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Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit

Author(s):Düppe, Till
Weintraub, E. Roy
Reviewer(s):Bjerkholt, Olav

Published by EH.Net (February 2015)

Till Düppe and E. Roy Weintraub, Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit.  Princeton, NJ: Princeton University Press, 2014. xxi + 276 pp. $39.50 (hardcover), ISBN: 978-0-691-15664-4.

Reviewed for EH.Net by Olav Bjerkholt, Department of Economics, University of Oslo.

My first contact with this book happened in 2012 while attending a conference on economic thought in Saint Petersburg, when I walked unwittingly into a classroom and found Roy Weintraub mesmerizing the small audience while reading from a manuscript. When it finished I wanted to know about the book but while I turned my back for a second Weintraub vanished, like a character in a Bulgakov novel, no longer to be seen on Chaykovski ulica. I later found out he was not registered for the conference and I wondered if it all had been a figment of my imagination.

But the book was real and, as I found out two years later, even more fascinating than Roy’s forerunner. The main narrative told in the book is the hunt for the proof of the existence of equilibrium in a Walrasian economy by the three key protagonists, Kenneth Arrow, Gerard Debreu, and Lionel McKenzie, with differences in thinking and ideas but pursuing the same aim. The papers claiming to have achieved the proof in a general setting were presented to Econometric Society in Chicago in December 1952. Arrow and Debreu had managed to write a joint paper despite being on somewhat different tracks and without ever having met in person until two weeks before the Chicago meeting. McKenzie submitted his own paper and he and Arrow-Debreu did not know about the other paper until they met at the meeting. The papers were published in successive issues of Econometrica in 1954, and have been standard references ever since.

The book has a marvelous and incredibly detailed reconstruction of the paths pursued by the three protagonists with mathematical details suppressed. These parallel stories are rich in content about how they got the impulses and the inspiration, how they picked up the new mathematical tools they needed, how they interacted or chose not to interact. The narrative has been built from reminiscences, reinforced by interviews, combined with contemporary evidence and painstakingly put together. The narrative continues in a fairly detailed account of the refereeing process which ran into various problems. As the editorial files of Econometrica are not available, the account has impressively been put together by evidence compiled from the authors, referees, and correspondence. There were rivalry concerns, primarily with Debreu and McKenzie, while Arrow took a grander view of the whole process. Arrow and Debreu went through rounds of agreeing on a revised joint paper while McKenzie was quicker to submit but unlucky with the referees who had to be replaced. Robert Solow was brought in as a pinch-hit editor in charge of McKenzie’s paper; but not knowing about the other paper and the tense competitive situation he ill-advisedly chose Debreu to review McKenzie’s paper. The editors of Econometrica were well aware of the importance of these papers. In the end the two papers were published in successive issues of the journal.

Students of Roy Weintraub’s work know that it is not much of an exaggeration to state that he has conducted research relevant for this book throughout much of his life. Weintraub’s Journal of Economic Literature paper in 1983 was a milestone and one of the pillars underpinning this book. Other published works by the authors were integrated into the book. Underneath the concern with the existence proofs there is in Weintraub’s world a wider interest in the mathematization of economics and the breakthrough of new mathematical tools for economic theory. Weintraub has paid much attention to the role of interwar impulses from Vienna in the shape of John von Neumann and Abraham Wald, providing crucial input for the three protagonists in their quest for finding equilibrium, with a key inspirational role played by the Vienna mathematical economist Karl Schlesinger, one of the earliest members of the Econometric Society. The overall scope of the story is really too much to be covered well in a thin book.

In addition to the centerpiece about the proofs, the book has background notes on the early life of the three protagonists to find “what sense of meaning, what hopes led them into mathematical economics” and further “to understand the choices and needs that committed their intellectual lives to the emerging field of mathematical economics.” This reviewer found these quasi-philosophical concerns of less interest than the down-to-earth story about the three protagonists’ respective experiences. The authors label Debreu as “the odd man out,” while McKenzie is characterized by his “frustrations.” Till Düppe has done very interesting research on Debreu’s life and career. The respective oddities of Debreu and McKenzie make Arrow loom larger; he is free of the obsessions and the self-centeredness of the other two and comes through as a curious and interested student who looks into and tries his hand along a much broader range of mathematical economics.

The authors pay very great attention to a small Cowles Commission conference in June 1949 on “linear programming.” (It was indeed the fourth CC conference; the first one in January 1945 brought forth the papers for the famous CC Monograph 10.) The preparation of the conference was discussed in an earlier paper by Düppe and Weintraub, opening with the enticing sentence: “In December 1948 in one of the hotel rooms at the annual meeting of the American Economic Association, seven scholars with various backgrounds, but similar interests conceived the idea of a conference: Tjalling C. Koopmans, Harold Kuhn, George Dantzig, Albert Tucker, Oskar Morgenstern, and Wassily Leontief.” It made me ponder who the seventh man was: David Gale and some other names came to my mind. In Finding Equilibrium the same enticing sentence opens chapter 5 but with “seven” changed to “several” (sic). That was a glib way out; who was the seventh man? My thoughts wandered to the “third man” incarnated by Orson Welles, which premiered the same year.

