Biography:Kenneth Arrow

From HandWiki
Revision as of 06:27, 7 February 2024 by Rtextdoc (talk | contribs) (update)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Short description: American economist (1921–2017)


Kenneth Arrow
Kenneth Arrow, Stanford University.jpg
Arrow in 1996
Born
Kenneth Joseph Arrow

August 23, 1921
New York City, U.S.
DiedFebruary 21, 2017
Palo Alto, California, U.S.
InstitutionStanford University
University of Chicago
Field
School or
tradition		Neoclassical economics
Alma mater
Doctoral
advisor		Harold Hotelling
Doctoral
students
Influences
Contributions
Awards
  • John Bates Clark Medal (1957)
  • Nobel Prize in Economics (1972)
  • von Neumann Theory Prize (1986)
  • National Medal of Science (2004)
  • ForMemRS (2006)
Information at IDEAS / RePEc
Websitehealthpolicy.fsi.stanford.edu/people/kenneth_j_arrow

Kenneth Joseph Arrow (August 23, 1921 – February 21, 2017) was an American economist, mathematician, writer, and political theorist. Along with John Hicks, he won the Nobel Memorial Prize in Economic Sciences in 1972.

In economics, Arrow was a major figure in post-World War II neoclassical economic theory. Many of his former graduate students have gone on to win the Nobel Memorial Prize themselves. His most significant works are his contributions to social choice theory, notably "Arrow's impossibility theorem," and his work on general equilibrium analysis. He has also provided foundational work in many other areas of economics, including endogenous growth theory and the economics of information.

Education and early career

Arrow was born on August 23, 1921, in New York City .[3] Arrow's mother, Lilian (Greenberg), was from Iași, Romania, and his father, Harry Arrow, was from nearby Podu Iloaiei.[4][5] The Arrow family were Romanian Jews.[3][6][7] His family was very supportive of his education.[3] Growing up during the Great Depression, he embraced socialism in his youth. He would later move away from socialism, but his views retained a left-leaning philosophy.[8]

He graduated from Townsend Harris High School and then earned a bachelor’s degree in mathematics from the City College of New York in 1940, where he was a member of Sigma Phi Epsilon. He then attended Columbia University for graduate studies, obtaining a master's degree in mathematics in June 1941.[9] At Columbia, Arrow studied under Harold Hotelling, who influenced him to switch fields to economics.[8] He served as a weather officer in the United States Army Air Forces from 1942 to 1946.[10][3]

Academic career

From 1946 to 1949 Arrow spent his time partly as a graduate student at Columbia and partly as a research associate at the Cowles Commission for Research in Economics, then at the University of Chicago. During that time he also held the rank of Assistant Professor in Economics at the University of Chicago and worked at the RAND Corporation in California. He left Chicago to take up the post of Acting Assistant Professor of Economics and Statistics at Stanford University. In 1951, he earned his PhD from Columbia.[9] He served in the government on the staff of the Council of Economic Advisers in the 1960s with Robert Solow.[11] In 1968, he left Stanford for the position of Professor of Economics at Harvard University. It was during his tenure there that he received the Nobel Prize in Economics.[9]

Arrow returned to Stanford in 1979 and became the Joan Kenney Professor of Economics and Professor of Operations Research. He retired in 1991. As a Fulbright Distinguished Chair, in 1995 he taught economics at the University of Siena. He was also a founding member of the Pontifical Academy of Social Sciences and a member of the Science Board of Santa Fe Institute. At various stages in his career he was a Fellow of Churchill College, Cambridge.[9] He was one of the founding editors of the Annual Review of Economics, which was first published in 2009.[12]

Five of his former students have gone on to become Nobel Prize winners, namely John Harsanyi, Eric Maskin, Roger Myerson, Michael Spence and Joseph E. Stiglitz.[13] A collection of Arrow's papers is housed at the Rubenstein Library at Duke University.[14]

Arrow's impossibility theorem

Main page: Arrow's impossibility theorem

Arrow's monograph Social Choice and Individual Values derives from his 1951 PhD thesis.

