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The urgency to find solutions for the climate crisis, which is threatening the existence of the human species on the planet, has put the discipline of economics in the dock. Pursuit of relentless economic growth, which economists seem to imply should be the driver of governments’ policies, is now suspected to be the culprit. They did not seem to have any other prescription for the improvement of human well-being.
Debates are stirring among economists themselves to change their theories and to improve economists’ toolkits. The hoary maxims of rational self-interest as the sole motivation of individuals’ and enterprises’ decisions, and “the invisible hand” as the mechanism of producing social welfare, are being questioned. Concern for others and for Nature, and the design of institutions for enabling sustainable and inclusive progress, not just more GDP, is compelling economists to go back to the drawing board.
Economists are unlikely to find out of the box solutions if they keep debating among themselves, because they are all conditioned to think about the essentials of economics’ methods in the same way. Indeed, it is their belief in the power of their logical and quantitative methods that makes them believe that economics is superior to other social sciences such as anthropology, for example, which relies on stories and historical narratives to explain what matters to people and the progress in their lives.
Economists have seen competition among humans, among business ventures, and among nations too, as the primal driving force for innovation and progress. The invisible hand has not worked equitably. Climate change requires new solutions, based on conscious cooperation among nations and citizens and with Nature, for the sake of the survival of all.
The fundamental questions that all scientists, and economists, must urgently return to are:
- How do we know what we really know?
- What are the meanings of the numbers in our equations?
- What is the nature of games we play in real life?
What cannot be counted
The power of information technology to read, manipulate, and store data in digital form has expanded unimaginably in the last twenty years. Digital devices communicating directly with each other are making human intervention unnecessary and human beings even irrelevant. Big data analytics is the new game of power and progress.
The Prisoner’s Dilemma is a basic game in the science of game theory. It examines the question of whether cheating or cooperating with another is a more gainful strategy. Kaushik Basu has introduced a variant of this game, Greta’s Dilemma, to explain the conundrum in demanding sacrifices in the present to save the planet for future generations. Applying the principles of game theory, it seems the future would be worse if leaders were to accept Greta’s demands.
The problem is that it is impossible to get agreement on what the objective of any broad policy should be. When there are diverse interests, whose concerns should matter most? Kenneth Arrow (who won the Nobel Prize in economics in 1972) propounded the Impossibility Theorem. He proved, mathematically, that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide agreement. The Arrow Impossibility Theorem is a fundamental dilemma in social choice theory, a discipline within economics in which Nobel Laureates Douglass North and Amartya Sen worked extensively too.
The Impossibility Theorem proves there is no voting method, in which voters by merely expressing their votes as yay or nay can produce a unanimous outcome, no matter how many rounds of votes there are. The mathematical problem here is that individual voters’ preferences cannot be sliced and diced; nor can the choice before them be made too simply as ‘this or that’ to enable easy voting and counting (as was done for Brexit for example.) Human beings’ preferences are formed by combinations of many factors in their histories and in their present circumstances; also, by what they value most, which may not be the same as other citizens’ values.
Choices must be framed clearly for digital voting. Therefore, deliberations among citizens who have diverse views are essential before votes are called. The Brexit vote, though close, was quickly counted. But the dispute within Britain continues about what all citizens really want.
The Prisoner’s Dilemma is a simple game, often referred to by game theorists. It pits two players against each other. The players could be corporations or nations, but it is always one against another. The players are stripped of their histories, their values, and their qualities. They are given a simple, digital identity instead for the convenience of the game. When there are millions playing simultaneously, they are aggregated among themselves—those who “think like Greta” and those who do not—so that two “strategies” can be pitted against each other to play the game and determine which is a better strategy. The over-simplification of their identities and preferences, for the sake of playing a mathematical game, can make whatever theories are derived from it wrong in real life.
What must count
In a diverse society, people speak in many languages. In an economy, they adopt money as their common language. While this enables efficiency in transactions, it can strip out what is human among the transactors. Digital platforms for financial transactions reduce the costs and increase the efficiencies of transactions. The platforms are not concerned with the values that the parties are exchanging among themselves.
The value of money is precise, whereas the meanings of justice and the values of happiness cannot be expressed digitally. When people speak to demand justice or demand more happiness, what they want is not measurable in monetary terms. Therefore, it is confusing for economists to listen to what they are saying, as Milton Friedman, the author of the theory that “the business of business must be only business”, had complained according to his contemporary, Albert O. Hirschman, an eminent political scientist.
Friedman had expressed difficulty in accepting the notion that people should desire to speak their views to make them prevail. He described people’s desires to be heard as a resort to ‘cumbersome political channels’. He would much rather they resorted to ‘efficient market mechanisms’ and used their money to make their opinions known. In markets, consumers have a choice to buy or not buy a product. Consumers can make themselves heard by simply walking out. “Exit is the sort of mechanism economics thrives on. It is neat—either one exits, or one does not; it is impersonal—any face-to-face confrontation between customer and firm with its imponderable and unpredictable elements is avoided,” Hirschman explained.
