Superlinear scaling of cities
Luis Bettencourt of the Santa Fe Institute and his team have proposed a different way of looking at how exceptional cities are. The widely used per-capita is a linear measurement while cities’ attributes tend to scale nonlinearly (or superlinearly).
The researchers have shown, in fact, that with each doubling of city population, each inhabitant is, on average, 15 percent wealthier, 15 percent more productive, 15 percent more innovative, and 15 percent more likely to be victimized by violent crime regardless of the city’s geography or the decade in which you pull the data.
Remarkably, this 15 percent rule holds for a number of other statistics as well - so much so that if you tell Bettencourt and West the population of an anonymous city, they can tell you the average speed at which its inhabitants walk.
Scientists call this phenomenon “superlinear scaling.” Rather than metrics increasing proportionally with population - in a “linear,” or one-for-one fashion - measures that scale superlinearly increase consistently at a nonlinear rate greater than one for one.
“Almost anything that you can measure about a city scales nonlinearly, either showing economies in infrastructure or per capita gains in socioeconomic quantities,” Bettencourt says. “This is the reason we have cities in the first place. But if you don’t correct for these effects, you are not capturing the essence of particular places.”
Using this method, cities like LA, New York, and Houston are average while San Francisco and Boulder are above average.