individuals to specify how much extra utility he or she received from the preferred bundle of goods or services in comparison to other bundles. They are only required to tell which bundles they prefer. When ordinal utilities are used, differences in utils (values assumed by the utility function) are treated as ethically or behaviorally meaningless: the utility index encodes a full behavioral ordering between members of a choice set, but tells nothing about the related strength of preferences. For the above example, it would only be possible to say that juice is preferred to tea to water. Thus, ordinal utility utilizes comparisons, such as "preferred to", "no more", "less than", etc. If a function is ordinal, it is equivalent to the function , because taking the 3rd power is an increasing monotone (or monotonic) transformation. This means that the ordinal preference induced by these functions is the same (although they are two different functions). In contrast, if is cardinal, it is not equivalent to . Constructing utility functions For many decision models, utility functions are determined by the problem formulation. For some situations, the decision maker's preference must be elicited and represented by a utility (or objective) scalar-valued function. The methods existing for constructing such functions are collected in the proceedings of two dedicated conferences. The mathematical foundations for the most common types of utility functions — quadratic and additive — were laid down by Gerard Debreu, and the methods for their construction from both ordinal and cardinal data, in particular from interviewing a decision maker, were developed by Andranik Tangian. Examples In order to simplify calculations, various alternative assumptions have been made concerning details of human preferences, and these imply various alternative utility functions such as: CES (constant elasticity of substitution). Isoelastic utility Exponential utility Quasilinear utility Homothetic preferences Stone–Geary utility function Gorman polar form Greenwood–Hercowitz–Huffman preferences King–Plosser–Rebelo preferences Hyperbolic absolute risk aversion Most utility functions used for modeling or theory are well-behaved. They are usually monotonic and quasi-concave. However, it is possible for preferences not to be representable by a utility function. An example is lexicographic preferences which are not continuous and cannot be represented by a continuous utility function. Marginal utility Economists distinguish between total utility and marginal utility. Total utility is the utility of an alternative, an entire consumption bundle or situation in life. The rate of change of utility from changing the quantity of one