“Put your money where your mouth is”, is the way in a market economy. And “money must be heard”, is morally right too for otherwise the economy would not work. Thus, money speaks loudly to shape economic policies even in electoral democracies. People who have little money, or no money, count less in businesses and political lobbies.
Friedman’s Dilemma is a dilemma of measurement that pervades economics. Marianna Mazucatto explains, in The Value of Everything: Making and Taking in the Global Economy (2017), how the concept of ‘value’ has been corrupted in the financialized world where ‘valuations’ in money terms matter more that ‘values’. The philosopher Michael Sandel goes further. In What Money Can’t Buy: The Moral Limits of Markets (2012), he explains how societies can be corrupted when human values are replaced by money values.
I seem to be venturing into politics myself! Let me return to economic games, dispassionate mathematics, and computable economic models, the subject of this essay.
Godel’s Incompleteness Theorem
Kurt Godel, winner of the Albert Einstein Award in 1951, is considered one of the most significant logicians in history (sometimes ranked alongside Aristotle). He brought three disciplines together: the theory of axiomatic reasoning, the study of mechanical computation, and the psychology of intelligence. Godel’s Incompleteness Theorem (explained in his paper “On Formally Undecidable Propositions of Principia Mathematica and Related Systems 1” in 1939) is an even more formidable theorem than Arrow’s Impossibility Theorem. Whereas Arrow demonstrated that a single, universally satisfying, outcome is not possible to achieve mathematically while making social choices, Godel showed that no mathematical system can use its own logic to prove its own accuracy and universal validity. Therefore, the results of economists’ experimental games cannot prove how the world outside their games actually works.
Every mathematical system is founded on a few axioms, along with some acceptable rules of computation. Axioms are statements or propositions which are regarded as being established, accepted, or self-evidently true. Godel proved that, in their attempt to achieve internal consistency, mathematical systems can become disconnected from external reality and externally inconsistent. They become inaccurate abstractions able to explain only some parts of complex reality, not the whole. Thus, they are always inherently ‘incomplete’.
Euclid’s geometry, which for two thousand years had seemed eternally valid, was founded on elementary notions of what a point in space is, and what a straight line looks like. In the twentieth century physicists found Euclidean geometry inadequate for explaining micro-level phenomena in physics, and even for explaining inter-stellar gravity. New concepts of multi-dimensional space and flexible time were required as axioms of new mathematical systems—even though these axioms defied common sense!
Godel did not seek to find the truth. He only showed why mathematics cannot prove what is true. His theorem of ‘incompleteness’ is a theorem of mathematical ‘unprovability’. Readers interested in understanding Godel’s proof, and its implications for the development of artificial intelligence systems would enjoy reading computer and cognition scientist Douglas Hofstadter’s Pulitzer Prize winning book (1989), Godel, Escher, Bach: The Eternal Golden Braid. He explains the complications in extracting information from data and meaning from information. He shows that the axioms (or hypotheses) on which scientific systems are founded always come from outside the system, as intuitions. They are an ‘induction’ from outside and cannot be ‘deduced’ from within the system itself. Nevertheless, for the equations in the mathematical system to consistently compute, they must be considered valid even when they challenge common sense.
Hofstadter uses examples from music (Bach), and art (Escher), as well as Lewis Carrol’s style of amusing conversations on profound matters between peculiar characters, such as the Walrus and the Carpenter. Though more famous for Alice in Wonderland and other books he wrote for children, Lewis Carrol was a logician and mathematician. He had borrowed the characters, Achilles, and the Tortoise, from Zeno of Elea, a 5th century BCE Greek philosopher known for many ingenious paradoxes.
Zeno is one of the earliest remembered philosophers in the West who highlighted problems in applying quantitative conceptions to physical bodies and to spatial expanses as ordinarily conceived. He anticipated 2,500 years ahead, the problems that the paradigm changing physicists—Max Plank, Nils Bohr, Werner Heisenberg, Albert Einstein, and others—encountered in the twentieth century: problems of space that seems to curve and time that seems to go backwards.
I am getting diverted again from Greta’s Paradox and game theory. In fact, Zeno’s most famous paradox was explained by him as a game—a physical race, as well as a mental game—between Achilles and the Tortoise.
Back to playing games
All games are constructed with rules the players must follow. The objective of playing a game is to win. Competition is a foundational principle for designing interesting games. Players must play to win, not to arrive at a draw—a consensus as it were. A game in which no one is expected to win because everyone must win would not be an exciting game to watch. Who would one bet on?
