In this post I'm going to attempt the death-defying stunt of
connecting social network theory, wealth distribution, the behavior of
atoms in a gas and gangsta rap. Coherence would be a plus.
In my Etech speech I listed several interesting economic questions I was hoping to answer about the Long Tail in the book. One of the was whether the LT had a "fractal dimension", by which I meant whether the shape of the popularity curve in the many niches is the same, at a smaller scale, as the overall shape of the total demand curve. Functions that have this characteristic are said to exhibit self-similarity at multiple scales. I speculated that this was indeed the case in many industries, and that the Long Tail is in fact made up of many "minitails" (below), all adding up to the powerlaw ("Pareto") shape we know so well.
This is important because it explains why a very effective network-effect (viral word-of-mouth) recommendation system, which is essential in driving demand down the tail, does not actually do the opposite: drive content up the tail to further amplify hit/niche inequality. The explanation, I argue, lies in the only semi-permeable membrane between niches and mass-markets. Popularity exists at multiple scales, and ruling a clique doesn't necessarily make you the homecoming queen.
It's possible, for example, to be the most popular drum-and-bass artist at the very head of the drum-and-bass popularity curve, but that doesn't mean that you're about to knock 50 Cent off his top-ten perch. Music is made up of thousands of niche micromarkets, miniature ecosystems that, when smooshed together into an overall ranking, look like one Long Tail. But look closer and each has its own head and tail.
My question was whether these minitails resemble the Long Tail under a microscope, or whether they have a different shape. (Clearly this depends on the size of the niche, but I was focusing on relatively substantial ones where the n is large enough to be statistically significant).
This is a reasonable question. Ducan Watts and Albert-Laszlo Barabasi's work on "small worlds" suggests that the microstructure of small social networks is distinctly different from large ones, going from a near-broadcast relationship to narrowcast to multilateral as the group size shrinks. That would tend to lead to very different popularity curves, assuming that social network theory does indeed apply to the shape of the Long Tail (further research for my to-do list).
I'm still gathering data to answer this empirically, but in the course of my digging I came across (thanks to Julian Bond) a fascinating New Scientist article about new "econophysics" thinking on the best-known of the Pareto distributions--wealth. It explains why we appear to have two economic classes, one in which the rich grow richer and the other in which the poor stay poor:
In 1897, a Paris-born engineer named Vilfredo Pareto showed that the distribution of wealth in Europe followed a simple power-law pattern, which essentially meant that the extremely rich hogged most of a nation's wealth (New Scientist, 19 August 2000, p 22). Economists later realized that this law applied to just the very rich, and not necessarily to how wealth was distributed among the rest.
Now it seems that while the rich have Pareto's law to thank, the vast majority of people are governed by a completely different law. Physicist Victor Yakovenko of the University of Maryland in College Park and his colleagues analyzed income data from the US Internal Revenue Service from 1983 to 2001. They found that while the income distribution among the super-wealthy - about 3 per cent of the population - does follow Pareto's law, incomes for the remaining 97 per cent fitted a different curve - one that also describes the spread of energies of atoms in a gas
(see graph at right)
In the gas model, people exchange money in random interactions, much as atoms exchange energy when they collide. While economists' models traditionally regard humans as rational beings who always make intelligent decisions, econophysicists argue that in large systems the behavior of each individual is influenced by so many factors that the net result is random, so it makes sense to treat people like atoms in a gas....The atoms assume an exponential distribution of energy when they are in thermal equilibrium, and pushing the gas away from this state takes a lot of energy. It could prove similarly difficult to shift an economy to a different state.
Basically, it's so hard being poor that there's no time to work on getting rich. Is that true for struggling artists at the butt end of the tail, too? I've assumed that demand can shift down the tail and quality can rise up it, almost without limit. But there may indeed be a threshold at which this egalitarian mobility no longer works.