The concept of ordinality belongs to the broad issue of utility, preferences, and measurement of pleasure or consumer satisfaction. Economists and social philosophers have always aimed at explaining how to overcome the omnipresent scarcity that nature imposes upon humans, and thus to achieve a state of higher satisfaction. The concept of utility was developed to mean the quality that makes a commodity—through whose consumption the satisfaction can be achieved—desired. It has always been recognized that utility is a subjective matter, because the outside observer cannot know much about why and to what extent a commodity is desired, but originally it was believed (by early utility theorists such as H. H. Gossen, W Stanley Jevons, and Leon Walras) that utility is measurable and additive—that is, that numbers can be attached to each intensity of satisfaction (cardinal utility theory) and can be summed up to get a "total utility." In criticizing this idea, two points were made: first, that utility is nonadditive and fundamentally unmeasureable within an individual (and much less across two individuals); and second, that one actually does not even need to assume cardinality in order to make use of utility theory in economics (though cardinal utility still may exist). It came to be understood that there is an alternative approach, represented by the concept of ranking of available options that satisfy consumer preferences—ordinal utility theory. This is done in two different ways.
The first of them was based on the principle of indifference. In a standard model, the consumer maximizes her satisfaction by spending her limited budget on two goods. Any combination of the quantities of the two goods yields the same satisfaction (level of utility) to the consumer, which is why she is indifferent in her choice between these combinations. Considering all such combinations gives rise (under certain assumptions) to an "indifference curve"—a tool widely used in twentieth-century microeconomics. A set of such curves for different levels of satisfaction is an "indifference map." Similarly, considering all combinations of the two goods that can be purchased with the same limited budget gives rise to a "budget constraint." With these tools at hand, whether the cardinal utility exists or not is immaterial for the problem of decision making, because what matters is satisfaction ranking of all the ways in which the given budget can be spent on the two goods. Thus, when seen on a graph, the best use of the budget utility-wise is the combination of the two goods represented by the intersection of the budget constraint and the indifference curve, signifying the greatest possible satisfaction (which will typically be the one that is just "touched" by the budget constraint). This approach is associated with the work of Robert Edgeworth, Vilfredo Pareto, John Hicks, and Roy G. D. Allen, among others.
In the second approach to ordinal utility, every acting person can make a ranking of his alternative ends according to his values. This ranking, rooted in the process of subjective valuation, brings about the construction of an individual preference scale. In every action a choice is made and a part of the preference scale is demonstrated, so that the external observer can get "data" about other people’s utility ranking. For example, we can see that an individual who is buying a book ranks the $20 he is spending lower than he ranks the book on his preference scale, whereas a seller of the book has a reverse preference ranking—that is, she values the money more than the book, and therefore she is willing to sell. Value scales can be used to formulate the theory of exchange and build up a price theory and the whole of microeconomics. This approach was elaborated by Carl Menger and Eugen von Bohm-Bawerk and their followers of the so-called "Austrian school"—the Czech economist Franz Cuhel, the Austrian economists Ludwig von Mises and Friedrich Hayek, and their American followers Israel Kirzner and Murray Rothbard.
There is no doubt that utility theory is the cornerstone of the theory of consumer behavior, and yet there seems to be no general consensus on the underlining issues related to the nature of utility. On the one hand, defenders of value scales are criticized by those using indifference curves that working solely with ranked units of goods hinders the use of more sophisticated mathematical analysis and model building. Users of indifference curves are criticized on the other hand because indifference cannot be demonstrated in action—that is, an actor always prefers in his action A over B, so when observing actual behavior, the "data" we see is preference, not indifference. Thus, indifference should not then be a category of economics, but of psychology. Some argue, however, that utility theory needs more psychology, to provide more input into economics because actual preference ranking may be biased or uninformed. Lastly, some authors argue, the dichotomy between ordinality and cardinality is mostly artificial and does not play any significant role when policy implications are discussed.
