The basic shape is simple – in any system sorted by rank, the value for the Nth position will be 1/N. For whatever is being ranked — income, links, traffic — the value of second place will be half that of first place, and tenth place will be one-tenth of first place. (There are other, more complex formulae that make the slope more or less extreme, but they all relate to this curve.) We’ve seen this shape in many systems. What’ve we’ve been lacking, until recently, is a theory to go with these observed patterns.Now, thanks to a series of breakthroughs in network theory by researchers like Albert-Laszlo Barabasi, Duncan Watts, and Bernardo Huberman among others, breakthroughs being described in books like Linked, Six Degrees, and The Laws of the Web, we know that power law distributions tend to arise in social systems where many people express their preferences among many options. We also know that as the number of options rise, the curve becomes more extreme. This is a counter-intuitive finding – most of us would expect a rising number of choices to flatten the curve, but in fact, increasing the size of the system increases the gap between the #1 spot and the median spot.

A second counter-intuitive aspect of power laws is that most elements in a power law system are below average, because the curve is so heavily weighted towards the top performers. In Figure #1, the average number of inbound links (cumulative links divided by the number of blogs) is 31. The first blog below 31 links is 142nd on the list, meaning two-thirds of the listed blogs have a below average number of inbound links. We are so used to the evenness of the bell curve, where the median position has the average value, that the idea of two-thirds of a population being below average sounds strange. (The actual median, 217th of 433, has only 15 inbound links.)

Freedom of Choice Makes Stars Inevitable #

To see how freedom of choice could create such unequal distributions, consider a hypothetical population of a thousand people, each picking their 10 favorite blogs. One way to model such a system is simply to assume that each person has an equal chance of liking each blog. This distribution would be basically flat – most blogs will have the same number of people listing it as a favorite. A few blogs will be more popular than average and a few less, of course, but that will be statistical noise. The bulk of the blogs will be of average popularity, and the highs and lows will not be too far different from this average. In this model, neither the quality of the writing nor other people’s choices have any effect; there are no shared tastes, no preferred genres, no effects from marketing or recommendations from friends.

But people’s choices do affect one another. If we assume that any blog chosen by one user is more likely, by even a fractional amount, to be chosen by another user, the system changes dramatically. Alice, the first user, chooses her blogs unaffected by anyone else, but Bob has a slightly higher chance of liking Alice’s blogs than the others. When Bob is done, any blog that both he and Alice like has a higher chance of being picked by Carmen, and so on, with a small number of blogs becoming increasingly likely to be chosen in the future because they were chosen in the past.

Think of this positive feedback as a preference premium. The system assumes that later users come into an environment shaped by earlier users; the thousand-and-first user will not be selecting blogs at random, but will rather be affected, even if unconsciously, by the preference premiums built up in the system previously…