Kenneth Arrow

American neoclassical economist, political theorist, mathematician, and writer.

Author: Ananya Dutta
Ananya Dutta
Ananya Dutta

Audencia Winter Exchange | MBA 2022-24

Reviewed By: Freida Lee
Freida Lee
Freida Lee
Last Updated:June 21, 2024

Who Was Kenneth Arrow?

Kenneth Joseph Arrow (23 August 1921 - 21 February 2017) was an American neoclassical economist, political theorist, mathematician, and writer. 

He jointly won the Nobel Memorial Prize in Economic Sciences with Sir John Richard Hicks in 1972 for his contributions to welfare economics and general equilibrium analysis.

He was an essential economic figure in the post-World War II neo-classical economic theory.

His research explored the topics of the economics of racial discrimination, endogenous growth theory, social choice theory, and collective decision-making, among other issues.

His most notable contributions to economic theory are the advances of social choice theory and “Arrow’s Impossibility Theorem.”

Key Takeaways

  • Arrow is best known for his Impossibility Theorem, also known as Arrow’s Paradox, which demonstrates the difficulty of creating a voting system that accurately reflects individual preferences in a fair and consistent manner.
  • In 1972, Arrow was awarded the Nobel Memorial Prize in Economic Sciences, shared with Sir John Hicks, for their pioneering contributions to general equilibrium theory and welfare theory.
  • Arrow's work in social choice theory explored how individual preferences can be aggregated to reach collective decisions. His Impossibility Theorem revealed the inherent challenges in designing fair voting systems.
  • Arrow’s research intersected with various disciplines, including mathematics, political science, and operations research, demonstrating his interdisciplinary approach to solving complex economic problems.

Kenneth Arrow Early Career and Education

Kenneth Joseph Arrow was born in New York City on 23 August 1921. His family members were Romanian Jews. His mother’s name was Lilian (Greenberg), from Iași, Romania, and his father’s name was Harry Arrow, from Podu lloaiei.

His family was very supportive of his education. He embraced socialism in his youth as he grew up during the Great Depression. Although he later moved away from society, his views greatly impacted him.

He graduated from Townsend Harris High School and earned his Bachelor’s Degree from the City College of New York in Mathematics in 1940, where he was a member of Sigma Phi Epsilon. 

Later, he was admitted to Columbia University for further graduate studies and received a Master’s degree in Mathematics in June 1941. 

During his time at Columbia University, under the influence of the statistician-economist Harold Hotelling, he changed his field to economics for the rest of his graduate work.

Unfortunately, his graduate study was interrupted by World War II. From 1942 to 1946, he served as a United States Army Air Forces weather officer and then rose to Captain.

He was partly a graduate student at Columbia University from 1946 to 1949 and a research associate at the Cowles Commission for Research in Economics at the University of Chicago. 

Moreover, he was appointed as Assistant Professor in Economics at the University of Chicago and worked at the RAND Corporation in California from 1948 to 1949.

He was appointed as Acting Assistant Professor of Economics and Statistics at Stanford University in 1949 and remained there until 1968, later becoming a Professor of Economics, Operations Research, and Statistics.

He earned his Ph.D. from Columbia University in 1951.

During this period, he was a Social Science Research Fellow in 1952 and a Fellow of the Center for Advanced Study in the Behavioral Sciences from 1956 to 1957. In addition, he was an Economist on the United States Council of Economic Advisors staff in 1962.

Kenneth Arrow's Early Achievements

A few other achievements are listed below:

  1. He was Executive Head of the Department of Economics at Stanford University from 1953 through 1956 and 1962 to 1963, then a Fellow of Churchill College (Cambridge) from 1963 to 1964 and again in 1970.
  2. He was a Guest Lecturer at the Institute of Advanced Studies, Vienna, In June 1964 and again in 1971.
  3. He was appointed Professor of Economics at Harvard University in 1971.
  4. He received the John Bates Clark Medal of the American Economic Association in 1957 and was elected as a member of the National Academy of Sciences and American Philosophy.
  5. He was also a Fellow of the American Academy of Arts and Sciences, the Econometric Society, the American Statistical Association, and the Institute of Mathematical Statistics.
  6. He has also received the honorary degree of LL.D. from:
    • The University of Chicago in 1967.The 
    • The City University of New York in 1972.
    • In 1956, he was President of the Econometric Society, The Institute of Management Sciences in 1963, and a President-elect of the American Economic Association in 1972.

He returned to Stanford University in 1979 and retired in 1991. He then taught Economics at the University of Siena as a Fulbright Distinguished Chair in 1995. 

