An Arrow in the Black: Condorcet, Duncan Black and Kenneth Arrow

In the c18th, the Marquis de Condorcet was writing pioneering Political Economy. He demonstrated the possibility that out of three candidates: A, B and C, in a one on one vote A can beat B, B can beat C, and yet C could beat A.
This occurence would be intransitive and violate a fundamental law of economics. Intuitively, if you prefer Fosters to Budweiser (A>B), and Budweiser to Guiness (B>C), transitivity says that you prefer Fosters to Guiness (A>C).

In Politics, if this doesn't hold we have the possibility of vote cycles, and no definate outcome. Alas, Condorcet's career ended with the steely blade of Mdme Guilotine and his insight was lost. In 1876 Charles Dodgson produced the same voting system, where the winner should be he who win's each pair-wise contest. It seems unlikely that he was aware of Condorcet, but his work too was lost.

In the 1940s Public Choice (the application of economic methodology to political science) pioneer Duncan Black encountered the work of Dodgson and also Condorcet. He submitted an article to 'Econometrica' around 1948, but the article was held up in the refereeing process for 18 months, after which he received a rejection on the grounds that the work of Kenneth Arrow had not been cited. In 1951 Arrow's dissertation "Social Choice and Individual Values" was published, somewhat behind schedule, and included "Arrow's Impossibility Theorem":

Arrow's theorem says that if the decision-making body has at least two members and at least three options to decide among, then it is impossible to design a social choice function that satisfies all these conditions at once. (source).

Black refused to cite Arrow, so his paper was lost from history, and a mystery developed as to how Arrow suddenly decided on his thesis, in a field somewhat removed from what he'd been working on.

What if the referee was Kenneth Arrow?

Comments

[Gabriel]

OK, since you brought up this old thread, maybe you could explain how this is not a first class smear, based on innuendos and speculation. :-(

The history of Arrow's involvement with this subject is of public record and the set theoretic feel of his work matches well with the Cowles Commission atmosphere at the time and the interest in SWF of the Bergson-Samuelson type in that era.

I can't remember right now but there's an interview or memoir where Arrow mentions a political philosopher asking him to work out the details of what it means to use a SWF and that's how it got started.

If his story was B.S., either the people he mentions as involved or, for that matter, the editor of the journal could have come out any time.

[Gabriel]

Here's one...

Dubra, Juan (2005): Interview with Kenneth Arrow
http://mpra.ub.uni-muenchen.de/967/

From page 14:

The question that stimulated my social choice work arose at the Rand Corporation, where I spent the summer of 1948. Game theory was being developed there with the view that it would help analyze the diplomatic and military interactions between the United States and the Soviet Union.
In the intellectually adventurous attitude of Rand at that time, they had on their staff a philosopher, Olaf Helmer. He asked me one day how one could consider either of these abstract entities as players in a game, when each was in fact composed of many individuals with varying values. I glibly replied that welfare economists, particularly Abram Bergson, had discussed that question in the context of justifying economic policies. He asked me to write an expository account; when trying to do so, I was led to formulate the social choice problem and discover the impossibility of a general solution satisfying certain very natural appearing assumptions.

[aje]

I think these issues are important - the chronology and attribution of ideas, and also the mechanisms (and possible imperfections) of the academic publication process. Yes, this post isn't especially mature, but I'm telling a story that's more than mere speculation. It is important to know that Black's work pre-empted Arrow. It might also be important to know more about why Black's paper was held up for so long. I've heard on good authority that Arrow was the referee. Maybe he wasn't. It's worth pondering though, surely?

[Gabriel]

Well, from what you're telling me, Black's paper didn't prove theorems with anything like the generality of Arrow's results.

I would understand if you'd like to portray Black as a Condorcet scholar, but I don't see how he "pre-empted" Arrow...

Lastly, if the "good authority" you mention had any proof, (s)he could have come forward. So could Econometrica's editor(s). Any time during the last 60 years or so.

I'll admit that Arrow is not the guy to be shy about taking credit, but credit IS due, vastly so.

I guess I just didn't like the tone and the general implication of the post... that's life... Plus I really like Arrow. Regardless of how much of a lefty he is.