Santa Fe Institute

Why New York City is about average

Nov. 10, 2010 3 p.m.

Think New York is an exceptional city? It’s not. The Big Apple is just about average for a city of its size, and so are Los Angeles and Houston. But San Francisco is exceptional? Its inhabitants are wealthier, more productive, more innovative, and subject to fewer crimes than you would expect, given its size.

Turns out many of the cities we typically think of as great ones probably wouldn’t show up near the top of most rankings if SFI External Professor Luis Bettencourt has his way. He and his colleagues believe traditional per-capita measures are not very useful for determining what makes one city better or worse than another because they don’t treat separately the roles population size and local character play in making it so.

In their paper published today in PLoS One, they propose ditching per-capita comparisons for more scientific ones that take into account the natural advantages of larger cities. The research team includes Jose Lobo of Arizona State University, Deborah Strumsky of the University of North Carolina at Charlotte, SFI Distinguished Professor Geoffrey West, and Bettencourt.

It’s not that the scientists are against New York or L.A. Quite the contrary. “Clearly these are interesting places to be, and because they are populated by many interesting, innovative people they naturally attract other interesting, innovative people, and those people get together and do interesting, innovative things and make more money, and so on,” Bettencourt says.

Therein lies the problem, he says. You would expect New Yorkers to be wealthier, more productive, more innovative, and victimized by crime more often on a per-person basis simply because of the size and density of the city in which they live – and they are, as are the inhabitants of other large metropolitan areas.

Big cities have a statistical advantage because the agglomeration of people, more intense social interactions, and better developed infrastructures invoke efficiencies and speed up the pace at which things happen. This is a worldwide, historic fact and does not much depend on what is particular or special in a given city, he says.

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.”

Turns out, scaling phenomena are found in many other complex systems, including living things. The researchers have found, for example, that in species of mammals – from mice to whales – statistics such as lifespan, lifetime number of heartbeats, metabolic rate, and many other measures scale with body mass, but in a way that is sublinear – less than one for one – leading biological organisms to slow down and live longer as they get larger.

Still, he cautions, these mathematical regularities are averages. In biological systems and cities, there are outliers, and these exceptionalities are, to the researchers, more informative than those that look unremarkable for their size. For cities, it is the deviations that capture the local character, history, and contingencies of each specific place.

As part of their study, the researchers developed scale-adjusted metropolitan indicators (SAMIs) that allowed them to compare for the socioeconomic performances of large, midsized, and smaller U.S. cities.

By their measures, they found that exceptionality, both over- and under-performance, tends to be persistent. That is, when a city is more or less wealthy or more or less crime-ridden than its size suggests, it tends to stay that way for decades.

They also found that some features tend to pair up, such as wealth and safety; a wealthy but dangerous town like Fairbanks, Alaska is rare, as is a poor but safe city like Provo, Utah.

And they found that highly exceptional cities tend to be smaller and more monocultural, such as Corvallis, Oregon, which boasts a high number of patents for its size, and a large Hewlett-Packard laboratory.

“If we used per-capita comparisons, we would have seen different exceptions, with a bias towards many more large cities ranking closer to the top,” Bettencourt says.

So what does a city’s ranking matter? In and of itself, not much, he says. But when a city is under- or over-performing the expectations for its size, it is doing something uniquely right or wrong.

“Understanding what that is provides essential clues as to how a city can improve or further capitalize on its successes,” he says. “By looking at the history of our indicators we found to our surprise that cities cluster together in just a few groups, and these are not necessarily nearby geographically. That is, there are only a few ways main ways to be exceptional.”

In other words, the trajectory of Pittsburgh out of its industrial past into a high tech city may offer some concrete solutions to other kindred cities seeking better fortunes, such as Buffalo or Cleveland. Likewise, the model of technological innovation and economic prosperity, made famous in Silicon Valley, is at work today in places like Minneapolis or Denver.

“Our results reveal in a new, scientifically based way what is truly exceptional about a particular city, including the influence of its history, its policy choices, the consequences of its local flavor, the outcome of which can now be measured quantitatively,” he says. “Our hope is that this perspective and methodology can help us better understand cities and design more science-based and more effective policy.”

The study builds on SFI’s efforts to describe and explain scaling patterns in a wide range of systems, from living beings to cities, research that is now extending to companies – which, as SFI’s scientists are beginning to show, also have properties that scale predictably as companies grow.

Read the PLoS One paper (November 10, 2010)

See also:

New Scientist article (November 10, 2010)

Nature article calling for a science of cities (October 21, 2010)

SFI news article about SFI research on cities and companies (August 12, 2010)

Radiolab interview of West and Bettencourt on cities and scaling (October 8, 2010)

eWeek video interview of Geoffrey West on cities and companies (October 29, 2010)

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