Kenneth Arrow after receiving his Nobel Prize in economic sciences in Stockholm in 1972. (Associated Press)

Kenneth J. Arrow, a Nobel Prize-winning economist and mathematical theorist who made seminal contributions to social sciences as varied as election theory and health economics and was one of the most influential economists of his generation, died Feb. 21 at his home in Palo Alto, Calif. He was 95.

His son Andrew Arrow confirmed the death, but he did not know the immediate cause.

Dr. Arrow, who spent the majority of his career at Stanford University as an economics professor, was the youngest recipient of the Nobel Prize in economic sciences.

He was 51 when he shared the Nobel with British economist Sir John Hicks in 1972 for their contributions to welfare economics and general equilibrium theory, a branch of economics that studies the behavior of supply and demand for multiple firms in a competitive market.

Dr. Arrow came from a prodigious family of economists that includes his nephew Lawrence H. Summers, president emeritus of Harvard University, former treasury secretary and former director of the White House National Economic Council; and his late brother-in-law Paul A. Samuelson, the first American to win the Nobel Prize in economics, in 1970. His sister Anita and her late husband, Robert Summers, taught economics at the University of Pennsylvania.

Throughout his career in academia, Dr. Arrow was a mentor to scores of graduate students, several of whom became Nobel laureates: John C. Harsanyi, Eric S. Maskin, Roger B. Myerson, A. Michael Spence and Joseph E. Stiglitz.

The evolution of economics in the post-World War II decades was “very inspired by Arrow’s results, his systematic thoughts, the understanding he generated, the questions he raised and the inspiration [his work] provided to young people,” the economist and Nobel laureate Amartya Sen said in an interview with The Washington Post.

He was widely respected for the breadth and depth of his research — including its impact on disciplines as diverse as political science, philosophy and statistics.

“He is certainly one of the giants of 20th-century economic theory,” said Nobel laureate Robert Aumann, a mathematician. “More so, I think, in the second half of the 20th century, he absolutely had more of an impact than anyone else.”

Dr. Arrow helped transform economic theory into a mathematical science. He used his statistical and mathematical background to develop theorems that better explained holes in economic theory that had not been well defined or, in some circumstances, discovered.

“I think my biggest hopes were methodological — to apply new developments in mathematics to economics,” he told Challenge: The Magazine of Economic Affairs, in 2000.

Impossibility theorem

Dr. Arrow came to prominence with his 1951 landmark book, “Social Choice and Individual Values.” In it, he expanded on his doctoral thesis and explained his trailblazing impossibility theorem, which proved that no voting system can fairly aggregate voter preferences in an election involving three or more candidates while simultaneously satisfying several reasonable conditions.

In his analysis, using simple, elementary mathematics, he evaluated and compared existing voting systems and exposed their unavoidable limitations, flaws and trade-offs.

He “proved it was logically impossible for there to be a system of voting which is free of anomalies, no matter what kind of system it is,” Aumann said. “You can say, ‘There’s no really good way to run an election,’ but it is something else to prove it. . . . It’s like proving a bicycle cannot be stable.”

His discoveries catalyzed research on the economic theory of social choice and influenced fields that included philosophy (particularly philosophies of democracy and political economy), welfare economics and political science (particularly voting theory).

The impossibility theorem “fundamentally altered economic and political theory and practice,” Aumann said.

The theorem also encouraged people to think about what they wanted from a democracy and how they believed it should work, Sen said. “It is important to recognize that Arrow was not only establishing a theorem, he was opening up a whole subject to social choice.”

For his findings, Dr. Arrow in 1957 was awarded the American Economic Association’s John Bates Clark Medal, an honor given every two years to the nation’s most promising economist under 40.

The work that earned him a Nobel Prize built on the theoretical findings presented in John Hicks’s 1939 book, “Value and Capital.” Dr. Arrow worked with future Nobel laureate Gérald Debreu to co-design the Arrow-Debreu model in 1954.

It was the first rigorous mathematical proof of a market-clearing equilibrium — or the price at which the supply of an item is equal to its demand. It addressed the behavior of competitive markets, explained how prices operate to balance supply and demand, and described how different producers could maximize profit and efficiency.

“Their theory of value and price formation was really a fundamental element of economics,” Aumann said. “It’s the ABCs of economics and economic theory.”