If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial.[15]

In what he named the General Impossibility Theorem, he theorized that, unless we accept to compare the levels of utility reached by different individuals, it is impossible to formulate a social preference ordering that satisfies all of the following conditions:[16]

  1. Nondictatorship: The preferences of an individual should not become the group ranking without considering the preferences of others.
  2. Individual Sovereignty: each individual should be able to order the choices in any way and indicate ties
  3. Unanimity: If every individual prefers one choice to another, then the group ranking should do the same
  4. Freedom From Irrelevant Alternatives: If a choice is removed, then the others' order should not change
  5. Uniqueness of Group Rank: The method should yield the same result whenever applied to a set of preferences. The group ranking should be transitive.

The theorem has implications for welfare economics and theories of justice, and for voting theory (it extends the Condorcet paradox). Following Arrow's logical framework, Amartya Sen formulated the liberal paradox which argued that given a status of "Minimal Liberty" there was no way to obtain Pareto optimality, nor to avoid the problem of social choice of neutral but unequal results.[16]

General equilibrium theory

Main pages: General equilibrium theory and Finance:Arrow–Debreu model

Work by Arrow and Gérard Debreu and simultaneous work by Lionel McKenzie offered the first rigorous proofs of the existence of a market clearing equilibrium.[17] For this work and his other contributions, Debreu won the 1983 Nobel Prize in Economics.[18] Arrow went on to extend the model and its analysis to include uncertainty, the stability. His contributions to the general equilibrium theory were influenced by Adam Smith's Wealth of Nations.[3] Written in 1776, The Wealth of Nations is an examination of economic growth brought forward by the division of labor, by ensuring interdependence of individuals within society.[19]

In 1974, The American Economic Association published the paper written by Kenneth Arrow, General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice, where he states:

From the time of Adam Smith's Wealth of Nations in 1776, one recurrent theme of economic analysis has been the remarkable degree of coherence among the vast numbers of individual and seemingly separate decisions about the buying and selling of commodities. In everyday, normal experience, there is something of a balance between the amounts of goods and services that some individuals want to supply and the amounts that other, different individuals want to sell. Would-be buyers ordinarily count correctly on being able to carry out their intentions, and would-be sellers do not ordinarily find themselves producing great amounts of goods that they cannot sell. This experience of balance is indeed so widespread that it raises no intellectual disquiet among laymen; they take it so much for granted that they are not disposed to understand the mechanism by which it occurs.[20]

Fundamental theorems of welfare economics

In 1951, Arrow presented the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions.[21]

Endogenous-growth theory

Arrow was one of the precursors of endogenous growth theory, which seeks to explain the source of technical change, which is a key driver of economic growth. Until this theory came to prominence, technical change was assumed to occur exogenously — that is, it was assumed to occur outside economic activities, and was outside (exogenous) to common economic models. At the same time there was no economic explanation for why it occurred. Endogenous-growth theory provided standard economic reasons for why firms innovate, leading economists to think of innovation and technical change as determined by economic actors, that is endogenously to economic activities, and thus belong inside the model. Endogenous growth theory started with Paul Romer's 1986 paper,[22] borrowing from Arrow's 1962 "learning-by-doing" model which introduced a mechanism to eliminate diminishing returns in aggregate output.[3][23] A literature on this theory has developed subsequently to Arrow's work.[24]

Information economics

In other pioneering research, Arrow investigated the problems caused by asymmetric information in markets. In many transactions, one party (usually the seller) has more information about the product being sold than the other party. Asymmetric information creates incentives for the party with more information to cheat the party with less information; as a result, a number of market structures have developed, including warranties and third party authentication, which enable markets with asymmetric information to function. Arrow analysed this issue for medical care (a 1963 paper entitled "Uncertainty and the Welfare Economics of Medical Care", in the American Economic Review);[25] later researchers investigated many other markets, particularly second-hand assets, online auctions and insurance.

