journal of Economic Literature Vol. XXII (June 1984), pp. 507-530 Were the Ordinalists Wrong About Welfare Economics? By ROBERT COOTER University of California, Berkeley and PETER RAPPOPORT New York University Useful comments on earlier drafts were provided by Sean Flaherty, Marcia Marley, Tim Scanlon, Andrew Schotter, Mark Schankerman, Lloyd Ulman and two anonymous referees. We are grateful to the National Science Foundation and the C. V. Starr Center at New York University for financial support. Responsibility for accuracy rests with the authors. pE DEVELOPMENT of utility theory has economics.1 The intuitive idea of scientific experienced two definitive episodes: progress is that new theories are discov­ the "marginalist revolution" of the 1870s ered that explain more than old theories. and the "Hicksian" or "ordinalist revolu­ We shall contend that the ordinalist revo­ tion" of the 1930s. While the first event lution was not scientific progress in this established a central place for utility the­ sense. For example, the older school was ory in economics, the second restricted concerned with economic policies to the concept of utility acceptable to eco­ bring about income redistribution and al­ nomics. The term "ordinalist revolution" leviate poverty, and the ordinalists did not refers to the rejection of cardinal notions offer a more general theory for solving of utility and to the general acceptance these problems. Instead, the trick that car­ of the position that utility was not compa­ ried the day for the ordinalists was to ar­ rable across individuals. The purpose gue that the questions asked by the older of this paper is to analyze the events school, and the answers which they gave, comprising the ordinalist revolution with 1 For example, Kenneth Arrow, referring to the a view to determining whether they earlier school, wrote: achieved the advances in economic sci­ . the proponents of measurable utility have been ence usually claimed for them. unable to produce any proposition of economic behav­ ior which could be explained by their hypothesis and The developments of the 1930s are of­ not by those of the indifference-<!urve theorists [1963, ten regarded as unambiguous progress in p, 9]. 507 508 journal of EconomicLiterature, Vol. XXII (June 1984) were meaningless. 2 We shall argue that This essay aims to help the reader to re­ ordinalists offered different questions, not cover a clear view of the older framework better answers. Thus, the ordinalist revo­ and to understand why it was rejected by lution represented a change, not progress the ordinalists. in economics. In order to avoid misunderstanding, we In order to understand why the ques­ shall offer a brief explanation in contem­ tions asked by the older school seemed porary economic language of the material meaningless to the ordinalists, it is neces­ welfare conception of interpersonal util­ sary to understand the dramatic change ity. Economists of the older school are of­ in the conceptual framework of econom­ ten characterized as having relied exten­ ics. Important elements of a conceptual sively on the belief that utility is cardinally framework are a definition of the subject measurable (unique up to a positive affine matter to be studied, a method of investi­ transformation), a belief that cannot be gation and proof, and some substantive validated by examination of consumer be­ empirical claims. The older framework havior, and one that is unnecessary for de­ defined economics as the science of "ma­ riving results in the theory of consumer terial welfare"3 and employed an empiri­ demand. We do not consider in detail cist methodology. In addition, its practi­ whether economists at the turn of the cen­ tioners held that their conception of utility tury believed individual utility to be cardi­ was comparable across people. The newer nally measurable, since this issue is tan­ framework adopted a scarcity definition gentiaJ to the question of interpersonaJ of economics, and employed a positivist comparisons. Instead, we concentrate on methodology. The salient feature of utility the special assumptions concerning utility was held to be its ordinal nature. that justified the interpersonal compari­ The elements of the newer frame­ sons made by these economists. work-the scarcity definition, positivist The different roles of assumptions about methodology, and ordinal utility-are fa­ measurability and comparability of utility miliar to contemporary economists. In can be elucidated by borrowing from the contrast, the elements of the older frame­ modern approach to social welfare theory work-the material welfare definition, em­ (for example, Amartya Sen 1977). Let each piricist methodology, and interpersonal individual i = I, 2 be represented by a utility-are now viewed through the dis­ set, L;,,, of utility functions. Each utility torting lens of the ordinalist framework. function is defined over the set of social states, and, for the present purpose, is best 2 The following is a partial