Learning The Origin Of “Duality”

Learning The Origin Of “Duality”

 Yesterday I learned that the person who first used the term “duality” in connection with linear programming, indeed with anything in economics, was John von Neumann in a private conversation with George Dantzig in 1947, the “father of linear programming.”  That was the year Dantzig published his paper showing the simplex method for solving linear programming problems, bot their primals and their  duals.  Von Neumann wrote a paper on it the same year but did not publish it, with it only appearing in his Collected Papers in 1963, 6 years after he died.

It is not really surprising that it would be von Neumann as there are deep links between oprimizing programming and game theory.  This would be seen in 1951 when David Gale, Harold Kuhn, and Albert Tucker invented nonlinear programming.  Kuhn and Tucker would, of course, prove the Kuhn-Tucker theorem that deeply involves duality.  1951 would also be the year that Tucker’s student, John Nash, completed his PhD thesis with his ultimately Nobel-Prize-winning paper on non-cooperative game theory.  An irony is that while seeing the first prisoner’s dilemma experiments at RAND soon after, Nash would become disillusioned with game theory and economics, it would be Tucker who would coin the term “prisoner’s dilemma” in an address to the American Psychology Association.


While the term was introduced into linear programming by von Neumann, the concept itself had already been floating around in economics, with its first appearance being in 1886 when Antonelli first derived an indirect utility function.  It would be further developed by Harold Hotelling in a famous paper in 1932 with “Hotelling’s Lemma,” and the 1942 paper by Roy in which he introduced his famous identity.

While I had previously known bits of this, what I learned yesterday came from an ongoing project of mine to read the entire 3rd edition of the New Palgrave Dictionary of Economics, all 20 volumes of it, nearly 15,000 pages and about 3800 entries.  I am doing that because I am one of the coeditors of the fourth  edition, along with Matias Vernengo and Esteban Perez.  I have learned a great deal from this reading, which has now gotten me through entries for the letter D.  I have a ways to go, but I am genuinely impressed by the job that Steve Durlauf and Larry Blume did editing the third edition.

The original Palgrave Dictionary of Economics was published in 1893.  The current one still has entries from that original one by people like Edgeworth and Wicksteed.  Some of these oldies are really quite fascinating.  But the cumulative effect of reading all of it is really beginning to kind of blow my mind.

Oh, and returning to the original topic, for anyone who does not know, it has long been viewed by many as being one of the greatest mistakes and wrongs that when the Nobel Prize was given for linear programming, Dantzig was not one of the recipients, who were Leonid Kantorovich, the only actual Soviet economist to win a Nobel, and Tjalling Koopmans. There  was room for Dantzig (especially with von Neumann dead), but somehow he got left out.  But then, hey, they never gave it to Joan Robinson either.

Barkley Rosser

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