Awards and honors

Arrow was awarded the John Bates Clark Medal in 1957[26] and was elected a Fellow of the American Academy of Arts and Sciences in 1959.[27] In 1968, he was elected to both the United States National Academy of Sciences[28] and the American Philosophical Society.[29] He was the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972 and the 1986 recipient of the von Neumann Theory Prize.[9] He was one of the recipients of the 2004 National Medal of Science, the nation's highest scientific honor, presented by President George W. Bush for his contributions to research on the problem of making decisions using imperfect information and his research on bearing risk.[4][30]

He has received honorary doctorates from the University of Chicago (1967), the University of Vienna (1971) the City University of New York (1972).[9] On 2 June 1995 he received an honorary doctorate from the Faculty of Social Sciences at Uppsala University, Sweden.[31] He was elected a Foreign Member of the Royal Society (ForMemRS) in 2006.[32] He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences.[33]

Personal life and death

Arrow was a brother to the economist Anita Summers, uncle to economist and former Treasury Secretary and Harvard President Larry Summers, and brother-in-law of the late economists Robert Summers and Paul Samuelson.[34] In 1947, he married Selma Schweitzer, graduate in economics at the University of Chicago[35] and psychotherapist, who died in 2015; they had two children, David Michael (b. 1962), an actor,[36] and Andrew Seth (b. 1965), an actor/singer.[9]

Arrow was well known for being a polymath, possessing prodigious knowledge of subjects far removed from economics. On one occasion (recounted by Eric Maskin), in an attempt to artificially test Arrow's knowledge, the junior faculty agreed to closely study the breeding habits of gray whales — a suitably obscure topic — and discuss it in his presence. To their surprise, Arrow already was familiar with the work they had studied and, in addition, thought it had been refuted by other research.[34]

Arrow died in his Palo Alto, California, home on February 21, 2017 at the age of 95.[34]

