Scientific credit : the case of economics

Back when I was training as a historian of economics, I never imagined I'd run into so many debates about scientific credit. I should have known better. My postdoc supervisor was Roy Weintraub. At that time, he was actively working on Finding Equilibrium with Till Düppe. The book was to crown decades of investigation into the gap between the credit Gérard Debreu, Kenneth Arrow and Lionel McKenzie each received vs deserved for proving the existence of a competitive equilibrium in a general equilibrium setting. Roy recently shared the article that sparked his reflection on how historians should approach economists’ claims to scientific credit. He compared Arrow and Hurwicz’s identification of “precursors” in their famous 1958 Econometrica paper (Samuelson, Lange, Metlzer and Morishima) with the intellectual genealogies of study of the stability of a competitive equilibrium that each of them later provided in interviews. He also documented which stability questions Samuelson and Metlzer tackled.

The point is not to settle which genealogy is correct, but rather (1) to illustrate how “the creation of a model simultaneously creates and is created by history” and (2) to understand why economists construct genealogies (to assert claims of progress, as well as to establish legitimacy and authority – I work on this issue, as Keynes previously did. No one challenges how legitimate Keynes was so I am too). The Arrow-Debreu-McKenzie puzzle conundrum was however different. It’s not about precursors, it’s about the simultaneous discovery of a well-identified contribution: who first offered the proof of existence. The historian’s task is thus to reconstruct who wrote it down and presented it when, who reviewed it and what was published first – a classic case of Mertonian multiple independent discoveries in science.

The credit issues I encountered research are of a different kind. By construction, they lack a clear object - a proof, a model, an idea, a concept, a theory, a tool. In debates between heterodox and mainstream economists, successive generations of economists, or economists bringing different contributions to a common table (think experimentalists, game theorists and computer scientists in market design), the disagreement is over what a scholar should get credit for.

One episode where such disagreement is especially salient is the controversy between French mathematician Maurice Frechet and John von Neumann over who was the “initiator of the theory of psychological game and its application.”

The first Econometrica issue of 1953 featured three essays on strategic games published in French by mathematician Emile Borel between 1921 and 1927 – sandwiched between Gorman’s community preference paper and Nash’s 2 person cooperative games one. These were translated by Savage and accompanied by a note in which Frechet argued that Borel made the first attempt to provide systematic mathematical foundations to gamers’ psychology and envision various applications. He was also “the first to indicate the potential importance for this theory of knowing whether [the minimax] theorem, applied to n manners of playing, is true for arbitrary n.” Adding insult to injury, Frechet concluded that Von Neumann “simply entered an open door.”

Von Neumann, needless to say, struck back. He acknowledged that Borel ‘was the first author to evolve the concept of a strategy pure as well as mixed.” But crucially, Borel didn’t prove the minimax theorem. “As far as I can see,” he added, “there could be no theory of fames on these bases without that theorem… there was nothing worth publishing until the ‘minimax theorem’ was proved.”  In fact, Von Neumann added, Borel did not believe the minimax theorem was true, which gave a “discouraging” and “negative” flavor to his notes.  He went on to offer his own genealogy of discoveries and to articulate his own notion of credit: “"It is common and tempting fallacy to view the later steps in a mathematical evolution as much more obvious and cogent after the fact than they were beforehand."

I recently learned from the history of the reception of game theory in France penned by Rabia Nessah, Tarik Tadzaït and Mehrdad Vahabi that the exchange didn’t stop there.^[1] In 1959, Frechet had the exchange translated in French published in the Revue d’Economie Politique with a further rejoinder. This time, Frechet emphasized Von Neumann’s confession that he had read Borel’s notes before writing his dissertation, and outlined four stages of discovery:

I. To dare to conceive the audacious project to translate gamers' psychology into mathematics. How many economists and mathematicians would have balked before the obstacle at such an undertaking, considering the players' skills beyond the scope of mathematics?

II. — With this project in mind, to construct a system of hypotheses satisfying these two contradictory conditions: to remain plausible (not straying too far from reality) and lending themselves to a mathematical translation, which, in turn, would raise a mathematical problem

III. — To grapple with and resolve this purely mathematical problem.

IV. — To understand that the set of hypotheses crafted for a theory of psychological games could be extended to other domains.

Frechet contended that Borel “initiated” I, II and IV, leaving III to Von Neumann. Thus, Frechet and von Neumann disagreed on what game theorists should get credit for: a concept, its mathematical formulation, a proof, or some applications? Their exchange also illuminates a key difference in how economists and historians approach credit. Historians ask “who was the first” and dig out more distant precursors in the successive layers of the past. What matters is where it began.^[2] Economists ask ‘who was the last’ and some strive to establish themselves as proposing the “definite” theory/model/technique, not just the shoulders for the next generations, but their workhorse. What matters is where it ended.

These disagreements are significant, because what receives credit determines what is seen as a “definite contribution” in a particular field. For instance, there’s a large literature on how Von Neumann’s mathematical apparatus, as well as view of games as a suitable analogy for economic rationality have shaped later development in game theory. But did his view of what constitute a definite contribution also shaped the field and how long? Bob Wilson, for instance, believes that the notion “that the goal of game theory should be to find the “solution” to each class of game, that would “solve” each kind of theory,” was “inherited from von Neumann and Morgenstern.” “An existence proof was often regarded as the main contribution of Nash (1950), rather than his novel formulation of strategic equilibrium,” he explained.^[3]

I also wonder whether the vaguely articulated views of credit we have as historians might clash with the vaguely articulated views of credit that our protagonists hold. Even when we don’t have a fully formed view of credit, how do we approach bodies of economic literature where underlying competing claims for scientific credit surface? Are you more on the Borel side, the Von Neumann side, agnostic, or have the rise of econometrics, simulations, lab and field experiments fueled other notions of credit that you woulds endorse?^[4]

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^[1] Did you know that Lacan and Levi-Strauss each played a role in advancing game theory? No? Then read the paper, it’s really cool.

^[2] See for instance Dimand and Dimand’s paper on those minimax solutions predating Borel and Von Neumann.

^[3] What does and doesn’t count as a definite contribution is also the mechanism at work in the invisibilization of women from science (see the use of Photograph 51 in erasing Rosalind Franklin from the history of DNA discovery, Lise Meitner on nuclear fission, or Jocelyn Burnell on pulsar.

^[4] Some of us have recently asked how much credit economists should get from writing the algorithms and softwares that allow to solve new classes of models.