The world is a complex system operating according to its own rules which scientists are continuing to seek. Godel (and the paradigm changing physicists of the twentieth century too), had discovered the fundamental need for ‘isomorphism’ between knowledge systems and reality. The knowledge system must map reality accurately. Scientists’ mathematical models run according to the rules of the game they lay down for them. Their mathematical games may be internally consistent, but they are not practically useful if their architecture does not map the real world.
Whereas physicists’ ambitions are limited to explaining how systems of materials and physical energy work, economics is a social science which must encompass an understanding of how human beings feel and think. The axioms of economics must be isomorphic with social realities.
Economists’ models seem to have drifted too far from social realities in their attempts to achieve the mathematical precision that physicists seem to get from their models. Rational self-interest became an axiom for economists’ calculus since Adam Smith’s time. That competition is essential for progress is another axiom in economics. In economists’ games, the protagonists are assumed to be self-interested players and are assumed to be always seeking strategies to win. If the outcome turns out to be a win-win (or lose-lose) situation—a solution fair to both, it is arrived at only by default, and not as a deliberate strategy by either player.
All competitive games, like internally consistent mathematical systems, are ‘closed’ systems. The number of participants in the game is limited. The objectives of the participants are clear: they must play to win. The space in which the game is played is bounded: the board or the field. The rules (axioms) are prescribed a priori. Nevertheless, it does take great intelligence to win complex games, like chess or go (weiqi), even though they are well-bounded games.
When AI machines have beaten human masters in chess and go, it is taken as proof that computers have caught up with (or even exceeded) human intelligence. However, victory in these bounded games is not proof that artificial intelligence is of the same type as, and isomorphic with human intelligence. Human intelligence operates in unbounded systems. Human minds can reason inductively without much data, and they can come up with creative concepts ‘out of the blue’ as it were. AI machines have not developed such abilities so far, and their digital mathematical models may never be able to.
Real life games are played in ‘open’ systems. It is not clear what the objective of the game is: whether to compete for personal gain or to cooperate with others to achieve ‘win-win’ outcomes. The number of participants is unlimited. The rules of the game are not known a priori: they are discovered and made up as the game proceeds. The game evolves, and the participants adapt to the game as it evolves. They dance with the game. Their moves shape the form of the game, and the evolving rules of the game determine further possibilities for their moves. (They are redesigning the airplane in which they are flying while it is in the air and they in it).
The real game of life is a complex, evolving dance: not a dilemma on a chess board. The complex world of Nature (and human society in it) is not a digital machine. It is a learning, evolving, living system, composed of diverse forms of life, diverse species, diverse human cultures, and diverse human beings, all co-evolving. The quality of the world around them is shaped by their interactions—their competition as well as their cooperation. The quality of their life also depends on the health of the universe around them that has brought them forth.
We are only small parts of something much larger than us that surrounds us, that existed before us, and that sustains our lives. What are the bounds of human knowledge will always remain a mystery to human minds. Such profound, epistemic questions which have been sources of wonder for ages, are stirring up philosophers and scientists again.
The “Song of Creation” in the Rig Veda (circa 1500BC) asks:
Who really knows? Who will proclaim it?
Whence was it produced? Whence is this creation?
The gods came afterwards, with the creation of this universe.
Who knows whence it has arisen? Whence this creation has arisen
—perhaps it formed itself,
or perhaps it did not
—the one who looks down on it,
in the highest heaven, only he knows
—or perhaps he does not know.”
Count less; Listen more
Before economists began to apply their theories of rational self-interest and competition for progress, human beings had, for ages, been playing games of cooperation and compassion in real life. They had developed ways of sharing and sustaining their ‘commons’ and they had lived harmoniously with Nature. Their cultures, their faiths, and their ways of cooperation have been swept aside with the colonization of their lands and their minds by a supposedly superior, modern scientific civilization spreading since the seventeenth century from the European Enlightenment.
The time has come to return from systems of mathematics to ways of wisdom; to return to a world of more qualities and less quantities; and to a world of cooperation not competition.
Mathematised modern sciences and economics have arrived in a cul-de-sac. They must now go back to reality; begin with new axioms; and apply new methods of inquiry to develop new strategies for human beings to cooperate with each other and to cooperate with Nature, rather than trying to control it.
We must listen to each other and learn from each other to save the world for everyone. We must understand others’ aspirations and others’ fears. We may never arrive at an unanimity of outlook on everything: and perhaps should not because then there would be nothing more to learn. It would be the end of evolution and life. However, we must strive for a workable consensus very soon, which means an agreement about the contours of a solution in which no one is harmed for the sake of gain for others, now or in the future.
This is Greta’s Dilemma, to resolve which we must get out of the framework of the Prisoner’s Dilemma.
Social consensus can never be achieved by mathematical computations and digitally expressible choices as Arrow’s Impossibility Theorem proved. Before we jump to formulate global solutions and to calculate gains and losses, we must learn to listen deeply to people who seem to be not like us, and not as smart as us; and even to people we don’t like, and who don’t seem to like us.
