Any thoughts on Zipf’s Law?

I don’t have time to do posts on what I’d really like to talk about, the new Krugman and Wells article or Russ Roberts’ piece on banking.  So I’ll defer those until after my trip to Oxford, and instead do a short fun piece on Zipf’s Law.  Well, fun for nerds like me, who find descriptive statistics to be endlessly fascinating.  (Not the other kind of statistics.)

Mankiw recently linked to an Edward Glaeser article on Zipf’s Law, which reminded me of a table of skyscraper statistics.  It may be that everything I say is already widely known, and fully explained.  If so I can count on my very smart commenters to point that out.  For those who don’t know, Zipf’s Law says that in a ranking of entities by size, the second on the list will be about 1/2 the size of the first, the third will be 1/3 the size of the first, the 10th largest will be one tenth the size of the first, etc.  A good example is the population of US cities:

Rank↓  City↓  State↓  Population↓
1  New York  New York  8,363,710
2  Los Angeles  California  3,833,995
3  Chicago  Illinois  2,853,114
4  Houston  Texas          2,242,193
5  Phoenix  Arizona  1,567,924
6  Philadelphia   Pennsylvania  1,540,351
7  San Antonio  Texas          1,351,305
8  Dallas  Texas                  1,279,910
9  San Diego  California  1,279,329
10  San Jose  California  948,279

I find this kind of spooky, as these cities grew spontaneously.  Note that if you look at this Wikipedia list you will find that the big cities are actually a bit too small when compared to cities ranked, 20, 30, etc.  The Glaeser article shows that metro populations have the same problem–big cities are a bit too small.
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