i agree with you qualitatively. it is certainly a popularity contest, and indeed, it would be absurd to suggest that bundchen is twice as beautiful as heidi klum who is at

#2!

but quantitatively? note that income isn't proportional to ranking, but inversely proportional. i just don't see why it should be that, and not say, 1/sqrt(rank). the difference is huge and would easily show up in the chart.

the beauty of rich-get-richer explanations for power laws is that

*the rank doesn't even appear in the formulation of the hypothesis*, and then there's a proof showing how the hypothesis translates into a certain distribution for the top-ranked items. for example, the standard argument for social networks goes like this: "assume that a newcomer to the network makes friends via a random walk on the existing nodes. we prove that the above random process produces the following degree distribution..."

your explanation misses that magic by making the popularity hypothesis explicitly dependent on the rank. it is thus less elegant as well as harder to swallow. that doesn't make it wrong, but it does mean you need to find more evidence for your hypothesis. does that make sense?

zipf's original explanation in linguistics involved similar magic -- a word introduction/coalescence process, iirc. you would know that better :-) note that you can't just say, "every word/model gets used/paid in proportion it's/her popularity," because

*every* distribution would be an eigenvector for that hypothesis!

so i do think this stuff is somewhat subtle and needs delicate argument.