# Decision theory

**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 the optimal decisions to be taken under particular circumstances.

## Normative and descriptive decision theory

## What kinds of decision need a theory?

- riskless choice between incommensurable commodities
- choice under uncertainty
- intertemporal choice
- social decisions

### Choice between incommensurable commmodities

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.

### 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 no-one 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 subjectively expected utility or SEU theory. 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 non-belief in God is the choice to be made.

### Intertemporal choice

### 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

## 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.