Chessonomics – The Case for Formalism in Economics

By Max Schröder

I studied Metaphysics to understand Economics: After all, how can one make sense of the usual objects of Economic Theory if not via the route of the transcendental and strictly non-physical? Take for example one of the basic foundations of (neoclassical) Microeconomics: Consumers are supposed to optimise their decisions by picking – from a plethora of choices – the one basket of goods and services that maximises their personal well-being, given their preferences and budget constraint. Where, I was wondering, are all these baskets? Clearly not in any supermarket I have ever been to. Neither can they be located in the mind of the consumer, as some might claim. Personally, I can hardly fill my trolley with the few things I have put on my grocery list – too plentiful are the distractions provided by 2 for 1 offers and spontaneous advertisement-induced impulse purchases. In short: when I go to the shops I might have many things on my mind, but comparing baskets of goods at the margin is not one of them.

However, as W. V. O. Quine would insist: if the Science of Economics is to employ models containing millions and billions of baskets of goods, then Economists are committed to the existence of these mountains of baskets. They have to be somewhere – only where? Luckily philosophers (being notoriously non-commonsensical) have long pondered such questions and one might draw an analogy with the existence of numbers in the Philosophy of Mathematics. The similarity is striking – numbers, presumably do not exist in the real (read physical) world. No one has ever seen the number 3, or tripped over the decimal extension of pi. And yet most (if not all) of our technology depends crucially on these number-entities. Since Plato´s time philosophers had a neat explanation for the fact that numbers are clearly not physical and yet seem to be real: They are real and they do exist – specifically they are even more real than real stuff. Platonists believe that numbers (and other stuff that we cannot locate on earth yet need for our mental activities, such as “the good” and “the colour purple”) occupy some non-physical realm that can somehow be accessed by our minds. This opens an exciting possibility for the struggling economist: Instead of trying to defend the notion of rational economic man by searching (increasingly unsuccessfully) for earthly evidence of his existence one can relocate homo oeconomicus and his mountain of baskets to this fantastic land of ideas, where the former can compare the constituents of the latter at his leisure.

Unfortunately however, few will be satisfied with this solution. After all, which serious commonsensical person would readily believe in such a mythical realm? To most people with a scientific mind the physical universe is a closed economy. The world is constituted of material blips and blops (quarks and other mysterious particles) and that is it. And even if there were such a mysterious non-physical world it would be necessarily and utterly separated from ours to the extent that there could not be any interaction of any kind in any direction between here and there (after all this would violate certain laws of thermodynamics). But setting the epistemological issues aside: The belief in the existence of a platonic realm of perfect forms is – at least amongst the majority of the scientifically educated (read physicalists) – somewhat on par with believing in ghosts, or leprechauns. Thus, if economics and economists are to be taken serious by other scientists (something that is close to the heart of every member of an economics department), homo oeconomicus needs to be driven from this unearthly paradise. But where to go?

Again the solution can be found in the analogy with Mathematics and it is here that I want to present my proposal. At the beginning of the 20th century some German mathematicians (Thomae, Heine & Hilbert) decided that it was time to do away with the ghosts in mathematics. They each devised theories that are broadly recognizable under the name “Formalism” and share an essential trait: That the expressions and symbols of mathematics are largely meaningless – they do not refer to anything, not in the real world and not in the heavens.

One of these theories, dubbed Game Formalism, is of particular interest to the economist. This theory holds that the manipulations of sequences of symbols in mathematics resembles a game – like chess – where set pieces (i.e. numbers) are manipulated according to the rules of the game.

In my view economists have a lot to gain by embracing some form of game formalism: No longer would one’s theoretical work be vulnerable on grounds that the assumptions of the model are “too simplified” or “nowhere near resembling reality”. It is up to anyone to choose the kind of game one wants to play, so don´t be a killjoy. Formalism would also justify a large chunk of what is already practised by (mainstream) academics today: Many players (academic economists) make moves in a game (write papers) using set pieces (models) following certain rules (mathematics) and sometimes someone wins (writes a very elegant/complicated model) – no reference to reality required.

By all means, I am not saying that playing the economics game is pointless (we are playful creatures after all). A lot can be learned by playing games, but it is important to distinguish between the game world and the real world. Crucially this mean that governments and other decision makers would have to take responsibility. Instead of blindly relying on the “truth” of economic theories and “expert advice” they would have to consider the nature of the theory game played in economics departments around the globe and appreciate that homo economicus resembles a rook more closely than any actual person. No one would think of handing over city planning to a reigning SimCity champion, so why do it with the economy?

The discipline of economics has a lot to gain if different variations of the game (different schools of economic thought) were allowed to be played on an equal footing. Instead of arguing about which game is better one should appreciate that some would rather play rugby than football. One could also understand that different games recommend different strategies for the same situation – depending on the specific rules of the game and the pieces that are available. From this standpoint a pluralist economics profession could once again emerge, where many different game strategies are acceptable for the same real world problems.

To sum up my case: Formalism could be a great asset to economists and the general public. It captures the nature of much of economic theory today – practised as a model-writing game with little reference to reality. It would serve as a wakeup call to all those who excessively rely on economic theory to make decisions that affect us all. And finally it would break the hegemony of a single school of economic thinking and promote pluralism in economics.

Lastly there is an advantage that a formalist economics would have – above and beyond its mathematical parent: A main criticism that is levelled against mathematical formalism goes as follows: “If it´s all just a game – then why do the models work so well?” It can be doubted that economics would encounter this problem anytime soon.

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