Chapter 13 · Where the Mathematics Stops
Kenneth J. Arrow
1921 – 2017
Photograph: Linda A. Cicero / Stanford News Service, Kenneth Arrow (4 November 1996), CC BY 3.0, via Wikimedia Commons. Shown toned. File and licence
The problem on the desk
Can individual rankings be combined into a social ranking while preserving several attractive requirements at once? Arrow’s impossibility result showed that the specified requirements cannot all hold together.1
A life in moments
- 1921
New York City
Born on 23 August.2
- 1940
City College of New York · New York City
Graduated with a social-science degree and a mathematics major.2
- 1941
Columbia University · New York City
Completed a master’s degree in mathematics.2
- 1951
Columbia University · New York City
Received his doctorate for Social Choice and Individual Values.3
- 1968
Harvard University · Cambridge, Massachusetts
Moved from Stanford to Harvard.3
- 1979
Stanford University · Stanford
Returned to Stanford.3
- 2017
Died on 21 February.4
Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.
In their own words
That’s a topic I know virtually nothing about. Therefore, I am especially interested in getting involved and learning about it.
A recurring reply to invitations to work on an unfamiliar topic, as recalled by Levin and Dixit.
A story
A question at RAND
The INFORMS memorial locates the formulation of Arrow’s social-choice theory and impossibility theorem in his RAND work. That research became the doctoral dissertation and the subsequent book.5
Around Arrow
- co-author Theodore E. Harris Arrow, Theodore Harris and Jacob Marschak co-authored a 1951 paper on inventory theory.5
Recorded as advisor Harold Hotelling Recorded as students John Harsanyi (formal supervision disputed), A. Michael Spence, Eric Maskin Mathematics Genealogy Project record
The genealogy lists only what the database records; a missing name is not a missing teacher.
The card in the book
Born in New York City, he studied at the City College of New York (B.S. in social science with a mathematics major, 1940) and at Columbia University (M.A. in mathematics, 1941), and served as a weather officer in the US Army Air Corps from 1942 to 1946. After research at the Cowles Commission in Chicago he joined Stanford in 1949, moved to Harvard in 1968, and returned to Stanford in 1979. His Columbia doctoral dissertation was Social Choice and Individual Values, with the impossibility theorem; with Gérard Debreu he proved the existence of competitive equilibrium; and he studied information as an economic variable, in medical care, insurance and learning by doing. He shared the 1972 Nobel Memorial Prize in Economic Sciences with John Hicks.
Main works Social Choice and Individual Values (1951; 2nd ed. 1963); “Existence of an equilibrium for a competitive economy”, with G. Debreu (Econometrica 22, 1954); “Uncertainty and the welfare economics of medical care” (American Economic Review 53, 1963); Essays in the Theory of Risk-Bearing (1971).
To read further
- Kenneth Joseph Arrow, 1921–2017, Simon A. Levin and Avinash Dixit (2023) · NAS biographical memoir
Sources (6)
- Kenneth Joseph Arrow, 1921–2017, Simon A. Levin and Avinash Dixit, 2023; PDF p. 2, social-choice discussion
- Autobiography, Kenneth J. Arrow, 1973; Nobel autobiography reproduced in RePEc abstract; opening education paragraph
- Kenneth Joseph Arrow, 1921–2017, Simon A. Levin and Avinash Dixit, 2023; PDF p. 2
- Kenneth Joseph Arrow, 1921–2017, Simon A. Levin and Avinash Dixit, 2023; PDF p. 1
- Kenneth J. Arrow (1921–2017), INFORMS, OR/MS Today, 2017; Biography: RAND, social choice, inventory theory
- Kenneth Joseph Arrow, 1921–2017, Simon A. Levin and Avinash K. Dixit, 2023; National Academy of Sciences Biographical Memoirs, PDF p. 1, paragraph on his response to invitations to collaborate in an unfamiliar area
The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.