Decision theory
From Academic Kids

Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. It is concerned with how real decisionmakers make decisions, and with how optimal decisions can be reached.
Contents 
Normative and descriptive decision theory
Most of decision theory is normative or prescriptive, i.e. it is concerned with identifying the best decision to take, assuming an ideal decision taker who is fully informed, able to compute with perfect accuracy, and fully rational. The practical application of this prescriptive approach (how people should make decisions) is called decision analysis, and aimed at finding tools, methodologies and software to help people make better decisions. The most systematic and comprehensive software tools developed in this way are called decision support systems.
Since it is obvious that people do not typically behave in optimal ways, there is also a related area of study, which is a positive or descriptive discipline, attempting to describe what people will actually do. Since the normative, optimal decision often creates hypotheses for testing against actual behaviour, the two fields are closely linked. Furthermore it is possible to relax the assumptions of perfect information, rationality and so forth in various ways, and produce a series of different prescriptions or predictions about behaviour, allowing for further tests of the kind of decisionmaking that occurs in practice.
What kinds of decisions need a theory?
Decision theory is only relevant in decisions that are difficult for some reason. A few types of decision have attracted particular attention:
 riskless choice between incommensurable commodities
 choice under uncertainty
 intertemporal choice
 social decisions
Choice between incommensurable commodities
This area is concerned with the decision whether to have, say, one ton of guns and 3 tons of butter, or 2 tons of guns and 1 ton of butter. This is the classic subject of study of microeconomics and is rarely considered under the heading of decision theory, but such choices are often in fact part of the issues that are considered within decision theory. (editor's note: this is not an accepted use of the term 'commensurable'.)
Choice under uncertainty
This area represents the heartland of decision theory. Daniel Bernoulli stated 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 they will result from each course of action, and multiply the two to give an expected value. The action to be chosen should be the one that gives rise to the highest total expected value. In reality people do not behave like this, at least if "value" is taken to mean "objective financial value"  otherwise noone would either gamble or take out insurance. Within behavioural decision theory, this has led to various dilutions of the expected value theory; for example, objective probabilities can be replaced by subjective estimates, and objective values by subjective utilities, giving rise to the subjective expected utility or SEU theory, developed by Savage. The prospect theory of Daniel Kahneman and Amos Tversky is another alternative to the expected value model within behavioural decision theory....
Pascal's wager is a classic example of a choice under uncertainty. The uncertainty, according to Pascal, is whether or not God exists. And the personal belief or nonbelief in God is the choice to be made. However, the reward for belief in God if God actually does exist is infinite, therefore however small the probability of God's existence the expected value of belief exceeds that of nonbelief, so it is better to believe in God.
A highly controversial issue is whether one can replace the use of probability in decision theory by other alternatives. The proponents of fuzzy logic, possibility theory and DempsterShafer theory maintain that probability is only one of many alternatives and point to many examples where nonstandard alternatives have been implemented with apparent success. 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 from departures from the probability axioms and to
 the complete class theorems which show that all admissible decision rules are equivalent to a Bayesian decision rule with some prior distribution (possibly improper) and some utility function. Thus, for any decision rule generated by nonprobabilistic methods either there is an equivalent rule derivable by Bayesian means, or there is a rule derivable by Bayesian means which is never worse and (at least) sometimes better.
Intertemporal choice
This area is concerned with the kind of choice where different actions lead to outcomes that are realised at different points in time. If I receive a windfall of several thousand dollars, I could spend it on an expensive holiday, giving me immediate pleasure, or I could invest it in a pension scheme, giving me 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 rates of interest and inflation, my life expectancy, and my confidence in the pensions industry. However even with all those factors taken into account, human behaviour again deviates greatly from the predictions of prescriptive decision theory, leading to alternative models in which, for example, objective interest rates are replaced by subjective discount rates.
Social decisions
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 the business of game theory, and is not normally considered part of decision theory, though it is closely related.
Complex decisions
Other areas of decision theory are concerned with decisions that are difficult simply because of their complexity, or the complexity of the organisation that has to take them. In such cases the issue is not the deviation between real and optimal behaviour, but the difficulty of determining the optimal behaviour in the first place.
Paradox of choice
Observed in many cases is the paradox that more choices may lead to a poorer decision or a failure to make a decision at all. It is sometimes theorized to be caused by analysis paralysis, real or percieved, or perhaps from rational ignorance. An number of researchers including Dr. Sheena S. Iyengar, now of Columbia, and Dr. Mark R. Lepper, of Stanford have published studies on this phenomenon. (Goode, 2001)
See also
References
 Robert Clemen. Making Hard Decisions: An Introduction to Decision Analysis, 2nd edition. Belmont CA: Duxbury Press, 1996. (covers normative decision theory)
 D.W. North. "A tutorial introduction to decision theory". IEEE Trans. Systems Science and Cybernetics, 4(3), 1968. Reprinted in Pearl & Shafer. (also about normative decision theory)
 Glenn Shafer and Judea Pearl, editors. Readings in uncertain reasoning. Morgan Kaufmann, San Mateo, CA, 1990.
 Howard Raiffa Decision Analysis: Introductory Readings on Choices Under Uncertainty. McGraw Hill. 1997. ISBN 007052579X
 Morris De Groot Optimal Statistical Decisions. Wiley Classics Library. 2004. (Originally published 1970.) ISBN 047168029X.
 Khemani , Karan, Ignorance is Bliss: A study on how and why humans depend on recognition heuristics in social relationships, the equity markets and the brand marketplace, thereby making successful decisions, 2005.
 J.Q. Smith Decision Analysis: A Bayesian Approach. Chapman and Hall. 1988. ISBN 0412275201
 Akerlof, George A. and Janet L. YELLEN, Rational Models of Irrational Behavior
 Arthur, W. Brian, Designing Economic Agents that Act like Human Agents: A Behavioral Approach to Bounded Rationality
 James O. Berger Statistical Decision Theory and Bayesian Analysis. Second Edition. 1980. Springer Series in Statistics. ISBN 0387960988.
 Goode, Erica. (2001) In Weird Math of Choices, 6 Choices Can Beat 600 (http://www.columbia.edu/~ss957/nytimes.html). The [[New York Times. Retrieved May 16, 2005.de:Entscheidungstheorie