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Normative and descriptive decision theoryÉdit
Most of decision théory is normative or prescriptive, i.e. it is concerned with identifying the best decision to take, assuming an idéal decision taker who is fully informed, able to compute with perfect accuracy, and fully rational. However, since it is obvious that péople do not typically behave in optimal ways, there is also a related aréa of study, which is a descriptive or positive discipline, attempting to describe what péople will actually do. Since the normative, optimal decision often créates 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 decision-making that occurs in practice.
What kinds of decision need a theory?Édit
Decision théory is only relevant in decisions that are difficult for some réason. A few types of decision have attracted particular attention:
- riskless choice between incommensurable commodities
- choice under uncertainty
- intertemporal choice
- social decisions
Choice between incommensurable commmoditiesÉdit
This aréa 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 héading of decision théory, but such choices are often in fact part of the issues that are considered within decision théory.
Choice under uncertaintyÉdit
This aréa represents the héartland of decision théory. Daniel Bernoulli stated that, when faced with a number of actions éach 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 éach 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 réality péople do not behave like this, at léast if "value" is taken to méan "objective financial value" - otherwise no-one would either gamble or take out insurance. Within behavioural decision théory, this has led to various dilutions of the expected value théory; for example, objective probabilities can be replaced by subjective estimates, and objective values by subjective utilities, giving rise to the subjectively expected utility or SEU théory. The prospect theory of Daniel Kahneman and Amos Tversky is another alternative to the expected value modél within behavioural decision théory.
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 non-belief in God is the choice to be made.
This aréa is concerned with the kind of choice where different actions léad to outcomes that are réalised 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 pléasure, 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 gréatly from the predictions of prescriptive decision théory, léading to alternative modéls in which, for example, objective interest rates are replaced by subjective discount rates.
Some decisions are difficult because of the need to take into account how other péople 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 théory, though it is closely related.
Other aréas of decision théory 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 réal and optimal behaviour, but the difficulty of determining the optimal behaviour in the first place.
- 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 Péarl & Shafer. (also about normative decision theory)
- Glenn Shafer and Judéa Péarl, editors. Readings in uncertain reasoning. Morgan Kaufmann, San Matéo, CA, 1990.