Open letter: 'The Invisible Hand' showcases dismal failure of free market economics

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Statue of Adam Smith. (Photo: james_clear / flickr)

As a professional mathematician and practising scientist in the life sciences I am aghast and dismayed by the utter and complete intellectual dishonesty of the radio show The Invisible Hand.

Your first episode clearly demonstrates the obvious cognitive dissonance and compartmentalized thought in the field of economics. By admission, in the episode, you have clearly conceded that free market prices reflect the relative perceived value of goods by the participants in the free market. Given the utility functions of the actors, this is a trivial corollary to the Strong Law of Large Numbers, and demonstrates only that free markets optimally distribute goods according to the perceived values, not that they optimally distribute goods to reflect social justice, improved outcomes in well-being and the safeguarding of future generations.

Free market theory fails in three major assumptions.

The first flaw is the assumption that people value goods appropriately for their own well-being, and the long-term benefit of others. People clearly perceive a great value in a large number of goods that lead to poor well-being, harm to others and eventually great financial cost.

Not to the least of which is our individual infatuation with a large number of consumer activities that are killing us in the most expensive and drawn out manner possible, as well as leaving a large social, economic and environmental debt to future generations.

To wit, a few of the more notorious highlights are: fast food, including poor nutritional high fat and high sugar heavily processed products, smoking, sedentary lifestyles, including driving, car ownership and passive entertainment, a heavy reliance on disposable carcinogenic organic compounds such as plastics, and fossil fuels in general.

As well individuals have not perceived value in many goods that are of extreme importance to their own well being, and the long term benefit of society, of high priority are: clean and pollution free air and water, an ecologically intact biosphere capable of sustaining human life agriculture and development, exercise and fitness, education and intellectual growth, child care, compassion, justice, peace, and many, many other goods which do not fall into the category of consumer products.

So while it is true that free markets distribute goods optimally according to the perceived values of the actors in the market, those perceived values are often heavily skewed and are easily susceptible to undue influence by those who explicitly do not have the best interest of humanity at heart.

There are many mechanisms to prejudice the value perceptions of people such as marketing, religious and political coercion, threats of violence and criminality; one could go as far to argue that warfare is merely economics by other means.

This leads nicely into the second flaw: which is the assumption that the actors in a free market are perfectly empirical.

Namely, that the actors have complete knowledge and are are completely logical. Not only is this an utterly unrealistic condition, as there clearly exists enormous information asymmetries, reasoning asymmetries and emotional asymmetries amongst the human race, this condition is also self-contradictory.

Clearly, by Godel's Incompleteness Theorems any axiomatic decision system can only finitely compute on a subset of encodable knowledge, in fact it has been proven that there does not exist a general method for deciding which encoded knowledge is decidable -- this is the famous Halting Problem.

Thus there will always be information for which no logical decision can be made in any finite amount of time in the given axioms. To make a decision under these circumstances, the axiomatic system must be extended. Fortunately for the great variety of human life, the axiomatic extensions are peculiar to each person, and are often emotionally driven. After all, if you have ever gone through a toy store with a three year old you will be well aware of how poorly equipped humans are at ranking the relative desirability of goods. It is possible to digress at great length about both the impossibility of symmetry across people, and the enormous benefit of having these large asymmetries, but we will withhold that discussion for a future day.

The third flaw is in the assumption that the conditions that are required to apply the Strong Law of Large Numbers to the distribution of goods according the perceived values of the actors in a free market are met by reality. The application of the Strong Law of Large Numbers requires that every transaction of a particular good between particular actors be identically and independently distributed and that the mean of the utility function is finite; both of the conditions of independence and identity are of such a severe nature as to be wholly unacceptable in practice, and the first two flaws discussed call into question the very existence and meaning
of utility functions for economic actors, regardless of the function having a finite mean.

The condition of independence requires that every transaction be completed without any influence from any other transaction, thus contradicting the complete knowledge assumption, and further that it has no impact on any other transactions. Clearly for a functioning society economic transactions must have an affect that correlates with other outcomes, and generally must occur for some known reason.

But even worse is the requirement of identical transactions of a goods between actors, this effectively requires resetting the market state after every transaction -- that is, returning the goods to the previous owners and removing all knowledge of the transaction. You would be hard pressed to find any economic actor willing to engage in such activities.

There is also a fourth flaw in economics -- this one extends beyond free market theory -- in that economics does not recognize or even postulate on the thermodynamic limitations of the thermal gradient in which the Earth exists.

Economics has completely ignored the fact that, like all food webs, the transactions in an economic system are fundamentally energy transfers that eventual lead to the cooling of the thermal bath of solar photons in which the Earth sits. (We will leave this discussion to a later date, as it is a deeply theoretical topic.)

In short, the contribution of The Invisible Hand fills a necessary gap in the literature, and your time would be better spent attempting to emulate a Universal Turing Machine with a Thomas the Train Set.

In the future you would be well advised to remember that the social sciences are neither. It is unfortunate that your show, caught up in the sophistry of economic theory, has, by incautiously accepting the tenets of economics, further propagated the lack of introspection in economics; in that, unlike the sciences, economics does not interrogate its own assumptions for validity through falsifiability, and does not assess the biases, uncertainties and errors in its limited and lacklustre observations.

Concisely: economics does not consider knowing about knowing. The day when economists can safely run refugee camps is the day when economists can be called empirical decision makers.


Aaron Sheldon is a graduate student in the Department of Mathematics and Statistics at the University of Calgary. His current research is in developing statistical methodologies for the calibration of systematic uncertainties in administrative data sets derived from health care management.


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