Their findings increased economists’ understanding of monetary policy, business cycles, international trade, market predictions, and evaluation of public and government investment policies, and even extended to urban economic development.

“You cannot get a full understanding of the behavior of any part of the economy without understanding its reaction on other parts,” Dr. Arrow told the New York Times in 1972.

Health-care economics

Dr. Arrow also laid the foundations of modern health economics by identifying the special market characteristics of and issues surrounding health-care markets, as well as the underlying problems of the medical insurance industry, in his influential 1963 paper “Uncertainty and the Welfare Economics of Medical Care.”

He found that the delivery of health care deviated in fundamental ways from the traditional competitive market and, for this reason, was a nonmarket relationship.

For example, in a perfect market, the buyer and seller in theory have access to the same information about market price and value. However, in the health-care market, the supplier (doctor) commonly has a superior knowledge of the quality, provision and distribution of health-care services — all of which puts the consumer (patient) at a relative disadvantage.

This creates a problem of information asymmetry. “The customer cannot test the product before consuming it, and there is an element of trust in the relationship,” he wrote in 1985.

Consumers also do not always know when they will need health care until the moment they require it (as with a stroke or heart attack). So when consumers purchase insurance, the cost can be prohibitive.

Insurance companies worry that offering coverage to protect consumers against losses could create moral hazards, such as risk-taking and irresponsible behavior.

As a result, government, insurance companies and health maintenance organizations step in to overcome abuse and overuse of goods.

“The economics of insurance, medical care, prescription drug testing . . . will never be the same after Arrow,” Samuelson wrote in 1972.

Dr. Arrow also contributed foundational research in other areas of economics. Among them: new growth theory, which emphasizes the economic role of innovation and new ideas; risk aversion, an economics and finance concept based on human behavior when exposed to uncertainty; and information economics, the study of how information and information systems affect the economy.

Dr. Arrow served on President John F. Kennedy’s White House Council of Economic Advisers alongside economists and future Nobel laureates James Tobin and Robert Solow and taught economics at Harvard from 1968 to 1979.

He then returned to Stanford — whose faculty he joined in 1949 — and was a professor of economics, statistics and operations research until he retired in 1991.

Sense of order

Kenneth Joseph Arrow was born in New York City on Aug. 23, 1921, to Jewish immigrants from Romania. He was placed in an accelerated program at Townsend Harris High School, a magnet school in New York that also produced Nobel laureates Herbert Hauptman, a chemist; and Julian Schwinger, a physicist.

“I was an omnivorous reader, and I added to that a desire to systematize my understanding,” Dr. Arrow said in a 1984 university lecture. “As a result, history, for example, was not merely a set of dates and colorful stories; I could understand it as a sequence in which one event flowed out of another. This sense of order crystallized . . . into a predominant interest in mathematics and mathematical logic.”

He graduated from City College of New York in 1940 and the next year, at 20, received a master’s degree in mathematics from Columbia University. After a stint as a weather officer in the U.S. Army Air Forces during World War II, he returned to Columbia and received a doctorate in economics in 1951.

Dr. Arrow received the National Medal of Science, the nation’s highest scientific honor, from President George W. Bush in 2004. He was a past president of the American Economic Association, the Econometric Society, the American Association of the Advancement of Science and the International Economic Association.

He was an editor of the Annual Review of Economics and a trustee of what is now Economists for Peace & Security, an organization that promotes nonmilitary solutions to global issues. Pope John Paul II appointed him to the Pontifical Academy of Social Sciences, a group of scholars who help advise the Vatican.

His wife, Selma Schweitzer Arrow, died in 2015. Survivors include two sons, actors David Arrow of Manhattan and Andrew Arrow of Los Angeles; a sister; and a grandson.

Dr. Arrow was known as a skillful storyteller with a quick wit. While serving in the Army Air Forces, he was tasked with producing long-range weather forecasts. He and his colleagues soon realized that the prevailing techniques were no more accurate than random guessing.

His team brought this to the attention of his supervisors, and Dr. Arrow published his first scholarly paper on how optimal flight formulas could be improved. His efforts were rebuffed by his boss.

“The commanding general is well aware that the forecasts are no good,” he was told. “However, he needs them for planning purposes.”