The emergence of social choice at the Cowles Commission, 1948–1952: Arrow’s Social Choice and Individual Values in context

Abstract

Kenneth Arrow’s Social Choice and Individual Values (Cowles Monograph No. 12, 1951), a work that established the field of social choice and set the limits for what public economic theory could hope to achieve, was formulated at the Cowles Commission at the University of Chicago from 1947 to 1949 (and during the summer of 1948 at the RAND Corporation) in a context in which concern with using economic theory to guide the economy was intense. During the period just before he shared in developing the Arrow-Debreu-McKenzie proof of existence of general equilibrium, Arrow moved through a series of papers to prove the non-existence of a social welfare function. The context of Arrow’s non-existence proof for aggregation of individual preferences into social welfare function and to Arrow’s shift from trying to prove a possibility theorem for social welfare to proving an impossibility theorem has been confused by a reprinted and influential reminiscence in which Arrow mis-remembered when he had spent a summer at RAND and when he had presented his impossibility theorem to the Econometric Society.

Keywords:

• Arrow impossibility theorem
• Cowles Commission
• Arrow on social choice

JEL CLASSIFICATIONS:

• B21 History of economic thought since 1925: microeconomics
• D71 social choice

Acknowledgments

This paper is part of larger project on the history of the Cowles Commission for Research in Economics. Presented online to the Graz workshop on “From Public Finance to Public Economics.” I am grateful to Maxime Desmarais-Tremblay, Herrade Igersheim, Marianne Johnson and other participants in the workshop, and to two anonymous referees, for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Fisher’s ideal index number, the geometric mean of the Paasche and Laspeyres indices, satisfied six of his seven tests, but Frisch showed that no index could satisfy all seven without contradiction.

2 Düppe and Weintraub (2014, 22) cite Hildreth (1986, 92) on Arrow presenting six discussion papers on social choice to the weekly or bi-weekly Cowles staff seminars (as distinct from the more formal monthly seminars, usually given by outside speakers) but give no titles or other details. Although Hildreth mentioned the existence, but not the titles, of Arrow’s discussion papers, he did not list them or any other Cowles Commission Discussion Papers in his bibliography (1986, 138–163), citing Goodman and Markowitz (1952) and Hildreth (1953) from their subsequent published versions.

3 Arrow (writing in French in 1952, translated in Arrow 1983, 50) later preferred the term social choice function to Bergson’s social welfare function, on the grounds that only individuals, not society, can make value judgments about welfare: “the social choice function (based on individual preferences) is only a means of making social decisions and not at all an expression of some interpersonal ethic. Nevertheless, the social choice function does have a very close formal resemblance to the concept of the social welfare function introduced by Bergson some years ago; both functions define an ordering constructed by aggregation of individual orderings.”

4 Abram Bergson, the Columbia and later Harvard economist whose 1938 article formulated a social welfare function for a single profile of individual offerings, was a lifelong student of the Soviet economy and especially of Soviet planning (e.g., Bergson 1964). Bergson was a member of Arrow’s dissertation committee and Arrow ([1951] 1963, 3) cited Bergson’s survey article on “Socialist Economics” in the American Economic Association’s Survey of Contemporary Economics (Ellis 1948, Chapter XII).

5 On Friedman’s attitude towards the Cowles Commission researchers, including Arrow, see Düppe and Weintraub (2014, 79–81), Johanna Bockman (2011), and Dimand and Rivot (2021), and, more generally on the impact of Cold War tensions on post-World War II studies of rational choice and collective decision-making in and beyond Chicago, see Amadae (2003, 2016) and Cherrier and Fleury (2017). According to the Cowles Commission’s annual report for 1947, Friedman’s Cowles Commission seminar on “Utility Analysis of Gambling and Insurance” in October 1947 was the first Cowles seminar “held jointly with the Statistical Techniques Group of the Chicago Chapter of the American Statistical Association (Kenneth J. Arrow, Group Chairman)” but, despite this welcome, Friedman continued to view his role in the Cowles seminars as that of a hostile critic of the statist leanings of the Cowles mathematical economists (see Friedman and Friedman 1998; Dimand and Rivot 2021).

6 Arrow modestly did not mention his work on social choice in his essay “Cowles in the History of Economic Thought” in the Cowles 50th anniversary volume while Debreu referred to it only in passing in his essay in that volume on “Mathematical Economics at Cowles” (Arrow et al. 1991, 30).

7 Project Rand, subsequently the RAND Corporation (with RAND standing for Research and Development), initially had the US Air Force as its only client. At the time of Arrow’s summer at Rand, the Cowles Commission held a contract from Project Rand to study resource allocation. Arrow (in Kelly 1987, 51) explained that he was invited to RAND by the mathematical statistician M. A. Girschick (a Cowles Commission research consultant), for whom Arrow’s wife had worked at the Agriculture Department before Girschick moved to RAND and took up game theory.

8 As listed in the acknowledgements to Arrow ([1951] 1963), Simon’s affiliations were Cowles Commission and Carnegie-Mellon University, Modigliani’s were Cowles Commission and the University of Illinois, although each had begun his Cowles affiliation while at the University of Chicago. Arrow, whose Cowles monograph also served as his Columbia dissertation, thanked Abram Bergson and Albert G. Hart, along with Koopmans, for reading the entire manuscript (as well as that of Arrow 1950) and for improvements of presentation and clarification of meaning.

9 According to the Cowles Commission Annual Report (Cowles Commission, 1947–1954), Hicks also gave a seminar at the Cowles Commission in October 1946 on the aggregation of consumer surplus (presumably the same paper that Arrow heard at Columbia), and that year was offered a professorship at the Cowles Commission and the University of Chicago, which he declined, remaining at Oxford (see the online appendix of documents to Mitch 2016).

10 It is possible that Arrow suggested to Mathematical Reviews that he review Ville’s article. Arrow would have seen Black’s next articles on voting (1948b, c) at the latest when the July 1948 issue of Econometrica appeared. Arrow ([1951] 1963, 6 n17) credited Black (1948b, 262, 270; 1948d, 262–269) with making the analogy between voting and the market but did not attribute that analogy to Black (1948a).

11 Kenneth May disappeared from the annual reports of the Cowles Commission after the report for 1947, which mentioned that he presented two papers in September and December 1947 on the probability of unfair election results, both abstracted in the Bulletin of the American Mathematical Society. May attended Arrow’s Econometric Society presentation of the impossibility theorem (Arrow in Feiwel 1987, 56) and in the early 1950s he published Econometrica articles on necessary and sufficient conditions for simple majority decision to be optimal and on intransitivity, utility and aggregation (May 1952, 1953, 1954), the first two of which were cited several times in Arrow’s second edition ([1951] 1963, 96, 101, 102, 119n). Arrow ([1951] 1963, 101 n26) noted that while only majority voting satisfies all of May’s conditions if there are only two alternatives, many choice methods, such as plurality voting and rank-order summation, satisfy May’s conditions when there are more than two alternatives. As a research consultant rather than a research associate, May is omitted from Hildreth’s appendix listing Cowles Commission residents, 1939 to 1955 (Hildreth 1986, 132–135).

12 Arrow (1950) teased Modigliani about the value judgments implicit in Modigliani’s proposal in a press release to deal with the high price of food imports by an excise tax on farmers and subsidy to consumers (reprinted in Arrow 1983, 27).