Isenberg takes up Power Laws

David Isenberg says:

Yahoo and Google are permanently popular; they have low Zipf volatility. But my hypothesis is that there's a middle tier of blogs with high Zipf volatility, where a well expressed idea or a funny story or a new factoid can rapidly catapult a blog from #100,000 to #1000, or in rare cases even to #10, in a matter of hours.



I am not sure how you'd test this idea experimentally (comments appreciated), and I am afraid that if you take 100 blogs, say between #100 and #200, and look at their delta-rank over a one week period, they might not look any different than the blogs between #20,000 and #20,100. Despite this caution, I strongly suspect that blog rank (and web site rank, to a lesser extent) has a burstiness that is not characteristic of other media, that permits new ideas (and new sites and blogs) to bubble up and subside, to move more readily than other media along the x-axis of Zipf's Law.



His intuition is right, but it doesn't just apply to blogs. Consider other power-law distributed things, such as music and movies - their rankings suffer sudden volatility too.



In one sense, the argument is obviously true - with a true power law distribution, once you get down to the smaller numbers there are many with the same value, so a change of one in your value can move you a long way up (or down) the rankings.



However, the underlying catastrophe theory that predicts power laws also predicts cascades of arbritrary size too, so Isenberg's theory is likely to be right.