Were Jevons, Menger and Walras really cardinalists? On the notion of measurement in utility theory, psychology, mathematics and other disciplines, 1870–1910

This article 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 form of utility consistent with the so-called classical understanding of measurement should be added to the traditional picture. According to the classical view, measuring an object consists of assessing the numerical ratio between the object and some other object taken as a unit. In particular, we show that Jevons, Menger, and Walras understood measurement in the classical sense and applied this understanding to utility measurement; therefore, they were not cardinalists in the current sense of the term, which is associated with the ranking of utility differences. We also analyze 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, this article reviews the understanding of measurement in disciplines that bear some relation to utility theory. The 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.