Zipf's Law was first used to describe the distribution of city sizes by the German physicist Felix Auerbach in his 1913 work The Law of Population Concentration. It bears the name of the American linguist George Zipf, who in 1949 actively popularized this pattern, first proposing to use it to describe the distribution of economic forces and social status.
This law does not work in Russia.
Let's go back to 1949. Linguist George Zipf (Zipf) has noticed a strange tendency for people to use certain words in a language. He found that a small number of words are used consistently, and the vast majority are used very rarely. When you evaluate words by popularity, a striking thing is revealed: a first-class word is always used twice as often as a second-class word and three times as often as a third-class word.
Zipf found that the same rule applies to the distribution of people's incomes in a country: the richest person has twice as much money as the next richest person, and so on.
Later it became clear that this law also works with regard to the size of cities. The city with the largest population in any country is twice the size of the next largest city, and so on. Incredibly, Zipf's law has been valid in absolutely all countries of the world over the past century.
Just take a look at the list of the largest cities in the United States. So, according to the 2010 census, the population of the largest US city, New York, is 8,175,133. Number two is Los Angeles, with a population of 3,792,621. The next three cities, Chicago, Houston and Philadelphia, boast a population of 2,695,598, 2,100,263 and 1,526,006, respectively. Obviously these numbers are inaccurate, but nevertheless they are surprisingly consistent with Zipf's Law.
Paul Krugman, who wrote on the application of Zipf's law to cities, has excellently noted that economics is often accused of creating highly simplified models of complex, chaotic reality. Zipf's law shows that everything is exactly the opposite: we use overly complex, messy models, and reality is amazingly accurate and simple.
Promotional video:
The law of force
In 1999, the economist Xavier Gabet wrote a research paper in which he described Zipf's law as a "law of force."
Gabe noted that this law holds true even if cities grow in a chaotic manner. But this flat structure breaks down as soon as you move to cities outside the category of megacities. Small cities with a population of about 100,000 seem to obey a different law and show a more explicable size distribution.
One may wonder what is meant by the definition of "city"? Indeed, for example, Boston and Cambridge are considered two different cities, just like San Francisco and Oakland, separated by water. Two Swedish geographers also had this question, and they began to consider the so-called "natural" cities, united by population and road links, rather than political motives. And they found that even such "natural" cities obey Zipf's Law.
Why does Zipf's law work in cities?
So what makes cities so predictable in terms of population? Nobody can explain it for sure. We know that cities are expanding due to immigration, immigrants are flocking to big cities because there are more opportunities. But immigration is not enough to explain this law.
There are also economic motives, as big cities make big money and Zipf's law works for income distribution as well. However, this still does not give a clear answer to the question.
Last year, a team of researchers found that Zipf's law still has exceptions: the law only works if the cities in question are connected economically. This explains why the law is valid, for example, for an individual European country, but not for the entire EU.
How cities grow
There is another strange rule that applies to cities, and it has to do with the way cities consume resources when they grow. As cities grow, they become more stable. For example, if a city doubles in size, the number of gas stations it requires does not double.
The city will live quite comfortably if the number of gas stations increases by about 77%. While Zipf's law follows certain social laws, this law is closer to natural ones, for example, to how animals consume energy as they grow up.
Mathematician Stephen Strogatz describes it this way:
How many calories per day does a mouse need compared to an elephant? They are both mammals, so it can be assumed that at the cellular level they should not be very different. Indeed, if cells of ten different mammals are grown in a laboratory, all these cells will have the same metabolic rate, they do not remember at the genetic level how big their host is.
But if you take an elephant or a mouse as a full-fledged animal, a functioning cluster of billions of cells, then the cells of an elephant will consume much less energy for the same action than cells of a mouse. The law of metabolism, called Kleiber's law, states that the metabolic requirements of a mammal increase in proportion to its body weight by 0.74 times.
The 0.74 is very close to the 0.77 observed in the law governing the number of gas stations in the city. Coincidence? Maybe, but most likely not.
In Russia, the population of the largest city, Moscow, is officially about 11.5 million people. The number of the second city, St. Petersburg, is 5.2 million. As we can see, the ratio of the population of the two cities roughly corresponds to the “Zipf's law”. According to it, the third largest city in Russia should have about 4 million people, and the fourth - about 3 million. However, there are no such cities in Russia. In reality, the third city in Russia, Novosibirsk, has a population of 1.6 million (2.5 times less than the norm), and the fourth, Yekaterinburg, 1.4 million, which is also 2 times lower than the Zipf norm.
