only by scale and origin. In this case, "cardinality" means nothing more being able to give consistent answers to these particular questions. Note that this experiment does not require measurability of utility. Itzhak Gilboa gives a sound explanation of why measurability can never be attained solely by introspection: According to this view, those situations where a person just cannot tell the difference between and will lead to indifference not because of a consistency of preferences, but because of a misperception of the senses. Moreover, human senses adapt to a given level of stimulation and then register changes from that baseline. Construction Suppose a certain agent has a preference ordering over random outcomes (lotteries). If the agent can be queried about his preferences, it is possible to construct a cardinal utility function that represents these preferences. This is the core of the Von Neumann–Morgenstern utility theorem. Construction of cardinal utility functions from cardinal and ordinal data The mathematical foundations of most common types of utility functions — quadratic and additive — laid down by Gérard Debreu enabled Andranik Tangian to develop methods for their construction from ordinal data. In particular, additive and quadratic utility functions in variables can be constructed from interviews of decision makers, where questions are aimed at tracing totally 2D-indifference curves in coordinate planes — and in the case of quadratic utility additionally specifying one point of indifference in every other coordinate plane. If desired, decision makers can include cardinal utility estimates as well, making this approach universal regarding both cardinal and ordinal utilities. Applications Welfare economics Among welfare economists of the utilitarist school it has been the general tendency to take satisfaction (in some cases, pleasure) as the unit of welfare. If the function of welfare economics is to contribute data which will serve the social philosopher or the statesman in the making of welfare judgements, this tendency leads perhaps, to a hedonistic ethics. Under this framework, actions (including production of goods and provision of services) are judged by their contributions to the subjective wealth of people. In other words, it provides a way of judging the "greatest good to the greatest number of persons". An act that reduces one person's utility by 75 utils while increasing two others' by 50 utils each has increased overall utility by 25 utils and is thus a positive contribution; one that costs the first person 125 utils while giving the