list of questions that regarded simply as a list of numbers, one material welfare economists claimed to answer and for each state. Measurability assumptions ordinalists claimed were unanswerable by econom­ restrict L;, to particular classes of functions ics: Is a dollar more valuable to the average poor person than to the average rich person? Should econ­ or, equivalently, particular lists of num­ omists give different weight to additional income bers. For example, if utility is cardinally for the rich and poor when doing cost-benefit analy­ (ordinally) measurable, then each L;, will sis? Does a hungry person need food more than a bored person needs theater tickets? If income is re­ contain functions or sets of numbers that distributed to the poor, with no change in total in­ are related to each other by positive linear come, does national welfare go up or down? Is there (monotone) transformations. an economic justification for progressive income tax schemes? In this framework, we may view the 3 In his Essays on the Nature and Significance of problem of making interpersonal compar­ &anomic Science Lionel Robbins stated that this isons of utility as that of selecting a utility was "(t)he definition of Economics which would probably command most adherents, at any rate in function from each L;,. This determines Anglo-Saxon countries" (1937 [1932), p. 4). the magnitude of the number that will Cooter and Rappaport: Were the Ordinalists Wrong? 509 represent each person's utility in compari­ them. Essentially, goods were seen as hav­ sons. For reasons explained below, we will ing utility if they contributed to a person's call such a choice a "comparability con­ physical well-being, which was conceived vention." In general, there will be com­ as nearly equivalent to productive capac­ parability conventions from which it will ity. Physical well-being is objective, like follow that person 1 derives more utility the condition of a person's health, not sub­ than 2 in a particular state, and conven­ jective, like a person's enjoyment of a tions that entail the reverse. 4 In particular, good meal. Furthermore, productive ca­ even if individual utility is cardinally mea­ pacity of people is closely related to eco­ surable, it can be seen that the L;, have nomic efficiency, which is also objective. not been restricted sufficiently to make When ordinalist writers criticized this the outcome of a comparison independent comparability convention, they attributed of the comparability convention adopted. to the material welfare school their own For example, one can find a pair of utility conception of utility rankings, derived functions for which the state that yields from individuals' preference orderings. If 1 lowest utility has a higher number at­ utility is related tdpreference in this way, tached to it than 2's highest utility state, then interpersonal comparisons inevitably and a pair for which the reverse occurs. seem arbitrary, as if the writer were im­ A fortiori, we are not prevented from em­ posing his or her preferences on society. ploying conventions that yield these re­ However, the material welfare school did sults when utility is ordinally measurable. not equate utility with preference. It is apparent from the above that the The body of this paper examines the "arbitrariness" involved in making inter­ conceptual frameworks of the two schools. personal comparisons arises from the diffi­ The substantial difference between them culty of discriminating among compara­ is offered as evidence against the view that bility conventions. Restricting the L;, by the ordinalist revolution may be explained appeal to the standard measurability con­ as part of the progress of economic sci­ ditions does not materially limit the num­ ence. The fl.rst section summarizes general ber of possible comparability conventions. developments in utility theory up to the As we shall see, the material welfare early twentieth century. The next section school did opt for a particular comparabil­ describes the conceptual framework of ity convention, and evaluated social wel­ the material welfare school. Following fare on the basis of it. This choice could this, a comparison is made with the ordi­ be defended in the context of the inter­ nalist school, which reveals that the two pretation of utility employed by the mate­ schools were using the common elements rial welfare school. Utility rankings were in their vocabularies to refer to different not seen as coextensive with preference things. The fl.nal sections of the paper sum­ orderings, nor were they derived from marize the argument, and suggest lines along which to explain the success of the • This is so, even though, to be accurate, a compar­ ordinalist view. ability convention defines an equivalence class in L, the Cartesian product of L 1 L 2, in the sense that The aim of this paper is to demonstrate elements of this class will return the same results that the arguments developed some fl.fty for interpersonal comparisons of utility.