If the power law is a description of network clustering, then you could say that the power law is likely to shift from less than 1 to greater than 1 as the strength of preferential attachment increases.If you’re developing a long tail business or collaboration, you need to make sure the exponent in the power law is less than one. The smaller the exponent, the better off you’ll be.
How can you make the exponent as small as possible? In particular, how can you make sure it’s smaller than the magic value of one? To understand the answer to this question, we need to understand what actually determines the value of the exponent. There’s some nice simple mathematical models explaining how power laws emerge, and in particular how the power law exponent emerges. At some point in the future I’d like to come back and discuss those in detail, and what implications they have for site architecture. This post is already long enough, though, so let me make just make three simple comments.
First, focus on developing recommendation and search systems which spread attention out, rather than concentrating it in the short head of what’s already popular. This is difficult to do without sacrificing quality, but there’s some interesting academic work now being done on such recommendation systems – see, for example, some of the work described in this recent blog post by Daniel Lemire.
Second, in collaborative projects, ensure a low barrier to entry for newcomers. One problem Wikipedia faces is a small minority of established Wikipedians who are hostile to new editors. It’s not common, but it is there. This drives newcomers away, and so concentrates edits within the group of established editors, effectively increasing the exponent in the power law.
Third, the essence of these and other similar recommendations is that they are systematic efforts to spread attention and contribution out, not one-off efforts toward developing a long tail of sales or contributions. The problem with one-off efforts is that they do nothing to change the systematic architectural factors which actually determine the exponent in the power law, and it is that exponent which is the critical factor.
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