#zipfs law

Rank vs. Frequency Rule: Back in 1949, the linguist George Zipf noticed something odd about how often people use words in a given language. He found that a small number of words are used all the time, while the vast majority are used very rarely. If he ranked the words in order of popularity, a striking pattern emerged. The number one ranked word was always used twice as often as the second rank word, and three times as often as the third rank.

Later dubbed Zipf’s law, the rank vs. frequency rule also works if you apply it to the sizes of cities. The city with the largest population in any country is generally twice as large as the next-biggest, and so on. Incredibly, Zipf’s law for cities has held true for every country in the world, for the past century.

Just take a look at the top ranked cities in the United States by population. In the 2010 census, the biggest city in the U.S., New York, had a population of 8,175,133. Los Angeles, ranked number 2, had a population of 3,792,621. And the cities in the next three ranks, Chicago, Houston and Philadelphia, clock in at 2,695,598, 2,100,263 and 1,526,006 respectively. You can see that obviously the numbers aren’t exact, but looked at statistically, they are remarkably consistent with Zipf’s predictions.

The usual complaint about economic theory is that our models are oversimplified — that they offer excessively neat views of complex, messy reality. [With Zipf’s law] the reverse is true: we have complex, messy models, yet reality is startlingly neat and simple.

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