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The economist who studied social choice

With the death of Kenneth Arrow, the world has lost a great mind

The economist who studied social choice
Kenneth Arrow.

If you use metrics such as interest, values, and welfare to determine the rules of fair voting, you end up with the social choice theory propounded by Kenneth Arrow who died on February 21, aged 95 in San Francisco.

With Social Choice Theory (SCT), individual preferences are aggregated to produce a social welfare function. Essentially, it uses a preference ranking of the scenarios that are possible to society; in simpler words, SCT is the philosophical and mathematical study of the type of conclusions that can be determined through various aggregation methods. Started by Kenneth Arrow, SCT followed his introduction of the impossibility theorem in 1951.

SCT is not only applicable to economic processes, but as a growing discipline has entered the fields of decision making and negotiations. A Nobel Prize-winning economist, Arrow was professor of economics and operations research and his work went much beyond economic theory, focusing on areas such as risk bearing, medical economics, general equilibrium analysis, inventory theory, and the economics of information and innovation. Perhaps he was the first economist who noted the existence of a learning curve meaning that as producers increase output of a product, they gain experience and become more efficient. This experience increases productivity.

He showed that an economy reaches a general equilibrium under certain conditions. For his pioneering work, he won the Nobel Prize in economics with the British economist Sir John Hicks in 1972. Being more interested in politics than economics, one benefits from Arrow’s monograph Social Choice and Individual Values containing a theorem that created modern social choice theory. It enlightens us on social ethics and voting theory with a tinge of economics. He explained how each social choice is linked to the feasible set of laws passed by voting, which means the set of ordering — even if not every individual voted in favour of the laws.

Applied to Pakistan, we can understand it better just by looking at any recent set of laws passed by the parliament. For example, how many people voted for the law justifying jirgas and panchayats under the guise of alternative dispute resolution? Or in what set of ordering, people opted for establishing military courts or making Quranic education compulsory? Arrow’s General Possibility Theorem — later known as impossibility theorem — helps us understand how absent restrictions on either individual preferences or feasible alternatives result in no social choice rule. This generalises the voting paradox showing that majority voting may fail to yield a stable outcome.

Another area of interest for Arrow was welfare economics focusing on the optimal allocation of resources and goods and how the allocation of these resources affected social welfare.

This contrasts voting and markets with dictatorship and social convention e.g. in a religious dictum, both exemplifying social decisions. If dictatorship and convention limit social choices, voting and markets (V&M) are supposed to facilitate it. However, in real life, this is not always the case. V&M makes it possible to amalgamate diverse tastes and preferences in the making of a social choice; but, generalising such choices makes it difficult resulting in a voting paradox from use of majority rule as a value. At the world stage, this became clearer in 2016 with Brexit and Trump’s in-your-face victory.

Using Arrow’s ideas, we may ask if other methods of taste aggregation — be it voting or markets — using other values can solve the problem or satisfy us in other ways. Can logical consistency be used as a check on acceptability of all the values? Arrow’s answer is simple: remove the distinction between V&M in favour of a more general category of collective social choice. Arrow does not locate a social good as independent of individual values; in other words, to him social values mean nothing more than social choices.

Here, it is important to keep in mind that when Arrow uses ‘vote’ he means ‘a set of ordering’, and by society he means ‘collectivity’ composed of individuals’ i.e. voters. Ordering is essentially a ‘ranking’ by a voter of all social states. Arrow was the youngest-ever winner of a Nobel prize for economics. Most of his work focused on how people matter, how often they don’t behave rationally, and how it affected their own lives. Teaching at Harvard and Stanford Universities, he supervised at least five students who went on to become Nobel winners in their own right.

Many of Arrow’s ideas fundamentally altered economic and political theory and practice. Being interested in almost everything, his intellectual curiosity covered subjects as diverse as music, Chinese art and even whales. In one of his papers, he dealt with problems concerning the economics of medical care and health insurance. He argued that it is not a truly price-competitive situation when the buyer — the patient — has much less information than the doctor — the seller. The unequal sets of information about necessary treatment and options create an asymmetry which can be called ‘asymmetric information’. Unlike most economists who seem dry and abstract, most of Arrow’s work had real-world applications.

From insurance and medical care to drugs, bingo, and stock markets, he straddled a broad spectrum. He belonged to a Jewish immigrant family from Romania that settled in New York City and enriched the American intellectual landscape.

Another area of interest for Arrow was welfare economics focusing on the optimal allocation of resources and goods and how the allocation of these resources affected social welfare. For example, Arrow’s impossibility theorem is sometimes referred to as one of the fundamental theorems in welfare economics with Pareto efficient outcomes. Applying these principles, we get to the field of public economics that studies how government might intervene to improve social welfare.

At the height of the financial crisis in 2008, he identified two developments in the economic theory of uncertainty since 1950 that had opposite implications for the radical changes in the financial system. First, according to him, made explicit and understandable a long tradition that spreading risks among many bearers improves the functioning of the economy. The second was that there were large differences of information among market participants and that these differences were not well handled by market forces. The first argues for the expansion of markets, the second for recognising that they may fail to exist or benefit general economic situation.

With the death of Kenneth Arrow, the world has lost a great mind. One is inclined to place him with the likes of Paul Samuelson, John Nash, and Milton Friedman; arguably, the quartet comprises the four greatest economists of the late 20th century.

Dr Naazir Mahmood

Naazir Mahmood
The writer has been associated with the education sector since 1990 as teacher, teacher educator, project manager, monitor and evaluator.

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