Arrow joined forces with Debreu to rework the standard ‘existence proofs’ for general equilibrium. French economist Léon Walras, the 19th-century inventor of general equilibrium theory, believed that one can prove the existence of simultaneous equilibrium in all the markets of an economy simply by counting equations and unknowns to ensure that one has as many known demand-and-supply equations as unknown prices to be determined. A rigorous proof of the existence of a general equilibrium solution had defeated everyone before Arrow and Debreu. By using the new techniques of game theory, Arrow and Debreu discovered that the existence of multi-market equilibrium under conditions of perfect competition requires forward markets in all goods and services, that is, markets in which we can pay today to obtain delivery tomorrow, or accept delivery today for the promise of payment tomorrow. This finding threw doubt on the practical significance of general equilibrium theory and much of Arrow's work was concerned to demonstrate that general equilibrium theory was nevertheless ‘robust’, that is, of relevance even to economies with missing forward markets.

Born in New York City, Arrow graduated from City College, New York, in 1940 at the early age of 19. He went on to do postgraduate work in statistics at Columbia University under US economist Harold Hotelling, but wartime service in the US Air Force interrupted his studies for almost five years. Returning to Columbia after the war, there were further delays before he embarked on social choice as the topic of his doctoral dissertation. He joined the Cowles Commission in Chicago in 1947, moved to Stanford University in 1949, and took up a professorship at Harvard University in 1968, only to move back again to Stanford in 1979.

Arrow's Social Choice and Individual Values (1951) is in a class by itself as a doctoral dissertation and first publication of a young scholar. Employing the notational system of symbolic logic, at the time unfamiliar to economists, it proposed to solve a question in politics that no economist and few political scientists had ever posed: suppose all individuals can rank all states of the world in order of preference, is it possible to find a voting rule that will always select one of those states as ‘most preferred’? The most popular voting rule, majority choice, may easily fail to express a unique social preference. If the preferences of voters differ, their votes could cancel each other out leading to no overall winner, and the democratic method of majority choice leads to a stalemate.

Arrow demonstrated that this stalemate can occur not just under a constitution based on the principal of majority rule, but under every conceivable constitution except that of dictatorship. Outside the case of dictatorship it is not always logically possible to add up the choices of individuals into an unambiguous social choice, except by rigging the ‘constitution’, for example, by confining all choices to only two options, either directly or indirectly through political parties and parliamentary representatives. In short, there is no such thing as an ideal voting scheme that will respect the personal preferences of every voter and simultaneously ensure maximum social welfare.

Arrow's ‘impossibility theorem’ appeared to have such startling consequences for both political philosophy and welfare economics that literally hundreds of papers have been written to refute it. But Arrow's theorem has withstood all technical criticisms and has never been decisively challenged on its own grounds. It is not clear, however, whether the ‘impossibility theorem’ is only a theorem about politics or whether it cuts deeper into the very conception of social welfare.

Arrow's other work included the implications of risk aversion for economic activity as it relates to medical and other kinds of insurance. A much-studied paper on the economic implications of learning-by-doing represented his principal contribution to the modern theory of economic growth.

He has been honoured throughout his career: president of the Econometric Society in 1956, winner of the John Bates Clark medal of the American Economic Association in 1957 for the most distinguished work by an economist under the age of 40, president of the Institute of Management Science in 1963, the American Economic Association in 1973, the Western Economic Association in 1981, and a recipient of the Order of the Rising Sun (2nd class), Japan.

His works include Social Choice and Individual Values (1951), Essays in the Theory of Risk-Bearing (1971), General Competitive Analysis (1971), and six volumes of Collected Papers (1983-85).