Decision theory studies decisions and their consequences, using profit tables to map decisions to states of nature. Decision under uncertainty is a dominant field. Outcomes are assigned utility values, and expected utility is calculated as the sum of probabilities and utilities. Decision theory can be normative or descriptive, with descriptive theories helping to identify biases in decision-making.
Decision theory is an interdisciplinary area of study involving mathematicians, statisticians, economists, philosophers, managers, politicians, psychologists and anyone else interested in the analysis of decisions and their consequences. The basic formalism of decision theory is the profit table, which maps mutually exclusive decisions into mutually exclusive states of nature. For example, “Decision X leads to outcome Y”, “Decision Y leads to outcome Z” and so on. When the set of outcomes corresponding to a given decision is not known, we refer to this situation as decision under uncertainty, the field of study that dominates decision theory.
Outcomes in decision theory are usually assigned utility values. For example, from the point of view of a military planner, the deaths of 1000 men on the battlefield might be assigned a negative utility of 1000 and the deaths of 500 a negative utility of 500. Possible outcomes in a problem theory of decisions can be positive, negative or both. Utility assignments can be arbitrary and based on the opinions of the decision maker: for example, the deaths of 1000 men could be assigned twice as much utility as the deaths of 500 men.
The expected utility of a decision is calculated as the sum of the probability of each possible outcome times the utility of each outcome. For example, making a certain decision could lead to a positive utility of 100 with a 75% probability and a negative utility of 40 with a 25% probability. 75% times 100 equals 75 positive. 25% times -40 equals -10. 75 minus 10 gives 65, which means that the overall expected utility of the decision is 65.
Of course, such quantitative precision is only possible in problems where all numbers and probabilities are known in advance. This is true in some gambling problems, such as poker. Decision theory provides a number of suggestions on how to estimate complex probabilities under uncertainty, most of which derive from Bayesian inference.
Decision theory can be normative or descriptive. Normative decision theory refers to theories about how we should make decisions if we want to maximize expected utility. Descriptive decision theory refers to theories about how we actually make decisions. Descriptive theories of decisions are complex, often unnecessarily, and help teach us the ways in which human decisions systematically go wrong. This ties into the related field of heuristics and biases, which has come into vogue in the field of economics over the past decade.
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