Publications

  • Arrow, Kenneth J. (1951a). "Alternative approaches to the theory of choice in risk-taking situations". Econometrica (The Econometric Society) 19 (4): 404–37. doi:10.2307/1907465. 
  • Arrow, Kenneth J. (1951b). Social Choice and Individual Values (1st ed.). New Haven, New York / London: J. Wiley / Chapman & Hall. OCLC 892549124. 
Reprinted as: Arrow, Kenneth J. (1963). Social Choice and Individual Values (2nd ed.). New Haven: Yale University Press. ISBN 9780300013641. 
  • Arrow, Kenneth J.; Harris, Theodore; Marschak, Jacob (July 1951). "Optimal inventory policy". Econometrica (The Econometric Society) 19 (3): 250–72. doi:10.2307/1906813. 
  • Arrow, Kenneth J.; Hurwicz, Leonid (1953). Hurwicz's optimality criterion for decision making under ignorance. Technical Report 6. Stanford University. 
Also available as: Arrow, Kenneth J.; Hurwicz, Leonid (1977). Appendix: An optimality criterion for decision-making under ignorance. Cambridge Books Online. pp. 461–72. doi:10.1017/CBO9780511752940.015. ISBN 9780511752940. 
and as: Arrow, Kenneth J.; Hurwicz, Leonid (1977), "Appendix: An optimality criterion for decision-making under ignorance", Studies in resource allocation processes, Cambridge New York: Cambridge University Press, pp. 461–72, ISBN 9780521215220. 
  • Arrow, Kenneth J.; Debreu, Gérard (July 1954). "Existence of an equilibrium for a competitive economy". Econometrica (The Econometric Society) 22 (3): 265–90. doi:10.2307/1907353. 
  • Arrow, Kenneth J. (February 1959a). "Functions of a theory of behaviour under uncertainty". Metroeconomica (Wiley) 11 (1–2): 12–20. doi:10.1111/j.1467-999X.1959.tb00258.x. 
  • Arrow, Kenneth J. (1959b), "Toward a theory of price adjustment", The allocation of economic resources: essays in honor of Bernard Francis Haley, Stanford, California: Stanford University Press, OCLC 490147128. 
  • Arrow, Kenneth J. (1960), "Price-quantity adjustments in multiple markets with rising demands", Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium, Stanford mathematical studies in the social sciences, IV, Stanford, California: Stanford University Press, pp. 3–15, ISBN 9780804700214. 
  • Arrow, Kenneth J.; Suppes, Patrick; Karlin, Samuel (1960). Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium. Stanford, California: Stanford University Press. ISBN 9780804700214. 
Including: Arrow, Kenneth J. Price-quantity adjustments in multiple markets with rising demands, pp. 3–15.
Reprinted as: Arrow, Kenneth J. (1983b), "The organization of economic activity: issues pertinent to the choice of market versus non-market allocations", Collected papers of Kenneth J. Arrow, volume 2: general equilibrium, Cambridge, Massachusetts: Belknap Press, pp. 133–55, ISBN 9780674137615. 
Also reprinted as a pdf.
Reprinted as: Arrow, Kenneth J. (1983a), "Extended sympathy and the possibility of social choice", Collected papers of Kenneth J. Arrow, volume 1: social Choice and justice, Cambridge, Massachusetts: Belknap Press, ISBN 9780674137608. 
  • Arrow, Kenneth J.; Intriligator, Michael D. (1981). Handbook of mathematical economics. Handbook of Economics Series. Amsterdam New York, New York: Elsevier North-Holland. ISBN 9780444861269. 
  • Arrow, Kenneth J.. Collected papers of Kenneth J. Arrow. Cambridge, Massachusetts: Harvard University Press. :
Arrow, Kenneth J. (1983a). Collected papers of Kenneth J. Arrow, volume 1: social Choice and justice. Cambridge, Massachusetts: Belknap Press. ISBN 9780674137608. 
Arrow, Kenneth J. (1983b). Collected papers of Kenneth J. Arrow, volume 2: general equilibrium. Cambridge, Massachusetts: Belknap Press. ISBN 9780674137615. 
Arrow, Kenneth J. (1984a). Collected papers of Kenneth J. Arrow, volume 3: individual choice under certainty and uncertainty. Cambridge, Massachusetts: Belknap Press. ISBN 9780674137622. https://www.hup.harvard.edu/catalog.php?isbn=9780674137622. 
Arrow, Kenneth J. (1984b). Collected papers of Kenneth J. Arrow, volume 4: the economics of information. Cambridge, Massachusetts: Belknap Press. ISBN 9780674137639. 
Arrow, Kenneth J. (1985a). Collected papers of Kenneth J. Arrow, volume 5: production and capital. Cambridge, Massachusetts: Belknap Press. ISBN 9780674137776. 
Arrow, Kenneth J. (1985b). Collected papers of Kenneth J. Arrow, volume 6: applied economics. Cambridge, Massachusetts: Belknap Press. ISBN 9780674137783. https://www.hup.harvard.edu/catalog.php?isbn=9780674137783. 
Also available online as: Arrow, Kenneth J. (2008). "Arrow's theorem". The New Palgrave Dictionary of Economics (2nd ed.). Palgrave Macmillan. pp. 241–245. doi:10.1057/9780230226203.0061. ISBN 978-0-333-78676-5. 
Also available online as: Arrow, Kenneth J. (2008). "Hotelling, Harold (1895–1973)". The New Palgrave Dictionary of Economics (2nd ed.). Palgrave Macmillan. pp. 73–75. doi:10.1057/9780230226203.0747. ISBN 978-0-333-78676-5. 
  • Arrow, Kenneth J.; Debreu, Gérard (2001). Landmark papers in general equilibrium theory, social choice and welfare. Cheltenham, UK Northampton, Massachusetts, USA: Edward Elgar Publishing. ISBN 9781840645699. 
  • Arrow, Kenneth J. (June 2009). "Some developments in economic theory since 1940: an eyewitness account". Annual Review of Economics (Wiley) 1: 1–16. doi:10.1146/annurev.economics.050708.143405. 
  • Arrow, Kenneth J.; Anderson, Philip W.; Pines, David (1988). The economy as an evolving complex system: the proceedings of the evolutionary paths of the global economy workshop, held September, 1987 in Santa Fe, New Mexico. Redwood City, California: Addison-Wesley Pub. Co. ISBN 9780201156850. 
  • Arrow, Kenneth J.; Bensoussan, Alain; Feng, Qi; Sethi, Suresh P. (2007). "Optimal Savings and the value of population". PNAS 104 (47): 18421–18426. doi:10.1073/pnas.0708030104. PMID 17984059. Bibcode: 2007PNAS..10418421A. 


