Were Jevons, Menger and Walras Really Cardinalists?
In a paper under review for publication (Were Jevons, Menger and Walras Really Cardinalists? On the Notion of Measurement in Utility Theory, Psychology, Mathematics and other Disciplines, ca. 1870–1910, Università di Torino-CESMEP Working Paper Series 03/2010, revised and resubmitted to History of Political Economy) Ivan Moscati (Department of Economics) argues that the canonical dichotomy between cardinal utility and ordinal utility is inadequate to tell an accurate history of utility theory, and that a third and stronger form of utility consistent with the so-called classical understanding of measurement should be added to the traditional picture.
Much economic analysis of human decisions relies on the notion of utility, and current microeconomic theory basically refers to two forms of utility: ordinal utility and cardinal utility. In the ordinal-utility approach, it is assumed that the economic agent is able to rank the utility of alternatives, and so to state that, for example, the utility of alternative A is larger than the utility of alternative B. In the more demanding cardinal-utility approach, it is assumed that the economic agent is not only able to rank the utility of alternatives, but also that he can rank differences of utility and so state that the utility difference between alternatives A and B is larger than the difference between alternatives C and D.
The current microeconomic dichotomy between cardinal utility and ordinal utility has strongly influenced the way in which the history of utility theory is told. According to the canonical narrative of this history, in a first phase, lasting roughly from 1870 to 1910, William Stanley Jevons, Carl Menger, Léon Walras and the other early marginalists treated utility as cardinally measurable. In a second phase, inaugurated by Vilfredo Pareto around 1900 and concluded by John Hicks's Value and Capital (1939), utility theorists moved away from cardinalism and embraced an ordinal approach to utility.
According to the classical view, Moscati argues, measuring an object consists of assessing the numerical ratio between the object and some other object taken as a unit, and is not associated with the ranking of differences between objects, which is less demanding. In particular, the paper shows that Jevons, Menger and Walras understood measurement in the classical sense, applied this understanding to utility measurement, focused on the possibility of ascertaining a unit of utility and assessing utility ratios rather than on the ranking of utility differences as in current cardinal utility analysis, and therefore were not cardinalists in the current sense of the term.
Moscati also analyzes the argumentative strategies adopted by Jevons and Walras to address the conflict between the scientific importance they attributed to measurement, their classical understanding of it, and the apparent immeasurability of the utility featuring in their economic theories.
Finally, in order to appreciate the broad intellectual context within which their discussions on utility measurement took place, Moscati reviews the understanding of measurement in disciplines that bear some relation to utility theory. This review illustrates that in the years 1870-1910, the period in which Jevons, Menger and Walras were active, the classical understanding of measurement dominated not only utility theory but also all other disciplines surveyed. This circumstance helps to explain why the three marginalists remained committed to the classical understanding even though it did not square with their economic practices.