Development and Underdevelopment in the History of Economic Thought

On the shoulders of giants: Samuelson's (1938) reply to Lange (1934) on the "unique" measure of utility

Amélie Fievet, Université Paris 1 Panthéon-Sorbonne

This contribution discusses Samuelson's position on cardinality in his 1938 paper "The Numerical Representation of Ordered Classifications and the Concept of Utility", which replies to a paper by Lange (1934) on the unique measure of utility. Understanding today this debate between Lange (1934) and Samuelson (1938) faces a specific difficulty: in the 1930s (and at least until Stevens's contribution in 1946), there was no common theory of measurement scales shared by the various authors dealing with the measurement of utility. The construction of a reading grid using Stevens's theory of scales from 1946 thus makes it possible to evaluate the positions of Lange and Samuelson and to reveal that their divergence was rooted less in mathematical than in cognitive arguments. Unlike Lange, for whom cardinality was a continuation of ordinality (in the sense that it was just ordinality with something more added), Samuelson considered it a distinct cognitive ability, related to the specific ability to order differences, i.e. transitions or passages from one situation to another. The interesting point is that whereas Samuelson gave mathematical conditions for cardinality, he claimed, at the same time, that it was impossible to reach it because of the weak plausibility that agents have this cognitive capacity, relying on arguments much later used in the framework of reference-dependent approaches.

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Keywords: Paul Samuelson, Oskar Lange, utility, cardinality

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