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# What is Decision Theory?

Decision theory is an interdisciplinary area of study that concerns mathematicians, statisticians, economists, philosophers, managers, politicians, psychologists and anyone else interested in analyses of decisions and their consequences. The basic formalism of decision theory is the payoff table, which maps mutually exclusive decisions to 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 any given decision is not known, we refer to this situation as decision under uncertainty, the field of study which dominates decision theory.

Outcomes in decision theory are usually assigned utility values. For example, from the point of view of a military planner, the death of 1000 men on the battlefield might be assigned a negative utility of 1000, and the death of 500 a negative utility of 500. Possible outcomes in a decision theory problem may be positive, negative or both. Utility assignments can be arbitrary and based on the opinions of the decision maker -- for example, the death of 1000 men might be assigned greater than twice the negative utility of the death of 500 men.

The *expected utility* of a decision is computed as the sum of the probability of each possible outcome multiplied by the utility of each outcome. For example, making a given decision might lead to positive utility 100 with a probability of 75%, and a negative utility of 40 with probability 25%. 75% times 100 equals positive 75. 25% times -40 equals -10. 75 minus 10 gives 65, meaning the overall expected utility of the decision is 65.

Obviously, such quantitative precision is only possible in problems in which all the numbers and probabilities are known ahead of time. This is true in certain gambling problems, like poker. Decision theory provides a number of suggestions for how to estimate complex probabilities under uncertainty, most of which are derived 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 decision theories are complex, often unnecessarily so, and they help teach us the ways in which human decisions systematically go wrong. This connects to the related field of heuristics and biases, which has come into great vogue in the field of economics within the last decade.

## Discussion Comments

Value in decision making is ultimately assigned according to what the people involved find to be of worth. If the only criterion is money, then the decision will reflect an interest in money. If the decisions are selfish, than the decisions will reflect "what's best for me." Ultimately, the decisions which provide the longest contentment are those which are made for the sake of others, and for something bigger than oneself.

@FitzMaurice

I think there was more to this book than just that last sentence you mentioned there. It is important that we recognize that we can easily be bound by our own expectations, and even by our expectations of what "free choice" looks like. We live in an economy that exploits our feelings of entitlement and greatness, and this is ultimately what ruins us: an obsession with the self.

In his "The Paradox of Choice: Why More is Less," Barry Schwartz stipulates the fact that "freedom of choice" and decision making in the American economy has led to so many discontented people. It is ironic how we value our own free will and yet are so discontent with our own decisions. The only way to be sure that we are truly making the right decisions in any given situation would be to see the future. We can't do that, so maybe we should be content with our state.

Making goals and decisions measurable is an important part of weighing which decision to make. Assigning values to certain outcomes makes the process of decision making easy. The most common way to assign values to decisions is to predict the likely monetary gain which can come as a result of a given decision.

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