Kenneth Arrow was an economist who won the Nobel Memorial Prize in Economic Sciences in 1972. He was known for his contribution to equilibrium analysis and welfare economics. He also explored social choice theory, endogenous growth theory, collective decision-making, the economics of information, and economics of racial discrimination.
Kenneth Arrow was an economist who discovered and formulated the General Impossibility Theorem, which revolved around the voting system and how election results can not be accurately pinpointed and may be skewed in different manners.
He won the Nobel Memorial Prize in 1972.
Arrow’s General Impossibility Theorem is true, assuming competitive markets with zero third-party implications.
Biography of Kenneth Arrow
Arrow was born in New York City, NY in 1921 and taught in top post-secondary institutions, such as Harvard University, Stanford University, and the University of Chicago. He earned his Ph.D. from Columbia, writing a thesis on the General Impossibility Theorem.
In the theorem, Arrow proposed that election results could not be determined fairly because ideal voting methods were non-existent when more than two candidates initially tried to satisfy particular criteria. The criteria included:
Individual sovereignty: Voters should be able to choose the order of their choices. If there are ties, they should be able to express that.
Unanimity: If all individuals prefer one candidate over another, the group ranking should reflect the same.
Nondictatorship: Every individual’s wish should be considered.
Freedom and independence from irrelevant alternatives: If an option is removed, the results should not be altered. For example, if the fourth candidate dropped out, that should not affect how the first, second, or third candidate placed before the event.
Uniqueness of group rank: The results should be the same, regardless of the preferences.
Arrow’s General Impossibility Theorem is often used in both welfare economics and social justice. It was also linked to the liberal paradox. With both theories, there appears to be a conflict between the distribution of goods and services with individual freedom, where both cannot coincide and exist together.
Arrow is also known for discovering and introducing the learning curve.
Example of the Impossibility Theorem
The impossibility theorem can be described and depicted in the following manner:
Voters are asked to rank their preferences of candidates C, D, and E:
50 people prefer C over D and prefer D over E (C ← D ← E)
45 people prefer D over E and prefer E over C (D ← E ← C)
20 people prefer E over C and prefer C over D (E ← C ← D)
Evidently, C is the recipient of the highest number of votes. But, if D were eliminated or dropped out of the running, all the remaining votes would go to E; therefore, E would receive 65 votes and outrank C.
It is important to be cognizant that Arrow’s impossibility theorem is generally applicable when voters are requested to rank all candidates within the ballot sheet. If other voting methods, such as approval voting or plurality voting, are integrated instead, the impossibility theorem becomes invalid.
Arrow’s Personal Life
Kenneth Arrow was an uncle to economist and Harvard University President Larry Summers and a brother to economist Anita Summers. In 1947, Arrow married Selma Schweitzer, who died in 2015. They bore two children – David Michael and Andrew Seth. Michael was an actor while Seth was a singer.
Arrow was known for being a polymath, where he possessed great knowledge on subjects beyond economics. For example, to test Arrow’s knowledge, the junior faculty he worked alongside privately agreed to discuss the breeding of gray whales – a suitable obscure topic – while in Arrow’s presence. To their amazement, Arrow was able to share an observation relevant to the topic that was discussed.
Arrow passed away in Palo Alto, California in February 2017, at the age of 95.