Cardinal Utility - History

History

Modern work in cardinal utility theory began in the 18th century, when mathematician Daniel Bernoulli noted how the diminishing marginal utility of wealth would satisfactorily explain why a riddling game like the St. Petersburg paradox should not led to an infinite expected value. Bernoulli thought that a logarithmic utility function accounted well for the diminishing marginal utility of wealth since people consider money gains to be less and less satisfying the more they possess of it. This way, by attaching an act of human beings (consuming monetary units) to a functional form (the logarithm), the rational ground for a theory of utility was laid down, though it was yet to be linked to the economic analysis of demand.

Initial theories dealt with utility as a physical quantifiable attribute. One could tell if doing something would make people better off by looking at their change in utility. In this vein, Jeremy Bentham reflected on how satisfaction or utility could be measured by some complex introspective examination. He thought that social policies and laws needed to be based on the notion of utility. Bentham wrote a manuscript circa 1782 where he defines the unit of intensity as "the degree of intensity possessed by that pleasure which is the faintest of any that can be distinguished to be pleasure"; he also stated that, as these pleasures are perceived to be more and more intense, they may be represented by higher and higher numbers. In the 18th and 19th centuries utility's measurability received plenty of attention from European schools of political economy, most notably through the work of William Stanley Jevons, Léon Walras and Alfred Marshall. Jevons defined utility as a useful object, or something which could increase pleasurable feeling or remove pain. Nonetheless, he was characteristically frank and confused when referring to the measurability of utility, since he argued -in later editions of his works- that it was difficult to imagine how estimations of utility and summations can be made with any approach to accuracy. Overall, there was an enthusiasm for measurement in the Victorian era, and there were many aspects of life succumbing to quantification.

Supporters of cardinal utility theory in the 19th century suggested that the amount of utility obtained had to have a repercussion on the market price, although they did not say much about the problem of dealing with the subjectivity behind this alleged effect. Accurately measuring subjective pleasure (or pain) seemed awkward, and the thinkers of the time were aware of it; otherwise, they would not had renamed utility in imaginative ways such as subjective wealth, overall happiness, moral worth, psychic satisfaction, or ophélimité. During the second half of the 19th century, many studies related to this fictional magnitude -utility- were conducted, but the conclusion was always the same: unlike with distance or time, one cannot simply use a ruler or stopwatch to observe the number of "utils" obtained (that was the name actually given to the units in a utility scale). Not only it proved impossible to definitively say whether a good is worth 50, 75, or 125 utils to a person, or to two different people, but the mere dependence of utility on notions of hedonism, led academic circles to be skeptical of this theory.

Francis Edgeworth was also aware of the need to ground the theory of utility into the real world. He discussed the quantitative estimates that a person can make of his own pleasure or the pleasure of others, borrowing methods developed in psychology to study hedonic measurement: psychophysics. This field of psychology was built on work by Ernst H. Weber, but around the time of World War I, psychologists grew discouraged of it.

In the late 19th century, Carl Menger and his followers from the Austrian school of economics undertook the first successful departure from measurable utility, in the clever form of a theory of ranked uses. Despite abandoning the thought of quantifiable utility (i.e. psychological satisfaction mapped into the set of real numbers) Menger managed to establish a body of hypothesis about decision-making, resting solely on a few axioms of ranked preferences over the possible uses of goods and services.

Around the turn of the 19th century, a fraction of the marginalists known as the neoclassicals, started to embrace alternative ways to deal with the measurability issue. By 1900, Pareto was hesitant about accurately measuring pleasure or pain because he thought that such a self-reported subjective magnitude lacked scientific validity. He wanted to find an alternative way to treat utility that did not rely on erratic perceptions of the senses.

The works and manuals of Vilfredo Pareto, Francis Edgeworth, Irving Fischer, and Eugene Slutsky, were pivotal to the development of utility theory. According to Viner, these economic thinkers came up with a theory that explained the negative slopes of demand curves. Their method avoided the measurability of utility by constructing some abstract indifference curve map.

During the first three decades of the 20th century, economists from Italy and Russia became familiar with the idea of Pareto and Slutsky that utility did not needed to be cardinal. According to Schultz, by 1931 the idea of ordinal utility was not yet embraced by American economists. A theory of ordinal utility was put together by John Hicks and Roy Allen in 1934, in a seminal paper for the theory of consumer behavior under perfect competition and certainty. You can watch someone making an actual choice between a pastrami sandwich or, for the same money, a beef sandwich. By this choice, he reveals that he gets more pleasure from the pastrami.

In the decade of 1960 Parducci studied human judgements of magnitudes and suggested a range-frequency theory. Since the late 20th century economists are having a renewed interest in the measurement issues of happiness. This field has been developing methods, surveys and indices to measure happiness.