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Power Law Distributions and the Blogging World

Power law distributions were explored in class in the context of applying to the web as a whole, as well as other areas such as music and literature, with different exponents in the denominator modeling the exact popularity distributions. Power law distributions are good modeling tools for many areas such as these, and additionally, subsections of these areas. The web is full of an extreme variety of different types of websites, and power law distributions can be used to model these areas and tell us important information about them as well. Blogs are a prime example of this, and are interesting in how they are modeled in this way.

Data presented in the article show that, looking at a sample of some blogs, the distribution is roughly that of a power law. Similar areas such as Yahoo Groups mailings lists and friend amount for certain social networks can be modeled similarly. Inbound links to pages are similar as well, with all of these having the familiar power law distribution of having a few members of the data set with huge numbers, and quickly going down before slowly trailing off.

There are some interesting reasons for why power law distributions emerge, building off what was learned in class. Power law distributions appear in social systems with people expressing their opinions, and with many options. One might think that more options would lead to a less extreme power law distribution, but increasing the options actually increases the severity of the power law slope. Power law distributions also tell us that more than half of members of the data are below average. This sounds strange, and would be wrong for data distributions such as the bell curve, but the huge numbers of the first few members skews the average so that more than half of the members of the given population fall below that average.

Information cascades can also play into the power law distribution, especially for areas such as blogs. Once a good number of people have chosen to read a blog, it becomes more popular, and you hear about it more, and assume it must be the best blog. This is a similar concept to the web as a whole, with links determining popularity and driving views to other pages. Once a certain number of people have decided something, or chosen a blog or web page as their destination of choice, the popularity has the cascading effect.

Another interesting concept that appears due to the power law distribution is the lack of defined cutoffs for popularity. It is true that the first few blogs are much more popular than the rest. But the first half of those first few are also much more popular than the second half of the first few. Any subsection you look at near the beginning of the graph will have a sharp decrease in popularity as you go to less popular things due to the steep slope of the power law distribution. Any cutoff for popularity will be pretty arbitrary. This also relates to the fact that once a distribution like this exists, it is hard for newcomers to gain popularity, and very few new blogs can get to the top of the pack with extreme popularity numbers.

http://www.shirky.com/writings/powerlaw_weblog.html

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