Saturday, March 31, 2007

Mathematical Politics: Part 1

Complex Systems TheoryI recently watched the three episodes of “The Trap”, a documentary screened on BBC2 on Sunday night. The program studied the development of western political policy from the 1950s to date. As a rule I am not greatly interested in politics and I probably glanced at the entry in the Radio Times for the first episode and dismissed it. However, just by chance I happened to turn on the TV at the start of the first program and I immediately found myself lapping it up. The first program wasn’t an expose of the gossipy particulars and intrigues of political life, but told of the application of games theory to the cold-war stalemate. This really interested me because here was a program dealing with fundamental principles and not particulars. I have a nodding acquaintance with games theory, but as I have never really closely attended to politics I didn’t know, as the program alleged, that games theory had been so seriously applied during the cold war decades in order to deliberately create a stalemate that circumvented nuclear war. Although this passed me by at the time I was aware of another trend in politics that was alluded to in this first episode of ‘The Trap’; that is, the radical right’s application of complex systems theory to socio-economics during the nineteen eighties.


Complex systems theory is not a single theory as such but an interdisciplinary largely mathematical subject combining theoretical insights taken from a variety of disciplines, from physics, through information theory, to computational theory. It is of great generality having many applications, and encompasses games theory as a special case. It is a theory that deals with systems of relatively simple interacting parts, where each part obeys some basic rules determining just how it interacts with other parts of the system. What piques the interest of complex systems theorists is that so often these systems of interacting parts show “self organizing” behavior; that is, the parts of these complex systems organize themselves into highly ordered forms. Take for example the spectacle of synchronized flying displayed by a large flock of birds. This behavior can be simulated with computer models using the fundamental insight of systems theory – namely, that the complex organized behavior of flocks of birds emerges as result of some basic rules determining how each individual of the flock responds to its neighbors. The crucial observation is that to produce this self-organizing effect no central control is needed - just simple rules telling each part how to look after itself. In the cold war period the “players” in the nuclear deterrence game looked after themselves by responding to the threat that each posed on the other, and the result, it was inferred, would be a stalemate; or in terms of the mathematical speak of games theory “A Nash equilibrium”. All-out nuclear war was thereby avoided. Most people have an intuitive grasp of how mutual deterrence is supposed to prevent either side making an aggressive move, but games theory supports this intuitive notion with mathematical rigor. The self-organized outcome of the cold war game was, the theory suggests, a peaceful, if rather tense, coexistence. That was the theory anyway.

Complex systems theory in its general form made its presence felt in politics during the eighties with the swing toward free market economics under Margaret Thatcher and Ronald Reagan. In 1987 I watched a documentary in which the ‘radical right’, as they were called, stated their case. It was clear to me even then that the radical right really had got their intellectual act together. They bandied about terms such as ‘distributed processors’, ‘local information’, ‘self regulation’, ‘self organizing systems’ and the like – all things that are very familiar to a complex system theorist. According to the radical right, central government should refrain from interfering with the natural processes of the free market, processes that solve the problems of wealth creation and distribution in ways analogous to decentralized natural systems like the ant’s nest, the brain and the hypothetical Gaia. In these natural systems there is no central control; the ‘intelligence’ of the system is distributed over many relatively simple parts and these parts behave and interact with one another using some basic rules. Likewise, society, it is conjectured, can be modeled after the fashion of these decentralized systems. Government intervention, according to the radical right, is likely to disrupt the natural self-regulating mechanisms of the free market. In fact no central planner could ever have enough information or even the cognitive where-with-all to do what the market’s many decentralized processors do. The notions behind Adam Smith’s ‘Wealth of Nations’, so hated of Marx, were now seen as a special case of complex systems theory. Smith’s vision of a system of autonomous wealth producers making local decisions based on their surroundings thereby generating an economic order echoed the self-organizing properties of many natural systems. Intelligence, rationality and order “emerges” out of these distributed systems, and that, it is contended, also holds for the free market.

That’s the theory anyway.

To be continued...

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