being the same, more is better than less of the commodity. When a commodity is good, more of it is preferred to less. When a commodity is bad, less of it is preferred more, like pollution. Revealed preference It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer relative utilities from observed choice. These 'revealed preferences', as termed by Paul Samuelson, were revealed e.g. in people's willingness to pay: Utility is assumed to be correlative to Desire or Want. It has been argued already that desires cannot be measured directly, but only indirectly, by the outward phenomena which they cause: and that in those cases with which economics is mainly concerned the measure is found by the price which a person is willing to pay for the fulfillment or satisfaction of his desire. Revealed preference in finance For financial applications, e.g. portfolio optimization, an investor chooses a financial portfolio which maximizes his/her own utility function, or, equivalently, minimizes his/her risk measure. For example, modern portfolio theory selects variance as a measure of risk; other popular theories are expected utility theory, and prospect theory. To determine a specific utility function for any given investor, one could design a questionnaire procedure with questions in the form: How much would you pay for x% chance of getting y? Revealed preference theory suggests a more direct method: observe a portfolio X* which an investor currently has, and then find a utility function/risk measure such that X* becomes an optimal portfolio. There has been some controversy concerning whether the utility of a commodity can be measured or not. At one time, it was assumed that the consumer was able to say exactly how much utility he got from the commodity. The economists who made this assumption belonged to the 'cardinalist school' of economics. Presently utility functions, expressing utility as a function of the amounts of the various goods consumed, are treated as either cardinal or ordinal, depending on whether they are or are not interpreted as providing more information than simply the rank ordering of preferences among bundles of goods, such as information concerning the strength of preferences. Cardinal Cardinal utility states that the utilities obtained from consumption can be measured and ranked objectively and are representable by numbers. There are fundamental assumptions of cardinal utility. Economic agents should be able to rank different bundles