Tuesday, March 02, 2004

Chaos Theory in Economics

This post has been knocking around inside my head for some time now, and this post at Samizdata helped me to finally get it started. The link refers to a discussion over a quote by evolutionary biologist Richard Dawkins in his book Pyramids of Life:

As Adam Smith understood long ago, an illusion of harmony and real efficiency will emerge in an economy dominated by self-interest at a lower level.

Brian Micklethwait, the author of the Samizdata piece, then goes on to question the use of the word "illusion" in the above quotation and to analyze the assumed metaphor that underlies the quote. To paraphrase whichever poet, "Market, red in tooth and claw."

Dawkins's reference to Adam Smith in the quote credits Smith with a very early understanding of what has become a fundamental aspect of Chaos Theory, the idea of the self-organizing system, in which a large number of individual units acting independently give arise to a system that appears to act in a coordinated manner. The "appearance" or "illusion" of coordination is no more real than the coordination of ants in a colony (it is being learned that individual ants do what they do by instinct and that the queen is very far from being some sort of central brain), or the illusion that a storm is a singular thing rather than a huge conglomeration of air and water molecules dancing to the dictates of the laws of physics and thermodynamics. What is happening in all of these systems; market, ant colony, and storm; is the result of a large number of individuals acting in accordance with a set of rules. These rules are applied over and over again, with the situation each individual finding itself in being the result of the previous applications of the rules by itself and its neighbors.

What the field of self-organizing systems is discovering is that the complexity of the final system is not necessarily reflective of the complexity of the underlying rules. An individual ant's instincts are not very complex, and the rules of physics that apply to a molecule in the atmosphere are rather well known. The complexity arises from the repeated iteration of the rules. A classic example is the Game of Life. Each square on the grid can be either on or off (populated or unpopulated in this simulation) and its state is determined by a total of four rules. From these four rules many shapes occur that appear as if they must have been deliberately designed, the Large Exploder is my personal favorite.

An important thing to remember is that the rules remain constant. There is no cosideration made for the fact that a cell is part of a glider or and exploder or any other form that we might give a name to. The only elements that exist are the individual cells, any other pattern that occurs is an accident of the system.

These patterns can either be self-reinforcing or self-destroying. The difference between the two is whether continuing the pattern makes it easier or harder for the pattern to continue. Ant colonies are a good example of a self-reinforcing pattern. A species that destroys it's food supply is a self-destroying pattern.

Two important revelations about these types of systems emerge from their study. The first is that the patterns that emerge from the repeated applications of the rules can not be predicted merely from the rules. The only way to discover the results is to observe the system or to create a simulation.

The creation of simulations leads to the second revelation: the degree of change to the initial conditions does not create a proportional change to the final results. An arbitrarily small change can create a completely new result, the infamous Butterfly Effect. When we look at weather patterns, we wonder why we can not achieve predictions greater than five days with any reliability. The problem is that five days is the effective limit placed on predictions due to the sensitivity of our measuring tools. In order to have a perfect model for predicting the weather, we would need to know the initial conditions of every atom in the atmosphere to an infinite degree of precision. That would be an impossible standard to achieve, and that doesn't take into account some jerk in Bangladesh throwing it off by sneezing.

Tying it all back to economics, and by extension sociology, I hold that all of the patterns we see between individuals and government, namely communities, races, demographic subgroups, etc., are all illusory. They emerge from the interactions of individuals acting to basic sets of rules. The problems that arise from the study of the field of economics and sociology arise from trying to establish rules that apply to the larger scale patterns when there is no reality to those patterns in the first place.

Even greater problems occur when we try to manage the large scale patterns. Three problems arise: we do not know for certain the rules that individuals are using, we do not know to the necessarily infinite degree of precision our initial conditions, and we do not know to the necessarily infinite degree of precision how much change we are adding to the system. When we add uncertainty to uncertainty, you absolutely bet that we are going to be getting results that will be uncertain, the oft spoken of Law of Unintended Consequences. It is from this understanding that I say that Karl Popper was heading into Chaotic territory when he posited that any attempt to predict the "Historical Destiny of Society" would be an exercise in futility.

If you can not predict what is going to happen in the future, then it is equally futile to try to change what is going to happen. How can you change the direction of society when the whole appearance of a society is an accident? How do you change the direction of a storm? The storm is a huge mass of atoms moving in a temporary pattern.
Where would you push?

The temptation in social systems is to change the rules by which individuals operate. However, if the complexity of the final patterns can not be predicted merely by the rules, and if we do not truly know the initial conditions on which the rules are acting at every individual level, then it becomes impossible to predict the effect the change in rules would have, and consequentially it becomes impossible to judge which changes would be the ones to lead to the desired outcome.

My solution: leave each individual to seek to increase the value of their lives. Teach each individual to value the ability of others to increase the value of their lives. Empower each individual to reward or punish other individuals' adherence to those rules. Those patterns that are rewarded (an honest business, a friendly neighbor) with greater value, while those that are punished (a dishonest business, an unpleasant neighbor) will suffer or be removed. Only so long as everyone has some power to influence the world around them can everyone be influenced to do the greatest good.

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