The Butt Ugly Weblog

Blogosphere simulation

Had a lazy moment, so I decided to do something that has been bouncing in my head for a while: could the Power Law of weblogs be simulated? The basic idea of the Power Law is that in any blogosphere, certain blogs become more popular than others (and this without the help of any top-lists or anything). So I made a bunch of rules, hooked them to a graphing library, and lo! The Power Law formed in front of my eyes. In fact, it formed with almost any assumptions.

This very simple applet I wrote creates a blogosphere of 1000 bloggers. Each blogger follows the following rules:

• Initially, all bloggers have 20 subscriptions to random blogs.
• Every day, every blogger makes a post.
• There is a 10% chance for him to post a link to an another blog.
• Every day, the blogger updates his subscription list as follows:
  1. There is a <2% chance that a blogger drops a subscription (the probability is decreased if the blogger has fewer blogs in his subscription list.
  2. There is a 5% chance that the blogger subscribes to a blog if someone on his subscription list has linked to it.
  3. There is a 1% chance that a blogger subscribes to a blog that posts a link to his blog.
  4. There is a maximum of 40 blogs any blogger will subscribe to.

It turns out that very quickly, even after a few iterations, some bloggers become more popular than others (because it's more probable that people link to them), and therefore get more links. Which makes them, in the next turn, more popular. Very quickly, some bloggers gain a very large audience, whereas most of the bloggers will plateau to an average level.

So don't complain about something as trivial as the top-list making some Finnish bloggers more popular than others. This is something that is built-in the linking structure of the Blogosphere. It might be interesting to add some sort of an "interestingness" -feature on the blogs and see if these blogs bubble up to the top, but... There's only so much time :-)

Update: The following quote from Shirky's article, is the key thing (emphasis mine): "In systems where many people are free to choose between many options, a small subset of the whole will get a disproportionate amount of traffic (or attention, or income), even if no members of the system actively work towards such an outcome. This has nothing to do with moral weakness, selling out, or any other psychological explanation. The very act of choosing, spread widely enough and freely enough, creates a power law distribution."

(Standard disclaimer: this is not a scientific proof. It's in fact a very silly and simple proof, with perhaps bad assumptions. But it should validate the basic idea. Any statisticians in the audience are free to comment, and I shall attempt to make the code more robust.)