See also

References

  1. ↑ Dewar, Diane M. (2017) (in en). Essentials of Health Economics. Jones & Bartlett Publishers. ISBN 978-1-284-05462-0. https://books.google.com/books?id=jCvaCgAAQBAJ&dq=Nancy+Stokey+Arrow&pg=PA120. 
  2. ↑ On Ethics and Economics: Conversations with Kenneth J. Arrow. Routledge. 2017. pp. 12, 33. ISBN 978-1-138-67606-0. https://books.google.com/books?id=byjTjgEACAAJ. 
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 Maskin, Eric S. (2 August 2019). "The Economics of Kenneth J. Arrow: A Selective Review" (in en). Annual Review of Economics 11 (1): 1–26. doi:10.1146/annurev-economics-080218-030323. ISSN 1941-1383. 
  4. ↑ 4.0 4.1 Velupillai, K. Vela (December 2019). "Kenneth Joseph Arrow. 23 August 1921—21 February 2017" (in en). Biographical Memoirs of Fellows of the Royal Society 67: 9–28. doi:10.1098/rsbm.2019.0002. ISSN 0080-4606. 
  5. ↑ (in en) Arrow and the Foundations of the Theory of Economic Policy. Springer. 1 January 2016. ISBN 978-1-349-07357-3. https://books.google.com/books?id=ofWvCwAAQBAJ&dq=Lillian+Greenberg+Arrow&pg=PA2. 
  6. ↑ Wahid, Abu N.M. (2002). Frontiers of Economics: Nobel Laureates of the Twentieth Century. Greenwood Publishing. p. 5. ISBN 0-313-32073-X. 
  7. ↑ Pressman, Steven (1999). Fifty major economists: Business & Economics. Routledge Publishing. p. 177. ISBN 0-415-13480-3. 
  8. ↑ 8.0 8.1 Klein, Daniel B. (2013). "Kenneth J. Arrow [Ideological Profiles of the Economics Laureates"]. Econ Journal Watch 10 (3): 268–281. https://econjwatch.org/file_download/715/ArrowIPEL.pdf?mimetype=pdf. Retrieved 28 March 2023. 
  9. ↑ 9.0 9.1 9.2 9.3 9.4 9.5 9.6 Miss nobel-id as parameter
  10. ↑ "Kenneth J. Arrow, MA, PhD". Stanford University. http://fsi.stanford.edu/people/kenneth_j_arrow. 
  11. ↑ D., S. (Feb 25, 2010). "The best since the 1960s?". The Economist. https://www.economist.com/free-exchange/2010/02/25/the-best-since-the-1960s. 
  12. ↑ Arrow, Kenneth J.; Bresnahan, Timothy (2009). "Preface". Annual Review of Economics 1. doi:10.1146/annurev.ec.1.081709.100001. 
  13. ↑ Stefancic, Mitja (July 2021). "Review of J. Maesse et al. (2022) "Power and Influence of Economists: Contributions to the Social Studies of Economics" | World Economics Association". WEA Commentaries 11 (2): 11–12. https://www.worldeconomicsassociation.org/newsletterarticles/review-influence-of-economists/. Retrieved 28 March 2023. 
  14. ↑ "Kenneth J. Arrow Papers, 1939–2009.". Rubenstein Library, Duke University. http://library.duke.edu/rubenstein/findingaids/arrow/. 
  15. ↑ Arrow, Kenneth J. (1950). "A Difficulty in the Concept of Social Welfare". Journal of Political Economy 58 (4): 328–346. doi:10.1086/256963. ISSN 0022-3808. https://www.jstor.org/stable/1828886. 
  16. ↑ 16.0 16.1 Morreau, Michael (1 January 2016). "Arrow's Theorem". Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/arrows-theorem/. 
  17. ↑ Mas-Colell, Andreu; Whinston, Michael D.; Green, Jerry R. (1995). Microeconomic Theory. New York: Oxford University Press. pp. 691–93. ISBN 0-19-507340-1. https://books.google.com/books?id=KGtegVXqD8wC&pg=PA691. 
  18. ↑ "Gerard Debreu – Biographical". nobelprize.org. https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1983/debreu-bio.html. 
