The distribution of attention matters.
A power relationship can allocate very different shares to different ranks. Here, the probability of visiting a page is proportional to 1 / rankᵃ. Increasing a makes the highest ranks more dominant.
At exponent zero, every page has the same probability. Random counts still vary. As the exponent increases, a small minority of ranks receives much of the traffic even before sampling variation is added.
Inside this model
The probabilities are normalized over a finite set of 10 to 100 ranked pages. One thousand independent visits are drawn from that distribution. Ranks do not change after a visit.
The top-tenth statistic compares observed traffic with its exact expected share. This is a rank-based, Zipf-style model, not a sample from an unbounded continuous Pareto distribution.
Why it matters
An average can hide how strongly a total depends on a few contributors. Looking at concentration helps reveal that dependence.
A useful lens. Not a universal law.
- The model imposes a power law; it does not show how one emerges or establish that real data follow it.
- All moments are finite because the number of pages is bounded. Claims about infinite variance do not apply to this finite model.
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Easley and Kleinberg discuss popularity, cumulative advantage, and power laws in Networks, Crowds, and Markets.
Networks, Crowds, and Markets — Power Laws and Rich-Get-Richer Phenomena ↗