The Distribution of Demand: What kind of a law?
Chris Anderson describes The Long Tail as a power law that is not limited because of limited shelf space or disitribution channels, which is often the case in traditional markets, while a power law of Internet-based market is not limited thereby. A power law is a particular mathematical relationship between two quantities, incidents and frequency of occurrence events such as music tracks and the number of music downloads. A power law is, according to Chris Anderson, present when a small fraction of the numbers are representing a large proportion of the number of downloads.
An example is the Pareto 80/20- rule, often used to explain that 20% of products traditionally generates 80% of revenue. According to Anderson occurs power-laws on consumer markets where the following three conditions are present: (1) Variation and (2)varying quality of supply and (3) network effects (eg Word-of-mouth), which reinforces the difference in quality. Put another way success creates more success, which incidentally corresponds to Pareto 80/20-regel. According to Anderson was the 80/20 rule a possibility earlier, but the Long Tail is altering this situation today, and Anderson calls for not allowing a power law dominating the market: "While the 80/20 Rule is still alive and well, in a Long Tail Market it has lost its bite. ". One example highlighted is an online clothing store, where only 71% of sales came from 20% of the products. This means that sales in the increasingly come from niche products compared with 80/20- rule.
Chris Anderson acknowledges, however, demand in practice often is a power lawdistribution "... some things will sell a lot better than others, which is true in Long Tail markets as it is in traditional markets". The attentive reader has noticed that Anderson's arguments about a power law is contradictive. On the one hand, he uses a power law to demonstrate that there is a latent demand on the Internet, and therefore very positive about this "law". On the other hand, the urges to that "one" should not follow being dominated by a power law in Long Tail markets. This dispute leads on to Anderson's argument for why a power law does not dominate in a Long Tail market. As he writes: ".. why don’t network effect recommendation systems, which are essential in driving demand down the tail, actually do the opposite: drive content up the Tail, further amplifying hit/niche inequality? That’s what you’d expect with more powerful network effects, yet what we actually see in Long Tail markets is flattened powerlaw, with less of a difference between hits and niches”. The explanation from Anderson is that filters and other recommmendation mechanisms work better on niche level of individual genres and subgenres, while the effect is somewhat less across genres. It is an exception if the numbers in the less popular genres break through as a hit. Rather, it is more normal for the tracks in a popular genre becomes popular, but since there is hereby created a greater competition among several hits from other genres, it is rare that the tracks breaks through the really big hits. According to Anderson, it is thus network effects that will contribute to the demand becomes more niche-oriented in terms of popular products. Industries Anderson examines consists of entertainment and media industries and argues that "the long tail" exists in all industries. As an example of a Long Tail business highlights Anderson, the U.S. online music service The Rhapsody. In short, Anderson is convinced that companies should not only base the business in the most popular products, but include niche products, as they themselves today may represent a significant market share.
Another Analysis
Will Page, UK economist, conducted in 2008 an analysis of downloads in a period of an Internet-based music store in the UK. Apart from 13 million available tracks were 52,000 tracks (equivalent to 0.4%) for 80% of all downloads. The analysis showed, in other words, a shift in demand against a long thick tail did not exist. It showed in fact the opposite: It followed a lognormal distribution curve. Page's argument that no distribution follows a power law distribution, but lognormal (hits concentrated) is Matthew effect explained in detail below. Page's theoretical starting point is Robert Brown (1959) "Statistical Forecasting for Inventory Control", where the lognormal distribution is used as a method to analyze stock holdings. Within empirical data on the consumption of digital music exists in other words, an example of two completely opposite analysis: Chris Anderson's power law distribution on the Internet and Pages lognormal distribution.
Power Laws, Matthew effect & Distribution of Demand
In the following subsections the three closely related factors: distribution of demand, Matthew Effect and Power Laws are discussed in relation to the demand of digital music (e.g. songs bought on Itunes or TDC Musik/TDC PLAY).
Power Laws
Power Laws in economics was introduced by Vilfredo Pareto already in 1897. Pareto found that across different communities, countries or ages, the distribution of income and wealth followed a "power law". This power law showed that a small proportion of the population accounted for a disproportionate share of income and wealth in the countries concerned. The same type of law in a different context (the use of different words) took George Kingsley Zipf in his "Human Behavior & The Principle of Least Effort" (1949).