  19. ↑ Smith, Adam, and Andrew S. Skinner. The wealth of nations. London: Penguin Books, 1999. Print.
  20. ↑ Arrow, Kenneth (1974). "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice". American Economic Review 64 (3): 253–72. 
  21. ↑ "Kenneth Arrow (1921– )". Liberty Fund. 2008. http://www.econlib.org/library/Enc/bios/Arrow.html. 
  22. ↑ Romer, Paul M. (1986). "Increasing Returns and Long-Run Growth". Journal of Political Economy 94 (5): 1002–37. doi:10.1086/261420. http://www.dklevine.com/archive/refs42232.pdf. 
  23. ↑ Arrow, Kenneth J. (1962). "The Economic Implications of Learning by Doing". The Review of Economic Studies 29 (3): 155–73. doi:10.2307/2295952. 
  24. ↑ Barro, Robert J.; Sala-i-Martin, Xavier (2004). Economic Growth (2nd ed.). Cambridge: MIT Press. pp. 212–20. ISBN 0-262-02553-1. https://books.google.com/books?id=jD3ASoSQJ-AC&pg=PA212. 
  25. ↑ Savedoff, William D. (February 2004). "Kenneth Arrow and the birth of health economics" (in en). Bulletin of the World Health Organization 82 (2): 139–140. ISSN 0042-9686. PMID 15042237. PMC 2585899. https://scielosp.org/article/bwho/2004.v82n2/139-140/. Retrieved 27 March 2023. 
  26. ↑ "John Bates Clark Medal". American Economic Association. https://www.aeaweb.org/about-aea/honors-awards/bates-clark. 
  27. ↑ "Kenneth Joseph Arrow". American Academy of Arts and Sciences. https://www.amacad.org/person/kenneth-joseph-arrow. 
  28. ↑ "Kenneth J. Arrow". http://www.nasonline.org/member-directory/deceased-members/58161.html. 
  29. ↑ "Dr. Kenneth J. Arrow". https://search.amphilsoc.org/memhist/search?creator=Kenneth+Arrow&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced. 
  30. ↑ "The President's National Medal of Science: Recipient Details". https://www.nsf.gov/od/nms/recip_details.jsp?recip_id=5100000000424. 
  31. ↑ "Honorary Doctors of the Faculty of Social Sciences - Uppsala University, Sweden" (in en). http://www.uu.se/en/about-uu/traditions/prizes/honorary-doctorates/social-sciences/. 
  32. ↑ "Central Secretariat and Library and Information Services List of Fellows of the Royal Society 1660 - 201". February 2020. https://royalsociety.org/-/media/Royal_Society_Content/about-us/fellowship/Fellows1660-2019.pdf. 
  33. ↑ "INFORMS Fellows: Class of 2002". https://www.informs.org/Recognizing-Excellence/Fellows/INFORMS-Fellows-Class-of-2002. 
  34. ↑ 34.0 34.1 34.2 Weinstein, Michael M. (21 February 2017). "Kenneth Arrow, Nobel-Winning Economist Whose Influence Spanned Decades, Dies at 95". The New York Times. https://www.nytimes.com/2017/02/21/business/economy/kenneth-arrow-dead-nobel-laureate-in-economics.html. 
  35. ↑ Heller, Walter P.; Starr, Ross M.; Starrett, David A., eds (1986). "Kenneth J. Arrow". Social Choice and Public Decision Making: Essays in Honor of Kenneth J. Arrow, Volume I. Cambridge University Press. p. xiv. ISBN 0-521-30454-7. https://books.google.com/books?id=7hgxQyZZnKMC&pg=PR14. 
  36. ↑ David Arrow on IMDb

External links

Awards
Preceded by
Simon Kuznets 		Laureate of the Nobel Memorial Prize in Economics
1972
Served alongside: John R. Hicks 		Succeeded by
Wassily Leontief



Retrieved from "https://handwiki.org/wiki/index.php?title=Biography:Kenneth_Arrow&oldid=3405077"