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Fractal Inequality

I was just comparing a couple articles on income inequality, and thinking about how patterns in the natural world play out in the economic world. Here’s an account of a facet of the new “evolutionary economics:”

[Beinhocker argues that] economists should abandon blackboard deduction in favour of computer simulation. The economists he likes do not “solve” models of the economy—deducing the prices and quantities that will prevail in equilibrium—rather they grow them “in silico”, as he puts it. An early example is the sugarscape simulation done in 1995 by Joshua Epstein and Robert Axtell, of the Brookings Institution. On a computer-generated landscape, studded with “sugar” mountains, they scattered a variety of simple, sugar-eating creatures, which compete for this precious commodity. Some creatures move faster than others, some see farther, and some burn sugar at a higher metabolic rate than their rivals.

Surprisingly, the results of their myopic lives can be gripping. Even simple rules of behaviour result in collective patterns that are impossible to foresee yet easy to recognise. The sugarscape, for example, is quickly beset by a division between haves and have-nots, which bears a strong statistical resemblance to the distribution of income in real economies. These macro-results cannot be deduced from the micro-rules simulators write. Rather, they emerge from the interactions of the creatures in the model, just as “wetness” emerges from the interaction of water molecules, rather than being a property of the molecule itself.

It’s interesting to note how fractalized patterns of inequality are becoming. For example, here is Pogge on global inequality:

Though constituting 44 percent of the world’s population, the 2,735 million people the World Bank counts as living below its . . . $2 per day international poverty line consume only 1.3 percent of the global product. . . . The high-income countries, with 955 million citizens, by contrast, have about 81 percent of the global product.

And here is Tritch on U.S. inequality:

[F]rom 2003 to 2004, the latest year for which there is data . . . real average income for the top 1 percent of households – those making more than $315,000 in 2004 – grew by nearly 17 percent. . . . In all, the top 1 percent of households enjoyed 36 percent of all income gains in 2004, on top of an already stunning 30 percent in 2003.

So the fractal patterns observed by scientists in the natural world (where patterns repeat, over and over, on smaller or larger scales) somehow manage to describe (or at least map to) patterns in the social world. Philip Ball’s book Critical Mass explores some of the implications; certainly policymakers should consider these studies as they continue to study patterns of wealth and income distribution. From Wolfram’s A New Kind of Science, we may be able to develop a new kind of social science.

3 thoughts on “Fractal Inequality”

  1. This a fascinating area of research with which I have long wanted to become more familiar. There are many applications at the intersections of law, economics, and the various intellectual systems we regularly discuss. I have been meaning to welcome Jim Chen and his co-bloggers J.B. Ruhl and Dan Farber to the blogosphere, and this is a good opportunity — check out Jurisdynamics (at

  2. Cellular automata, which are used in these studies and the models to which Beinhocker refers, were invented by John von neumann, not S. Wolfram BTW. Philip Mirowski’s “Machine Dreams: How Economics Became a Cyborg Science” (Cambridge UP 2002) gives some good historical background as to how such methods have enetered into economics.

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