Andreas Heinrich Voigt and the Hicks-Allen Revolution in Consumer Theory

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I. INTRODUCTION

In a recent paper, Schmidt and Weber (2008) showed that a heretofore almost forgotten late nineteenth-century German mathematician and economist, Andreas Heinrich Voigt, (1) argued explicitly for an ordinal approach to utility in a paper published in 1893 in the German language journal Zeitschrifi fur die gesamte Staatswissenschaft (Voigt 1893c). Voigt's paper, "Zahl und Mass in der Okonomik: Eine kritische Untersuchung der mathematischen Methode und der mathematischen Preistheorie" ("Number and Measurement in Economics: A Critical Examination of the Mathematical Method and the Mathematical Theory of Price") appeared a full 5 years before Pareto (1898) argued for an ordinal view of utility (although he did not use that terminology) in a presentation to the Societe Stella of Paris. As such, this recent rediscovery of his work marks Voigt's paper as the earliest unambiguous statement of the idea that utility should be viewed as a purely ordinal rather than a cardinal magnitude, as well as the earliest known use of the cardinal versus ordinal terminology in economics. (2)

The present paper builds on recent contributions to the history of utility theory in five ways: First and most broadly, the narrative below parallels recent discussions which emphasize important philosophical differences between Lionel Robbins and his predecessors from Smith and Hume to Edgeworth as a key explanation for the post-1932 rise of ordinalism. (3) While there is much merit in this view, we argue here that even aside from Robbins' issues with utilitarian philosophy, there were other forces that also played an important role, coming as much from mathematics as from philosophy.

Second, we contribute further to recent efforts to shed light on the brief but path-breaking collaboration on demand and utility theory between Hicks and Allen (1934). Thus, this paper complements other recent advances in this area by Fernandez-Grela (2006) and Lenfant (2006).

Third, we trace the influence of Voigt's contribution to ordinal utility theory on subsequent writers. We show that Voigt is not merely some long forgotten pioneer who argued for an ordinal conception of utility 5 years before Pareto (1898), and whose notion of an ordinal utility function was taken much further by Hicks and Allen and other writers in the 1930s. Rather, we show that there is a strong case that Hicks and Allen (1934) obtained the cardinal/ordinal terminology directly from Edgeworth, and that Edgeworth in turn had learned it from Voigt.

Fourth, as we will show that Edgeworth passed Voigt's ordinalist views, as well as his terminology, along to later generations of economists without an unambiguous endorsement but also without any hint of criticism or disagreement, we also demonstrate that Edgeworth's views on utility appear to have been somewhat more differentiated than the uncompromising cardinalism which historians of economics have tended to attribute to him. (4) This paper thus contributes to ongoing efforts to develop a more nuanced view of Edgeworth's beliefs concerning the nature of utility. (5)

Fifth, we also discuss the important role that the young Rosenstein-Rodan appears to have played in stimulating the seminal contribution of Hicks and Allen (1934) (in the process apparently conveying some of the views on ordinalism that he had picked up from Voigt to Hicks and Allen), revealing a heretofore underappreciated contribution by Rosenstein-Rodan to the development of modern utility and demand theory. (6)

The remainder of the present paper is organized as follows: As Voigt and his work are almost completely unknown today, we begin in Section II by providing a brief overview of his ground-breaking contribution to ordinal utility theory. Sections III-VI then discuss Voigt's impact on later generations of economists. The emphasis in these sections is on the important direct impression which Voigt seems to have made on both Edgeworth and Rosenstein-Rodan, and the indirect influence he appears to have had via the work of these two men on Hicks and Allen (1934). …