Why "Zipf's Law" Doesn't Work in Russia? American sociologist Richard Florida answers this question in his book "The Creative Class". He writes that "Zipf's Law" does not work in empires (or countries having a relapse of empires) and planned economies. He names three such countries-exceptions: England (where after London there is not even a second city that is 2 times smaller in population), Russia and China.
Research on "Zipf's law" was also carried out by the Financial University under the Russian government. The conclusion was as follows:
“The real distribution of Russian cities in terms of population does not fully correspond to the Zipf curve for either developed or developing countries. Part of the real Zipf curve for Russia is located above the ideal one, which corresponds to the distribution of cities in developed countries, and part below - corresponds to the distribution of cities in developing countries. Thus, according to Zipf's rule, it turns out that in Russia the largest cities and million-plus cities play a dominant role. The deviation of the real curve from the ideal is due to the vast territory of the country and various socio-economic and natural-climatic factors."
Two megalopolises and small and medium-sized cities (up to 250 thousand people) fit well into the type of western urbanization. But large cities and cities with a population of one million are not.
Another study concluded:
“The revealed trends do not correspond to the assumptions made in the literature that the reason for Russia's deviation from the Zipf pattern is the centralized planning of spatial development, which included support for medium and small cities during the Soviet period. The transition to the market was supposed to eliminate these distortions and bring the rank-size relationship closer to the canonical form, however, despite the involvement of market mechanisms in the formation of the space of economic activity, there was a further deviation from it in the country”.
The circles indicate the population of the regions of Russia.
Those. deviation from the "Zipf's law" in Russia is not the result of a planned economy (as in China), but a consequence of the country's imperialism (when one or two cities play the role of a metropolis).
Based on these trends, the likelihood of urban development / regression in Russia is as follows:
- Most cities in Russia lie above the ideal Zipf curve, so the expected trend is a continued decline in the number and population of medium and small cities due to migration to large cities.
- 7 cities with a population of one million (St. Petersburg, Novosibirsk, Yekaterinburg, Nizhny Novgorod, Kazan, Chelyabinsk, Omsk), which are below the ideal Zipf curve, have a significant population growth reserve and expect population growth.
- There are risks of depopulation of the first city in the rank (Moscow), since the second city (St. Petersburg) and subsequent large cities lag far behind the ideal Zipf curve due to a decrease in demand for labor with a simultaneous increase in the cost of living, including, first of all, the cost buying and renting housing.
In the USSR, the "Zipf's law" also did not work - you can see the deviation of cities from the Zipf curve, where they should have been.
Richard Florida in The Creative Class notes another difference between American and Russian cities. In the United States, the concentration of the creative class is in medium-sized cities scattered throughout the country. So, the highest proportion of the creative class in cities such as San Jose, Boulder (Colorado), Huntsville (Alabama), Corvallis (Oregon), etc. - in them this share is 40-48%. But the largest city in the United States, New York, is among the middle peasants in terms of the share of the creative class - 35% of the total number of employees and 34th in the ranking, the second city in the country, Los Angeles - generally 60th. A similar trend is observed in other countries where the "Zipf's law" works (Germany, France, Italy, Sweden, etc.).
In Russia, almost the entire creative class of the country is concentrated in Moscow, and the rest of the cities remain the industrial zone of the mid-twentieth century.
All of this is terribly exciting, but perhaps less mysterious than Zipf's law. It is not so difficult to understand why a city, which is, in fact, an ecosystem, albeit built by people, must obey the natural laws of nature. But Zipf's law has no analogue in nature. This is a social phenomenon and it has only taken place over the past hundred years.
All we know is that Zipf's law also applies to other social systems, including economic and linguistic. So maybe there are some general social rules that create this strange law, and someday we will be able to understand them. Whoever solves this puzzle will perhaps discover the key to predicting much more important things than the growth of cities. Zipf's Law may only be a small aspect of the global rule of social dynamics that governs how we communicate, trade, form communities, and more.
P. S. personally, it seems to me that a law with such approximate assumptions to numbers and a bunch of exceptions is generally difficult to call a law. Just a coincidence.
What do you think?