This conference obviously was a very interesting event but this reviewer finds the importance of and the pretensions made about this conference blown out of proportions. It was one of many meeting places in those years for highly gifted mathematicians and economists to mingle and exchange ideas. The “New Beginning” (p.112), the “new future of economic research” (p.100) and the other solemn terms the authors use about the conference are perhaps only a highfalutin way of stating what was “in the air” as Arrow expressed it. The exalted tone and expressions used by authors about the conference seem oddly feigned. The authors claim that the impact on our three protagonists of the conference was that it “transformed their intellectual lives” (p.117).  Two of them were not even there and Arrow, who was present, was hardly “transformed” by the experience.

The book has weaknesses. It is sloppy on many details, surprising in view of the decades of research that went into it but perhaps a result of pieces written at different times being pasted together. The errors are numerous, so only some examples will be given. The main weakness is perhaps that most of what is written about the Cowles Commission is uninformed, incorrect or just made up. The Econometric Society which at the time was the only community for mathematical economics does not really appear in the book as an entity of importance, neither under “Sites” (chapter 4) nor under “Community” (chapter 5). The Econometric Society was established not least to promote mathematics in economics and the increased emphasis on mathematical economics that happened in the period under consideration in the book is more naturally seen as a continuation of the spearheading efforts of Irving Fisher and the other early members of the Society than as something completely new and different. The relationship between the Cowles Commission and the Econometric Society is even less well understood. The Cowles Commission was “affiliated with the Econometric Society”; for which it was also the “headquarters.” This close and important bond between the Commission and the Econometric Society seems poorly understood by the authors.

Then to some trivialities. The book is confused about the date when Arrow came to the Cowles Commission and similarly confused about when Debreu arrived. These are minor things but the carelessness is worrisome in a book that is very assertive about having got the facts right. The book mentions (p. 14) that Koopmans had a persuasive recruiting talk with Arrow at a meeting (undated) of the American Statistical Society at Cornell. There is no such thing as the American Statistical Society; in fact, the talk took place at a meeting of the Institute of Mathematical Statistics in August 1946. The American Statistical Society is mentioned again (p. 108) where it should have been the American Statistical Association. There are too many such infelicities.

One of the more colorful incorrect assertions is that Abraham Wald fled from Europe and got to the U.S. via Cuba. Totally wrong, Wald arrived to New York on July 4, 1938 on the North German Lloyd line from Bremen to New York, the most popular way of fleeing Europe; the ship had no luxury or first-class cabin. The source given is a 2010 volume about the creation of game theory by Robert Leonard who is likely to have taken the escape-via-Cuba story from Weintraub’s own 1983 paper! Why the false ornamentation when the event itself — Wald’s move from Europe to the U.S. — is of such path-breaking importance that it can hardly be exaggerated.

One mistake for which the authors can be exonerated is the label used for the so-called Nobel Prize in economics. Arrow received in 1972 the “Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel” but that was the first “Bank” prize awarded, and another prize with “Bank” in the name was not awarded until 1991. No “Bank” for Koopmans, or for Debreu. The almost incredible fact is that the Swedish Prize committee has used about eight different labels in English for the prize.

Towards the end of the book the authors follow Debreu and McKenzie to the end of their lives in 2002 and 2010, respectively, while Arrow is left standing erect as a live monument of times gone by, while he himself seems more concerned about current economic issues rather than the history he has helped create. Also these stories provide fascinating glimpses. After five years as research associate of the Cowles Commission, Debreu moved with the Commission to Yale, where he became associate professor, mainly assigned to the Cowles Foundation. Just around the time when his Theory of Value was published in 1959, Debreu was denied tenure at Yale, after a performance that was later found worthy of a Nobel Prize. The book mentions the incident but not why it happened. Perhaps it was the Cowles Foundation refraining from a clear recommendation rather than any other kind of backstabbing at Yale?

A missing item in the authors’ story about how Arrow got into mathematical economics is given a memory glimpse from 1942, when Arrow still had not decided whether to become a mathematician, a theoretical statistician, or choose the path he took. Wald brought Arrow with him to a seminar “where Haavelmo presented his new methods: Marschak in the chair, probing, questioning; Koopmans, even more ascetic-looking and soft-spoken than he is today, obviously understanding the issues better than anyone else; and Schumpeter, somehow ensconced more comfortably than the rest and treating the whole matter with the benevolent condescension of a lord among well-meaning and deserving but necessarily limited peasants. … an important turning-point had been reached, and Marschak saw the need for effective leadership.” It was Arrow’s first meeting with Marschak and Koopmans. Seventy years later it is Arrow who with benevolent condescension is ensconced among well-meaning and deserving but not necessarily limited historians of economic thought.

Olav Bjerkholt is the author of articles about Ragnar Frisch, Trygve Haavelmo and the early Econometric Society.

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Subject(s):History of Economic Thought; Methodology
Geographic Area(s):General, International, or Comparative
Time Period(s):20th Century: WWII and post-WWII