Unidimensional Problems

If the state of nature that will actually occur and the consequences associated with the decision alternatives are known, a decision is made under certainty. Under risk and uncertainty, the state of nature that would prevail is not known with certainty. Under risk, the probability of each state of nature occurring and, correspondingly, the probability distribution of consequences are known; otherwise, the decision is made under uncertainty.

The probabilities of the states of nature are rarely known, but it is often possible to estimate these probabilities. If objective probabilities can not be determined, subjective ones, based, for example, on expertise, may be used. This being the case, risk management methods can be applied also to support decision making under uncertainty. Therefore, the distinction between risk and uncertainty is not always clear. In addition to the future states of nature, uncertainty may be related to other elements of the decision making as well. These sources of uncertainty are dealt with in later chapters.