After WWII, when returning to Columbia in 1946, Kenneth Arrow was looking for a topic for his PhD dissertation, having persuaded himself that although he was an “excellent student”, he was not able to do anything original alone.
After WWII, when returning to Columbia in 1946, Kenneth Arrow was looking for a topic for his PhD dissertation, having persuaded himself that although he was an “excellent student”, he was not able to do anything original alone (Arrow 1986). Although he was not aware of Condorcet’s works, as he has insisted many times since, two years or so later, now at Cowles, he quickly developed the equivalent of Duncan Black’s single-peakedness theorem. He realized a month later that this result had been already published by Black in the June 1948 issue of the Journal of Political Economy (Black 1948). But before the 1948 summer he spent at the RAND Corporation in Santa Monica, Arrow had never thought of embarking on a PhD dissertation on these issues. At RAND, the visiting scholars were working on game theory and using it to analyze international relations and military conflict. During a famous coffee break, the German philosopher Olaf Helmer wondered how countries could have utility functions like individual players do. To answer him, Arrow began to work on this topic and, as attested by the RAND report entitled “The possibility of a universal social choice welfare function” dated September 26, 1948, devised his famous theorem, before going back to Chicago for the 1948 fall semester: “about three or four days later, I saw that the voting paradox would be replicated, no matter what you did” (Arrow in Horn 2009). He now had a topic for his PhD dissertation: “this was the first time I thought I had done something” (ibid.). Then Arrow’s seminal result was disseminated by the 1950 Journal of Political Economy paper and above all by his Social Choice and Individual Values, published in 1951 as a monograph of the Cowles Commission and thanks to which he came to be seen as the founder of social choice theory.
As claim by Amadae (2003, p 123), “the priority dispute between Black and Arrow over the mathematical analysis of election problems was bitter and unresolved. With his 1948 publication of “On the Rationale of Group Decision Making,” it would seem that Black priori understanding of collective decision problems was securely established. However, the dispute only intensified when Black’s second article, co-authored with RA Newing, slowly proceeded through what turned out to be a lengthy review process at the journal Econometrica. This paper was submitted in November 1949. A year and a half later, after badgering the managing editor William B. Simpson for some idea of the article’s status, Black was informed that it would be accepted on the condition that the authors thoroughly revise in consideration of Arrow’s recently published Social Choice and Individual Values. Black’s outrage was complete when he learned that Simpson played another professional role as assistant direction of research at the Cowles commission in Chicago, where Arrow worked. It took the better part of a decade for Black to regroup, finally publishing his book The Theory of Committees and Elections in 1958.”
While Black’s recollection of this episode regarding the way he obtains his 1948 result seems sincere (see Coase 1981, Black 1991 as well as Brady and Tullock 1996, McLean, McMillan and Monroe 1996 and 1998), it has to be acknowledged that Arrow’s remains rather vague. On the basis of Black’s (kept at the University of Glasgow) and Tullock’s papers (kept at the Hoover Archives – Stanford University), the aim of my article is twofold: on the one hand, it aims to reconstruct historically this dispute between the two authors; on the other hand, it takes this opportunity to highlight the different points of view of Arrow and Black concerning their work on collective decision. Whereas Arrow's work is profoundly normative, Black's is mainly focused on empirical/statistical considerations. The article will especially return to Black's unknown criticisms of Arrow’s impossibility theorem (Black 1969, 1991) and the help that Duncan Black received from American researchers from the 1960s onwards (Coase, Tullock, Riker), before finally being recognized as the 'founding father' of Public Choice (Tullock 1991).
Herrade Igersheim is a Research Director at the CNRS and BETA, University of Strasbourg