After Party Politics: Does the Free Market Live Up to the Hype?: An attempt to move past party lines.

Wall Street

It has been demonstrated with powerful logical and mathematical rigor in literature for at least a half-century that in reality the so-called "free market" economy doesn't really do what it's cheerleaders purport. Ironically it seems that those most in favor of laissez-faire policy are the one's that aren't informed about the serious intractible problems with it. When those that understand something the least are the one's cheering for it, that speaks for itself.

I understand it is difficult to make an anti-market argument in the United States without coming under fire, since it is espoused in all its glory. It's invisible hand working to ensure the efficient allocation of capital and resources, while eliminating waste. The stark reality is that there are only three economies that work like they do in economic textbooks: those with a single individual, one's created in computer simulations for the purpose of being tractable, and those in our minds.

Real economies (any economy that contains more than one participant) suffer from a well known problem called non-convexity. In one of the more accessible and well referenced journal articles, Economies with Non-Convex Production and Complexity Equilibria¹, the authors explain

...the theory of markets with non-convex productions is plagued with very bleak negative complexity results... We start by showing that computing a Pareto efficient outcome in a market with non-convex production is FΔ^P₂-hard. Economists regard Pareto efficiency as a sine qua non for any concept of stability or rationality in markets. Hence, our negative result for the complexity of finding Pareto efficient outcomes is a lower-bounds for any "reasonable" equilibrium concept. Finally, in sections 4 and 5, we give similar results for two concepts of stability more sophisticated than Pareto efficiency. It is FΔ^P₂-hard to tell if an allocation is in the core (no coalition of agents has an incentive to defect and create its own economy). And for a natural models of sequential production, we show that computing equilibria is FΣ^P₃-hard and PSPACE-hard, respectively.

Perhaps most significantly, we show in the process that such economies can have a novel kind of equilibrium, from which deviation may yield tremendous improvement for any and all agents, but the agents are stuck at a suboptimal solution of a particular instance of an NP-hard optimization problem. We call such a situation a complexity equilibrium (Definition 6.2). When agents are at such an equilibrium, standard complexity-theoretic assumptions imply that no computationally efficient procedure would generally allow them to improve indeed, it is even intractable to recognize that improvement is possible. With the exception of deliberate complexity-theoretic studies in game theory (e.g. [20]), we are not aware of other natural economic situations in which computational complexity begets stability.

The second paragraph is a rather stunning rebuke of free-marketeerism. The authors themselves demonstrate rigorously that agents find themselves in sub-optimal states of "complexity equilibrium." The authors get rather dense bringing up problem classes. In order of problem complexity they are: NP-hard, FΔ^P₂-hard, FΣ^P₃-hard, and PSPACE-hard. They are simply a classification Computer Scientists give to certain problems or queries they have based on how hard they are to solve. All of the one's mentioned cannot be computed efficiently at best, meaning a coin flip or dice toss to solve them no less efficiently than any other known method. PSPACE problems require infinite time and memory, and so are considered to be unsolvable. When stuck in these "complexity equilibria", flipping coins to make decisions is as good as anything else. So there is little incentive for improvement, though there might be profit to be had, if it could be known what to improve. No method is better than a wild guess at determining whether improvement is possible. Deciphering what procedures would to allow agents to improve, also suffer from this deficiency, known in academia as intractability. Using a coin flip or dice toss to solve intractable problems is no less efficient at finding a solution as any other method. Money is supposed to be a proxy for successful business operation. It is there to reward those that take the right steps. Yet how can success be judged if we can't know determine what success is because of these unsolvable intractabilities?

Another stunning realization is how removing the convexity requirement from economic theory to better represent reality, introduces outcomes where everyone loses. This is called a circle-of-death, and in this case results from problems that unsolvable in any real sense (requiring infinite amounts of computational space or time.) So this means that certain allocations of goods will lead to unknowable inefficiencies and unsolvable problems for resource allocations, that leave everyone involved worse off.

Non-convexity is remarkably commonplace, and not merely an academic issue. As an example, take what free marketeers nearly universally hold as axiomatic, the equilibrium price. Simply put, there is a price where supply and demand meet, and that point is the place where the price of a commodity will settle on. The tenth mink coat isn't as valuable as the first. By contrast, it would grate against common sense to think the first airplane off the assembly line would cost the same as the next 100. Economy of scale is not some academic construction, it is a widely accepted feature of a market economy. Yet something so basic flies in the face of the assumption of convexity. These asymmetries lead to the phenomenon of non-convexity and eventual intractability of solutions.

It could be rebutted that there is no other alternative to free market economics in its current formulation, because everything else is worse than capitalism. The results presented here demonstrate the free market has major deficiencies producing efficient outcomes because of structural flaws. Furthermore, many of these structural flaws are unknowable; to figure them out would be intractable. Free market capitalism has the burden of proof. It cannot be fully determined whether the system is truly working and it is demonstrable in many real world scenarios outside of academia it is not. The invisible hand of the market is as intractable as the problems presented. These results are not new, and have been available for review for at least 50 years. References for further reading are provided at the end of the post. In Economies, Papdimitriou et al. provide extensive literature as well.^1,2,3,4

The necessity of a independent authority representing us all and provide some resolution over these sub-optimal conditions that the market can get stuck in. There must be an alternative to the free-market system. Sadly, there is of course economic incentive to maintain the status quo, because those with money and influence would clearly seek to maintain their societal position. It is not a cut-and-dry issue of whether free markets work.

After Party Politics

Tuesday, September 25, 2012

Does the Free Market Live Up to the Hype?

Further Reading & References

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