He was the founding member of the Pontifical Academy of Social Sciences and a member of the Science Board of Santa Fe Institute.

He married the former Selma Schweitzer and has two sons, David Michael and Andrew Seth.

Arrow’s Impossibility Theorem

Arrow’s Impossibility Theorem is an important result of mathematics in welfare economics and collective choice. It deals with decisions being made at a collective level and is a subfield of economics.

It is a social-choice paradox that illustrates the voting system’s flaws in rankings. According to the theorem, a clear set order of preferences can never be determined while obeying the mandatory principles of fair voting procedures.

This theorem is named after the economist Kenneth Joseph Arrow who demonstrated it in his paper “A Difficulty in the Concept of Social Welfare.” 

It is also known as the “General Impossibility Theorem” or “Arrow’s Paradox” and is a study of social choice.

Arrow’s Impossibility Theorem is a study of a social choice theory that studies the combination of different individuals’ preferences, opinions, and welfare to reach community-wide decisions and social welfare. 

According to the theorem, whenever there are more than two choices, it is nearly impossible for a ranked voting system to reach a community-wide set of orders by gathering and converting every individual’s options while obeying a set of conditions.

Democracy depends on the fact that the people’s voices are being heard. For example, an election takes place during the formation of a new government, and people are called to the polls to vote according to their choice. 

After casting votes, millions of voting slips are counted to determine who is the most voted candidate and the next elected official.

According to the General Impossibility Theorem, a set of conditions cannot be violated to formulate a social ordering in the cases where the choices and preferences are ranked.

Conditions

The set of conditions to not violate are as follows:

  1. Non-Dictatorship: Non-Dictatorship means that the whole community cannot be represented by a single voter and the voter’s preference. Multiple voters’ preference needs to be considered for social welfare functions.
  2. Unrestricted Domain: Unrestricted Domain requires counting the preferences of every voter that conveys a total ranking of social preferences.
  3. Independence of Irrelevant Alternatives (IIA): The independence of irrelevant alternatives condition refers that if one choice is removed, then the order of preferences should not change. If the choice of any alternative individual is changed, then it should not impact the social rankings.
  4. Social Ordering: Social ordering refers to any individual having the freedom to order any choices in any unspecific order in a connected manner, indicating ties.
  5. Pareto Efficiency: According to Pareto Efficiency, the unanimous preferences of each individual is to be respected. The set order of social priorities must agree with the individual preferences if every individual voter strictly prefers to first choice over the other.

This theorem is an essential part of social choice theory. This economic theory considers if a society can be ordered in a particular way per the individual’s preferences, it was considered a breakthrough. 

Later on, it became widely used in welfare economics for analyzing problems.

Let us take an example to understand the Impossibility Theorem completely. In the following example, each voter is asked for their preference for three projects: A, B, and C.

This country has 66 voters, and they are each asked to rank orderly from best to worst, and in this order, the projects will receive the annual funding of tax dollars.

  • 22 votes A>B>C (⅓ prefer A over B and prefer B over C)
  • 22 votes B>C>A (⅓ prefer B over C and prefer C over A)
  • 22 votes C>A>B (⅓ prefer C over A and prefer A over B)

Therefore,

  • 44 voters prefer A over B
  • 44 voters prefer B over C
  • 44 voters prefer C over A

So a majority of two-thirds of voters prefer A over B, B over C, and C over A - a result based on the preferences’ rank order.

Legacy of Kenneth Arrow

The theoretical insights of Kenneth Joseph have proven their importance in economics over the decade. Still, he made sure that the results of his works in the competitive markets were truly used under the ideal conditions - unrealistic assumptions.

The existence of third-party effects was ruled out after the unrealistic assumptions.

The later research turned simple ideas into elegant mathematics.

He took his last breath on 21 February 2017.

According to many knowledgeable observers, he was the foremost economist in the second half of the 20th century. Paul Samuelson said Arrow was the most important economic theorist of the 20th century.

He pioneered general equilibrium theory, welfare theory, and other research fields. He launched modern health economics in a single article published by the American Economic Review in 1963.

With great accuracy, he observed that “adaptations can explain the special economic problems of medical care to uncertainty in the wake of diseases and their treatment.”

There was a tremendous impact of the Arrow on health economics. His research on asymmetrical information and health care insurance is the topic where “uncertainty” had a huge impact.

Not only did he contribute to the theoretical understanding of public goods, but also he was a major producer of them, both inside and outside the profession. 

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