I. Background. Utility is a measurement of consumer preferences made under a variety of assumptions with respect to the decision context being studied. The point of the utility measurement is to enable the study of behavior within the framework of the assumptions made in a fashion that takes advantage of mathematical tools. There are three decision frameworks:

Certainty: The consumer knows without risk or uncertainty the outcome of making a choice. Choices made are not differentiated with respect to the receipt of the outcome of a choice at different points in time. Standard consumer theory deals with consumer behavior under conditions of certainty.

Risk: The consumer, or agent making the choice, does not know the outcome of making the choice with certainty. Instead, the choice maker knows the possible outcomes of a choice and the probability of each possible outcome (uncertainty is when either all possibilities and/or probabilities are not known). Choices made are not differentiated with respect to the receipt of the outcome of a choice at different points in time.

Intertemporal: The consumer knows without risk or uncertainty the outcome of making a choice. The choices made are differentiated with respect to when in time a choice made will be received.

II. Measurement Scales. A measurement scale is the assignment of numbers to entities or objects. The point of the measurement is to have properties of the numbers assigned correspond to properties of the characteristics being measured. For utility the correspondence between numbers and entities (usually consumption bundles, or the outcomes of actions relating to production or consumption) is one-many, i.e., each entity has only one number assigned to it, but different entities can be assigned the same numbers. For a given scale, the "uniqueness transformation" identifies the degree to which the scale values can be transformed and still preserve the