No, this is nothing to do with lawyers or judges, this is about mathematical laws and nature (though it does seem to be a day for heavy stuff, doesn’t it).

You are probably all aware that many things in nature are more or less random and their populations follow a normal distribution (the central limit theorem, for the economists out there). But there is another mathematical relationship that is proving equally widespread. If is known as Zipf’s Law, or the power law, and it governs a wide range of things from the frequency of words in a document to the population of cities. Basically it holds that there will be a huge number of things that are only seen very rarely, a very small number of things that are hugely numerous, and a linear relationship between those points.

Recent work at the Swiss Federal Institute of Technology Zürich (using open source Linux software as the data set) has begun to illuminate this, and it seems that the phenomenon is bound up with linkages. It should be no surprise that this sort of thing governs blog popularity. There are vast numbers of blogs that hardly anyone reads, and a small number that are insanely popular.

But it goes much wider than that. It is, for example, the main flaw in the idea of the Long Tail, and it explains why publishers and bookstores want to concentrate on a few “blockbuster” books rather than a broad range of titles.

Power laws can be seen widely in economics, including the distribution of corporate wealth: lots of small businesses making just enough to get by, and a small number of multi-national mega-corporations. And if it applies to the wealth of companies then it probably applies to the salaries of their senior management as well. What is more, the bigger the sample, the bigger the difference between top and bottom, so as we move from small states, to huge markets like the USA and EU, to global markets, so we should expect bigger and bigger inequalities.