83. tm Ramsey, Frank Plumpton; “Truth and Probability” ( PDF ss.pdf)), Chapter VII in The Foundations of Mathematics and other Logical Essays (1931). de Finetti, Bruno (September 1989). "Probabilism: A Critical Essay on the Theory of Probability and on the Valueof Science". Erkenntnis 31. (translation of 1931 article) de Finetti, Bruno (1937). "La Prévision: ses lois logiques, ses sources subjectives". Annales de l'Institut HenriPoincaré.de Finetti, Bruno. "Foresight: its Logical Laws, Its Subjective Sources," (translation of the 1937 article (http:/ /www. numdam. org/ item?id AIHP 1937 7 1 1 0) in French) in H. E. Kyburg and H. E. Smokler (eds),Studies in Subjective Probability, New York: Wiley, 1964. de Finetti, Bruno. Theory of Probability, (translation by AFM Smith of 1970 book) 2 volumes, New York: Wiley,1974-5. Donald Davidson, Patrick Suppes and Sidney Siegel (1957). Decision-Making: An Experimental Approach.Stanford University Press. Pfanzagl, J (1967). "Subjective Probability Derived from the Morgenstern-von Neumann Utility Theory". InMartin Shubik. Essays in Mathematical Economics In Honor of Oskar Morgenstern. Princeton University Press.pp. 237–251. Pfanzagl, J. in cooperation with V. Baumann and H. Huber (1968). "Events, Utility and Subjective Probability".Theory of Measurement. Wiley. pp. 195–220. Morgenstern, Oskar (1976). "Some Reflections on Utility". In Andrew Schotter. Selected Economic Writings ofOskar Morgenstern. New York University Press. pp. 65–70. ISBN 0814777716.Source URL: http://www.en.wikipedia.org/wiki/Decision theorySaylor URL: http://www.saylor.org/courses/cs408Attributed to [Wikipedia]Saylor.orgPage 5 of 6
Article Sources and ContributorsDecision theory Source: http://en.wikipedia.org/w/index.php?oldid 412324525 Contributors: 3mta3, 7&6 thirteen, Adoniscik, Ados, Alan Dawrst, Alexwl, Andeggs, Angela, Anonyhole,Arthur Rubin, Bennose, BillieBC, Billjefferys, Bjoram11@yahoo.co.in, BlaiseFEgan, Bordley, Bracton, CRGreathouse, Cacophony, Canadaduane, ChangChienFu, ChristophDemmer,ComputerGeezer, Cretog8, Curious1i, D6, DRE, Dandv, David Eppstein, Dcljr, DimaDorfman, DoubleBlue, Duoduoduo, Esdaniel, Fennec, Finn Krogstad, Frymaster, Gandalf61, Giac, Giftlite,Gis72, Glumundrung, GoingBatty, Gomm, Goochelaar, Gurchzilla, Gustronico, Hactuary, Helgus, Hubbardaie, INic, Infarom, Ixfd64, J04n, JYOuyang, Jackdavinci, Jamelan, Jeff3000, Jheald,Jimmaths, Jiuguang Wang, Jmath666, John Quiggin, Jon Awbrey, Jwdietrich2, KSchutte, Karada, KenKendall, Kiefer.Wolfowitz, Kpmiyapuram, Kzollman, Lucidish, Magmi, Mandarax,Matdrodes, Matt.voroney, Mdd, Melcombe, Michael Hardy, Michael Slone, Miskin, Mmmarilyn, Nbarth, Neelix, NeoJustin, Nesbit, NewEconomist, NoychoH, Nrlsouza, Ohnoitsjamie, Orion88,Othercriteria, Pa68, Paulscrawl, Pbech, Phiwum, Phronetic, Posiebers, RDBrown, RJBurkhart, RJBurkhart3, Rd232, Rich Farmbrough, RichardF, Rjwilmsi, Rlsheehan, Robinh, Rodii, Seglea,Shoefly, Slach, Smellyfarts001, Snoyes, Stephensuleeman, Stw, Taxman, Terra Novus, Tesseract2, Themepark, Themusicgod1, Think Fast, Thomasmeeks, Trade2tradewell, Trialsanderrors,Twins Too!, U89djt, Verne Equinox, Volunteer Marek, WayneToms, WikiWikiWilson, Wile E. Heresiarch, Winterfors, Xyzzyplugh, Zvika, 124 anonymous editsLicenseCreative Commons Attribution-Share Alike 3.0 Unportedhttp:/ / creativecommons. org/ licenses/ by-sa/ 3. 0/Source URL: http://www.en.wikipedia.org/wiki/Decision theorySaylor URL: http://www.saylor.org/courses/cs408Attributed to [Wikipedia]Saylor.orgPage 6 of 6
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. It is very closely related to the field of game theory. Normative and descriptive decision theory
The distinction between normative and descriptive decision theories is, in principle, very simple. We may, therefore, expect descriptive falsifications of a decision theory to be accompanied by claims that the theory is invalid from a normative point of view.
1. What is decision theory?.5 1.1 The decision disciplines 5 1.2 Decision processes 7 1.3 Decision matrices 11 1.4 Classification of decision theories 13 1.4.1 Normative and descriptive theories 14 1.4.2 Individual and collective decision-making 15 1.4.3 Degrees of knowledge 16 2.
The levels view: Political and moral theories are concerned with different normative facts, which belong to different ontological levels. The normative facts of political theory belong to a higher—more coarse-grained—ontological level than those of moral theory. Normative political facts are “multiply realizable” by moral facts, so
while income had a large effect on normative beliefs, with no effect on positive beliefs. This would support the view that positive and normative economics are disconnected. On the other hand, if education were the main determinant of both positive and normative beliefs, this would bolster the theory that the two categories of belief are .
Consider the instance of rational and administrative models of decision-making. The former is regarded as a normative model, the latter as a descriptive one. Thus the first theory explains how good decisions should ideally be made, whereas the second describes how less than optimal decisions are in fact made. Placing myself in the shoes of .
types of influences: normative age graded, normative history graded, and non-normative. Normative age graded influences are'biolog:1 and environmental determinants that in terms of their onset and duration are highly correlated with chronological age. Examples are walking and talking, going
What influences of adult development result in change? Normative age-graded influences Normative history-graded influences Non-normative life events Let’s take a closer look at each of these! Normative age-graded influences include:
ANSI A300 Part 4 ( American National Standards Institute, Standard for Lightning protection Systems For Trees ) recommends designing the earth (ground) termination based on a visual inspection of the soil and its moisture content. This is not possible as water is an insulator not a conductor; it is the dissolved salts in the water that give it its conductive properties. These salts are not .
