Power Law

The way predictions are made is changing. Data scientists are competing with traditional statisticians, and “big data” analysis is competing with the study of "statistic samples." This change mirrors a wider paradigm shift in the conception of society and in what rules its structural dynamics. In order to understand this change, one needs to know the "power law."

If facts happen randomly, in a two-axis world, it is very much possible that they will distribute as in a Gaussian curve, in the shape of a bell, with a majority of happenings concentrating around the average. But if facts are interlinked and if they co-evolve in such a way that a change in one quantity results in a proportional change in the other quantity, it is more probable that they will distribute as in a power law graph, in a ski jump shape, in which the average is not important and polarization is unavoidable. 

The distributions of a large set of phenomena observed in physics, biology, astronomy follow a power law, but this kind of curve became very much discussed when it was applied to the understanding of the Internet. Studying the number of links to specific web pages, it was soon clear that some pages were attracting more links and that, with the growth of the network, it was more and more probable that new pages would link also to those very pages. In such a network, some nodes became hubs and other pages were only destinations: The number of links to pages followed the power law and it was possible to predict that the dynamics of the network was going to bring about a polarization of resources, as in the Barabási-Albert model, an algorithm invented by Albert-László Barabási and Réka Albert. This kind of understanding has consequences. 

As the Internet became more and more important for society, the network theory became part of the very notion of social dynamics. In a network society, the power law is becoming the fundamental pattern.

In social sciences, prediction has often been more a kind of shaping the future than a description of what will actually happen. That sort of shaping by predicting has often relied on the assumptions that were used in the predicting process: Predicting something that will happen in a society relied on an idea of society. When scholars shared the assumptions that were defined in the notion of the "mass society"—with mass production, mass consumption, mass media, in which almost everybody behaves the same, both at work and when consuming—in their vision, fundamental characters were the same and diversity was randomly distributed: so, Gauss ruled. In a mass society most people were average, different people were rare and extreme, thus society was described by a "bell curve," a Gaussian curve, the "normal" curve. Polls based on statistic samples were able to predict behaviors. 

But in a network society the fundamental assumptions are quite different. In a network society, all characters are linked and co-evolve because a change in a character will probably affect other characters. In such a society, the average doesn't predict much and scholars need a different fundamental pattern. 

The power law is such a fundamental pattern. In this kind of society, resources are not random: they co-evolve and they polarize. In finance, as in knowledge, resources are attracted by abundance. The richer get unavoidably richer.

Understanding this pattern is the only way for a network society to oppose inequality without looking for solutions that were good in a mass society. Bernardo Huberman, a network theorist, observed that the winner take-all in a category, that is to say in a meaningful context. For example, the best search engine wins in the search engine category, but not necessarily in the whole of the web, thus not necessarily in the social network category. In such a network, innovation is the most important dynamic to oppose inequality, and real competition is possible only if new categories can emerge. If finance is only one big market, then the winner takes all. If rules make sure that different banks can only play in different categories of financial services, then there is less concentration of resources and less global risk. 

In a mass society, everything tends to go toward the average: The middle class wins in a normal distribution of resources. In a network society, resources are attracted by the hub and differences inevitably grow. The mass society is an idea of the past, but the network society is a challenge for the future.

The power law can help understanding, and maybe correct the dynamics of networks by growing the awareness of its fundamental patterns. Predictions are narratives. And good narratives need some empirical observations. Moore's law is useful to those that share the techno-centered narrative of the exponential growth of computer abilities. The power law is useful to those that want to critically see the evolution of a network.