24 Feb 2017 19:20 IST

Kenneth Arrow, philosopher-economist: A tribute

Arrow made path-breaking contributions in general equilibrium theory and the economics of information

One of the towering figures in 20th century economics, Kenneth Arrow passed away a couple of days ago at the ripe old age of 95. He shared the Nobel Prize with Sir John Hicks in 1972 and, at 51, was the youngest to be awarded the prestigious prize.

Arrow is best known for his ‘Impossibility theorem’ enunciated in his book Social Choice and Individual Values in 1951. It is a slim, terse book with a heavy dose of mathematical logic. I remember picking it up from the American Library with great enthusiasm during my college days. But the moment I started reading it I realised I did not have the required mathematical background to understand the book, and the enthusiasm evaporated.

It was only years later that I understood the import of this ‘theorem’. It would not be an exaggeration to say that Arrow, through this slim book, pioneered a new area of research in welfare economics — social choice theory.

The theorem using mathematical logic says that when voters are given three or more choices it is impossible to arrive at a rational single choice without violating some basic tenet, such as fairness. Arrow’s theorem proved the difficulty in aggregating preferences among people — a problem that lies at the heart of modern welfare economics. Individual choices cannot be aggregated into collective choices. So the paradox here is that we probably need a ‘benevolent dictator’ to make a ‘rational’ choice for the welfare of the majority!

Social choice theory

The Stanford University Encyclopedia of Philosophy says that Arrow’s finding can be read as being deeply antithetical to the political ideals of enlightenment. But to quote Arrow, “Most systems are not going to work badly all the time. All I proved is all can work badly at times”.

Amartya Sen was deeply influenced by Arrow’s ideas. It was the late Sukhamoy Chakravarthy who introduced Sen to Arrow’s work way back in the early 1950s, when they were both students of Presidency College, Calcutta, during one of their ‘adda sessions’.

Sen himself went on to make seminal contributions in the area of social choice theory. He wrote a book on the subject in 1970 titled Collective Choice and Social Welfare, an updated version of which was released recently.

Impact of variables

Arrow also made some path-breaking contributions in the areas of general equilibrium theory, first postulated by French mathematician and economist Leon Walras in the 19th century, and the economics of information.

In general equilibrium theory, Arrow collaborated with Gerard Debreu, who also won the Nobel prize in the early 1980s. This theory shows how free markets generally tended towards an ‘equilibrium’, where various individual markets interact with one another and the resulting demand and supply lead to an ‘equilibrium’. This concept is used widely in formulating computable general equilibrium models, where economic data is used to estimate how an economy will react to changes in ‘variables’ such as prices, technology or external factors. Its impact on policy making cannot be over-emphasised.

Information asymmetry

The economics of information is another area where Arrow made important contributions, especially while studying the health sector, where ‘asymmetric information’, that is the different levels of information that ‘economic agents’ have, can lead to skewed or sub-opitmal outcomes. His studies showed that free market principles may not work in the health sector as people tend to overvalue the expertise of the medical community. Hence, the lack of a level playing field in information, which is impossible to achieve, often leads to outcomes that are not ‘market-efficient’.

Research in this area was taken forward by George Akerlof and Joseph Stiglitz, who also ended up sharing a Nobel prize with Michael Spence in 2001.

Economists often pride themselves for being practitioners of a discipline that is most scientific among the social sciences and rests on the pillar of ‘rationality’. Well, Arrow had this to say about rationality, “I want to stress that rationality is not the property of the individual alone, although it is usually presented that way. Rather it not only gathers its force but also its very meaning from the social context in which it is embedded.”

Arrow’s research was heavy on mathematics but there is no denying the fact that his contributions straddled a large swathe of economics. Arrow was one of those rare economists who also wore the philosopher’s hat with exceptional ease.

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