Kenneth Arrow, one of the most brilliant economic minds of the 20th century and, at 51, the youngest economist ever to win a Nobel, died on Wednesday (AEDT) at his home in Palo Alto, California.

He was 95.

Paul Samuelson, the first American to win the Nobel Memorial Prize in Economic Science, called Arrow "the most important theorist of the 20th century in economics". When Arrow received the award in 1972, Samuelson wrote: "The economics of insurance, medical care, prescription drug testing - to say nothing of bingo and the stock market - will never be the same after Arrow."

Arrow - a member of an extended family of distinguished economists, including Samuelson and Lawrence Summers, a former Treasury secretary and adviser to President Barack Obama - generated work that was technically forbidding even to mathematically-oriented colleagues.

But over the decades, economists have learned to apply his ideas to the modern design of insurance products, financial securities, employment contracts and much more.

The backdrop for Arrow's influential early work was the centuries-long recognition that majority voting can produce arbitrary outcomes.

Consider a legislature choosing its leader from among three candidates: Alice, Betty and Harry. If the legislature were to vote first on Alice versus Betty, with the winner running against Harry, it could come to a different decision than had it first started by voting on Alice versus Harry. Because the order with which the legislature takes votes is arbitrary, the ultimate winner of this system of majority voting becomes arbitrary.

That puts politics in an awkward corner.

In search of non-arbitrary outcomes, social scientists proffered different ways to conduct votes. For example, the legislature could run all three candidates in the initial round and structure some type of runoff. Or the legislature could give each member multiple votes to be assigned to the three candidates in proportion to the intensity of the member's preferences.

But no voting system, however cleverly designed, resolved the problems associated with majority voting. In a theorem of stunning generality, Arrow proved that no system of majority voting worked satisfactorily according to a carefully articulated definition of "satisfactory" (which social scientists generally accept).

What Arrow proved in his book Social Choice and Individual Values (1951) was far more sweeping. Not only would majority-voting rules prove unsatisfactory; so, too, would non-voting systems of making social choices if, as was fundamental to his way of thinking, those choices were based on the preferences of the individuals making up the society. (Arrow's rules did not allow for dictators.)

The Arrow "impossibility theorem" ricocheted around the social sciences, noteworthy for its use of abstract mathematical concepts to generate a conclusion of sweeping applicability.

Arrow's research opened the academic field of social choice - a literature that ranges from a countries picking presidents to corporate boards picking business strategies. Having learned from him that no system works entirely well, academics turned to challenging follow-up questions, like whether some voting systems were better than others.

Arrow's next major contributions, for which he shared the 1972 Nobel Memorial Prize in Economic Science with British economist John Hicks, were published later in the 1950s. They took a bird's-eye, "general equilibrium" view of market economies, setting out equations to capture the interplay between consumers and producers.

Arrow's theorems set out the precise conditions under which Adam Smith's famous conjecture in The Wealth of Nations holds true: that the "invisible hand" of market competition among self-serving individuals serves society well.

As was true of his earlier work on social choice, the magnitude of Arrow's theoretical insight was staggering. But, he made clear, his powerful conclusions about the workings of competitive markets held true only under ideal - that is to say, unrealistic - assumptions.

His assumptions, for example, ruled out the existence of third-party effects: The sale of a product by Harry to Joe was assumed not to affect the well-being of Sally - an assumption routinely violated in the real world by, for example, the sale of products that harm the environment.

The mathematics behind the general equilibrium proofs of Arrow and his co-authors were daunting. Few economists mastered the details. But Franklin Fisher, who taught graduate courses on general equilibrium at the Massachusetts Institute of Technology, acknowledged in a 2013 interview with The New York Times that all academic economists were in Arrow's intellectual debt. Arrow proved that the economists' workaday tools of supply-and-demand equations are built on a logically coherent foundation.

Arrow also created mathematical concepts by which economists could measure and analyse risk. William Sharpe, who won a Nobel in 1990 for analysing the relationship between financial risk and return, credited Arrow with helping to formulate the basis for modern theories of financial investment and corporate finance.

Arrow, he said, belonged in the "pantheon" of investment management. His ideas have worked their way into the design of complicated financial securities, known as derivatives. Businesses buy and sell financial derivatives to protect themselves from financial turmoil, and investors buy and sell them to speculate on future movements of security prices.

Arrow anticipated the modern analysis of markets in which buyers and sellers do not share accurate information (now known as markets with asymmetric information). In a strikingly prescient article published in the early 1960s, he teased apart the complexities that asymmetric information creates in the market for health insurance. He pointed to incentives for patients and their physicians to agree to medical procedures of questionable value when a third party, the insurer, pays the bills.

Arrow's work spawned the modern treatment of "moral hazard," whereby the fact of the purchase of insurance systematically affects the behaviour of the parties to the contract.

Kenneth Joseph Arrow was born on August 23, 1921, in New York City. After graduating from Townsend Harris High School in Manhattan, he raced through City College, finishing with a bachelor's degree in social science and in mathematics - what he called later "a paradoxical combination that was prognostic of my future interests".

He did his graduate work at Columbia University, interrupting it to serve as a weather officer, rising to captain, in the Army Air Corps during World War II. His first published paper, On the Optimal Use of Winds for Flight Planning, drew on this experience.

Early in his career he worked at RAND, the research and development organisation in Santa Monica, California, in what he described as "the heady days of emerging game theory and mathematical programming".

Arrow spent the bulk of his career at Stanford University, except for a teaching stint at Harvard from 1968 to 1979. He also served briefly on the staff of President John F. Kennedy's Council of Economic Advisers.

He retired from Stanford in 1991 but continued to accept short-term appointments in Europe and to serve on the external faculty and the science board of the Santa Fe Institute, a research centre in New Mexico focused on the interplay of the social and physical sciences.

He led the American Economic Association, served on the Intergovernmental Panel on Climate Change and, in 2004, was awarded the National Medal of Science, the nation's highest scientific honour, presented in 2006 by President George W. Bush.

"His politics are liberal, definitely," said Robert Solow, a longtime friend and fellow Nobel laureate in economics. "With other people, this might rub the right half of the economics profession the wrong way, but it doesn't with Kenneth."

Arrow's wife, the former Selma Schweitzer, whom he married in 1947, died in 2015. Besides his sister and son David, he is survived by another son, Andrew, and a grandson.