Pareto and the 53 Percent Ordinal Theory of Utility

Vilfredo Pareto died more than seventy-five years ago. His last major contribution to economic theory, "Économie mathématique," published in 1911 in the Encyclopedie des sciences mathematiques pures et appliques, is now ninety years old, and his earliest major contributions, the five-part "Considerazioni sui principii fondamentali dell'economia politica pura" (1892-93) and several other papers published at about the same time in the Giornale degli economisti, are now well over a century old. Pareto's work has extensively influenced so much of modern economics, and intellectual historians have had ample time to digest and interpret his work. Nevertheless, confusion persists on at least one important aspect of Pareto's contribution to modern economic theory. This confusion concerns the question of whether and to what extent Pareto adopted an ordinal theory of utility.

The answers that intellectual historians have given to this question are decidedly mixed. At one extreme, many authors, perhaps the majority of those who have addressed the issue, have claimed with little or no qualification that Pareto's utility theory is purely ordinal. In chronological order, this group includes, among others, J. R. Hicks and R. G. D. Allen (1934, 52-53), Eric Roll (1946, 454-55), John Bell (1953, 469), I. M. D. Little (1957, 52), Eduard Heimann (1964, 211), Richard Gill (1967, 60), Vincent Tarascio (1968, 121; 1972), Robert Lekachman (1976, 295), Renato Cirillo (1979, 88-91), Karl Pribram (1983, 309-10), Henry Spiegel (1983, 556-57, 623), Hans Brems (1986, 141-42), and Lionel Robbins (Medema and Samuels 1998, 301). All of these authors have credited Pareto with developing a purely ordinal utility theory. Of these discussions of the ordinal element in Pareto's utility theory, Tarascio's (1972) is arguably the most thorough, while Bell's claim on Pareto's behalf is more or less typical of this group: "In the Manuel, to explain his 'theory of choice,' Pareto made use of 'indifference curves' which could be used in place of the usual demand curve. Pareto used the indifference curve without any connotation of utility" (469; emphasis added). Although Mark Blaug (1997) has little to say about Pareto's contribution to pure demand theory, he does credit Pareto with developing a purely ordinal approach to welfare economics.

At the other extreme, Oskar Lange (1934, 223), Harro Bernardelli (1935, 69), William Fellner (1960, 191), and Nicholas Georgescu-Roegen (1987, 717) have argued in essence that Pareto's theory is purely cardinal. For example, Fellner claimed that Pareto (along with F. Y. Edgeworth and Irving Fisher) "made no consistent effort to exclude cardinal measurability from the tools they were employing" (191). Luigino Bruni and Francesco Guala (2001) offer the most recent and most thoroughly argued defense of the view that Pareto was in essence a lifelong cardinalist.

In between these two extreme sets of views, others have tended toward a more balanced interpretation. Thus, while Hicks (1946, 18-19) referred to Pareto's theory as ordinal in his Value and Capital, later in A Revision of Demand Theory (1956, 156) he attributed a cardinal theory to Pareto. Similarly, Paul Samuelson (1947, 93; 1993, 515) has sometimes referred to Pareto as having an ordinal theory of utility, while elsewhere (1974, 1256 n) he mentions a cardinal theory. Taking a chronological perspective, Edmund Whittaker (1960, 304), Emil Kauder (1965, 193-94), and, most recently, Roberto Marchionatti and Enrico Gambino (1997) all claim that in his early writings, Pareto used a cardinal approach, while his later work assumed only an ordinal utility function.

Perhaps not surprisingly, Joseph Schumpeter's (1954, 1062-64) assessment is among the most thorough. He argued, as Whittaker would later, that in his early works, Pareto assumed that utility was cardinally measurable, while in his later works he assumed only an ordinal utility function. However, Schumpeter also pointed out that Pareto "slid back again and again into the habits of thought he had acquired in his formative years."As I discuss below, this is almost certainly a reference to long sections of Pareto's Manual of Political Economy ([1906] 1971) and his "Économie math...