# Decision theory

The decision theory is in applied probability theory , a branch for evaluation of the consequences of decisions . Decision theory is widely used as a business instrument. Two well-known methods are the simple utility value analysis (NWA) and the more precise Analytic Hierarchy Process (AHP). In these methods, criteria and alternatives are presented, compared and evaluated in order to be able to find the optimal solution to a decision or problem .

## Sub-areas

There is a distinction in decision theory into three sub-areas:

1. The normative decision theory is based on the rational choice theory and normative models. Fundamental for this are axioms (for example axiom of the rationality of the decision maker), which people should consider when making a decision. The axiomatic approach allows logically consistent results to be derived. ⇒ (How should a decision be made?)
2. The prescriptive decision theory attempts to derive strategies and methods that help people make better decisions by using normative models. At the same time, the limited cognitive abilities of humans are examined. In addition, problems that arise when implementing rational decision models are dealt with in particular.
3. The descriptive contrast, decision theory examines empirically the question of how decisions are actually made in reality. ⇒ (How do you decide?)

The practical application of prescriptive decision theory is called decision analysis . Methods and software are developed to help people make decisions. In particular, legislation and the interpretation of the law often have to be oriented towards different, competing goals and interests and strive for a compromise between these “which appears to be fair and with this condition optimizes the benefit”. Decision analyzes are intended to “make visible the variety of factors ... that play a role in purpose-oriented decisions. This makes it easier to rationally discuss conflicting goals and to find the alternative decision that realizes these goals in an optimal way and to an optimal extent. "

The basic model of (normative) decision theory can be represented in a result matrix. This includes the decision-making field and the target system. The decision-making field includes:

• Action space : Set of possible alternative courses of action
• State space : set of possible environmental states
• Result function : Assignment of a value for the combination of action and status.

## Security and uncertainty

A common problem is that the real state of the environment is not known. Here one speaks of uncertainty . The opposite is a situation of security in which the state of the environment is known. The following structure can be made:

• Decision under security : The situation that occurs is known. (Deterministic decision model)
• Decision under uncertainty : It is not known with certainty which environmental situationoccurs, one further distinguishes between: ${\ displaystyle s_ {j}}$
• Decision under risk : The probabilityfor the possible environmental situationsis known. (Stochastic decision model)${\ displaystyle p_ {j}}$${\ displaystyle s_ {j}}$
• Decision under uncertainty : one knows the possible environmental situations, but not their probability of occurrence.
In the case of a decision under risk, expected values ​​can be calculated for all possible consequences of each individual decision , whereas this is not possible in a decision under uncertainty or the principle of insufficient reason ( principle of indifference ) is applied, which assigns the same probability to each option. On the basis of such probability assessments, a determination of the expected value can also be carried out under uncertainty .

The (single or multi-stage) decision-making process, including the various consequences, can be shown graphically as a decision tree.

## Demarcation

Decision theory cannot be used if a decision-maker competes with a rationally acting opponent (a competitor, for example) who also allows the respective competition to flow into his decision. The decision can no longer be mapped with the help of probability calculation alone: ​​the behavior of the opponent is not strictly deterministic, but not random. In such a case game theory comes into play .

Decision theory has recently also been used to assess investments. Under the name real option, the decision tree method (or options) is used to assess the value of flexibility with regard to decisions - i.e. H. to be able to decide the option (at a later date) - to assess.

Joint decisions by a group of individuals are the content of social choice theory .

## literature

• Anderson, Sweeney, Williams: An Introduction to Management Science. 7th edition. West Publishing, Minneapolis, et al. 1994, ISBN 0-314-02479-4 , chapter 14.
• Günter Bamberg, Adolf G. Coenenberg : Business decision-making. 14th edition. Verlag Vahlen, Munich 2008, ISBN 978-3-8006-3506-1 (standard textbook)
• Michael Bitz: Decision Theory. Vahlen, Munich 1981, ISBN 3-8006-0789-1 .
• Helmut Jungermann, Hans-Rüdiger Pfister, Katrin Fischer: The psychology of decision. An introduction. 3. Edition. Spectrum, Berlin / Heidelberg 2010, ISBN 978-3-8274-2386-3
• Egbert Kahle : Operational decisions. 6th edition. Oldenbourg, Munich / Vienna 2001. ISBN 3-486-25633-5 (standard textbook)
• Helmut Laux: Decision Theory. 7th edition. Springer, Berlin, 2007, ISBN 978-3-540-71161-2 .
• Michael Resnik: Choices: An Introduction to Decision Theory. Minneapolis / London 1987
• Christoph Schneeweiß: Planning 1. Springer, Berlin 1991, ISBN 3-540-54000-8 .
• FP Springer: For dealing with decisions under uncertainty. In: Der Betrieb , 1974, No. 6, pp. 249-251.
• FP Springer: The Evaluation of Uncertainty in Engineering Calculations by the Use of Non-Distributional Methods. Society of Petroleum Engineers of AIME Paper 4817, Dallas 1974