More generally, Zipf's and Pareto's laws are two different ways to represent the same phenomenon of power law. The phenomenon has since been found in other sciences. Caldarelli (2007:85) explains the power-laws by that they are expressed in self similar system, a system or object that is the same regardless of the observation scale increases or decreases. There are several power-law-generating mechanisms, some more complex than others. The mechanism that has relevance to consumer behavior is self-reinforcing processes, or in technical terms multiplicative processes.
Multiplicative processes & Matthew Effect
One of the most successful applications of a multiplicative process is found in preferential attachment. Generally, there is among scholars agreement that the first to introduce mechanism of preferential attachment was G. Yule (1925). Although Yule used the mechanism to explain the relative abundance of species and genera within biology world is the mechanism since used within e.g. behavioral economic theory in form of Simon's model named after Herbert Simon, who was one of the pioneers of behavioral economics' took in the 1950s onwards.
Interestingly, the mechanism is found in several independent studies across fields and time, and particularly in studies of how the network grows, the mechanism is often used as a reason. That is precisely why the mechanism has come to their several names: Yule process, Rich Gets Richer, Cumulative Advantage, preferential attachment and Matthew effect. In literature, the mechanism is often an argument for why a power law arises. Interestingly enough, one of Will Page's arguments is that the distribution of music demand is not power-law distributed, but lognormal distributed precisely the Matthew effect. As mentioned above Page's use of lognormal distribution for the demand is based of Robert Brown's book from 1959. Interestingly enough, Brown describes Zipf's Law as a plausible model for why the demand follows a lognormal distribution. Whether it is or other distribution, and the living used in the analysis of music consumption clarified below.
Lognormal or Power Law - distribution?
Often derived from simple power-laws and processes in nature are often phenomena is normally distributed, reflecting the central limit theorem. Because of this theorem, it is by multiplicative processes expected that the variables (here the consumption music downloads) either follows a power law or lognormal distribution (which can look like a power law). Distribution shall have the same form and can therefore in many cases confuse. Mitzenmacher (2004) finds that the two types of distribution in some cases are cohesive, such that the power law applies in the "tail", while the lognormal distribution applies to the second part of the "body" in a data set, which Tucker & Zhang (2007) supports. Although they do not differentiate between the two disitributions they find both a "Tail" and a "body" in a study of the popularity of websites that sell wedding services. Clausen et al (2009) finds that for some datasets can both apply a power law, lognormal and exponential distribution.
In studies in several scientific fields researchers have found different distributions may be due to unique circumstances in the respective analysis. This suggests that a power law is not a universally applicable law. As Clausen et al. (2009) claims: "Regardless of the true distribution from which our data was drawn, we can always fit a power law". Clausen et al. (2009) questions then the importance of a distribution proves to be a power law distribution or a lognormal distribution. Whether this is a problem for the examiner depends on the scientific objective of the study. As shown in the above subsection Matthew effect may exist in both distributions, which helps to emphasize the importance to investigate which factors are the basis for the Matthew Effect than it is to clarify the distribution demand for digital music follows. The argument is that understanding is important in relation to the use of filters and parts functions on the Internet and their impact on demand.
As a result of the above the question is whether the term "The Long Tail" is more wrong than correct when referring to the distribution of demand of goods like digital music.
Sources:
en.wikipedia.org/wiki/Behavioral_economics, September 5 2009
www.theregister.co.uk/2008/11/07/long_tail_debunked, June 19, 2009.
www.telco2.net/blog/2008/11/exclusive_interview_will_page.html, June 10, 2009
Anderson (2006): The Long Tail.
Caldarelli(2007:100)
Clauset, A. et al. (2009:14): Power‐law distributions in empirical data.
Goldstein et al. (2004)
Mitzenmacher(2004)
Malchow‐Moller & Wurtz(2003:123)
Simon, H.A.(1955): On a class of skew distribution function, Biometrika, 42, pp. 425‐440.
