The big cities are NOT taking over politics, nor are they wielding any more power than before. This is a dense read, please try to get through it, especially the math.
Zipf’s Law states that:
Zipf’s law typically holds when the “objects” themselves have a property (such as length or size) which is modelled by an exponential distribution or other skewed distribution that places restrictions on how often “larger” objects can occur.
An example of where Zipf’s law applies is in English texts, to frequency of word occurrence. The commonality of English words follows an exponential distribution, and the nature of communication is such that it is more efficient to place emphasis on using shorter words. Hence the most common words tend to be short and appear often, following Zipf’s law.
The value of θ typically ranges between 1 and 2, and is between 1.5 and 2 for the English text case.
Another example is the populations of cities. These follow Zipf’s law, with a few very populous cities, falling off to very numerous cities with a small population. In this case, there are societal forces which supply the same type of “restrictions” that limited which length of English words are used most often.
A final example is the income of companies. Once again the ranked incomes follow Zipf’s law, with competition pressures limiting the range of incomes available to most companies and determining the few most successful ones.
The underlying theme is that efficiency, competition, or attention with regards to resources or information tends to result in Zipf’s law holding to the ranking of objects or datum of concern.
So, let’s simplify this marvel of applied statistics into this:
The exact statement of Zipf’s Law involves more formal math than we usually explain here, but it basically states that if you take a specific country, count the number of cities at a certain population level and then count number of cities with twice that population, the former number will often be close to half of the latter.
Well, what does all of this mean?
Most people don’t think of New Mexico as a large state. Texas, California, Montana and Alaska are all significantly larger, and a number of other Western states are about the same size. But almost two-thirds of the U.S. population lives in a combined area about the size of New Mexico. That’s because most Americans live in or near cities.
And if you’ve been reading political commentary over the last decade or so, you might think that cities are about to take over (or have already taken over) our national politics. The urban population in the United States is expanding, and much of the economic growth related to technology and other new industries seems to be concentrated in cities and the surrounding areas.
But last month Sean Trende and I looked at the data and found that the largest urban centers in the United States hadn’t gained much political power over the last three decades. Moreover, Donald Trump won the presidency despite losing badly to Hillary Clinton in the largest cities. So it’s worth asking: What happened? Why hasn’t megalopolis America, with its increasing economic strength and growing population, taken over politics?
I looked into the data and found that while the largest American cities are growing, their relative power has been held down by similar levels of population growth in towns and smaller cities. And if we dive just a bit more deeply into these numbers, we’ll see that a simple, little-known but eerily accurate mathematical law might have predicted it all.
