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The Curious Science of Counting a Crowd

Popular Mechanics- Sep 12, 2011
Crowd-size estimation is tough for people who want to do it right. But when turnout implies clout, then politicians and event organizers have plenty of motivation to exaggerate the head count. Through careful research, though, it is possible to make better crowd-size estimates that aren’t the result of political bias.

On June 4, a huge crowd gathered in Hong Kong for a vigil to commemorate the 22nd anniversary of the Tiananmen Square massacre in Beijing. But just how huge? In some stories 77,000 people showed up. Another story, though, listed the attendance as nearly double that: 150,000.

There’s a reason for the disparity. The first figure—77,000—is a police estimate. The second is from the event’s coordinators, who probably had some motivation to pad their numbers. To find out which crowd size was correct, two professors—Paul Yip at the University of Hong Kong and Ray Watson at Melbourne University—ran the numbers. To fit 150,000 people into that space, they’d have to cram together at about one person per 2.7 square feet (four per square meter), so that estimate is unrealistic. That would be “mosh-pit density,” the researchers write in a new paper on crowd estimation techniques published in the journal Significance.

This story of competing head counts is not uncommon. Estimating large numbers is difficult even with the best of intention. If you count the number of jellybeans in a jar three times, you’ll probably have three different numbers, because people simply cannot count very large numbers without some error. Now, imagine trying to count a shifting mass of heads, some stooping to tie shoes, some sharing the same umbrella, some arriving late or leaving early. Plus, this is one field in which good intentions are rare. Crowd-size estimation is a murky science, positioned at the intersection of statistical precision and political sleight-of-hand, and plenty of people are motivated to either exaggerate or low-ball an event’s attendance.

“Almost everyone who has tried to make a crowd estimate has a vested interest in what the outcome of the estimate is,” Charles Seife says. Seife is a journalism professor at New York University who writes about math and physics. [Disclosure: I had a class with Seife at NYU.] His newest book Proofiness tackles the ways that people try to fool others (and sometimes fool themselves) with numbers. “Whenever you see a crowd estimate,” he says, “you have to wonder where it’s coming from.” Nevertheless, Seife says, if you do your math carefully, it is possible to count a large crowd to within a couple of tens of thousands. And researchers like Yip and Watson are now applying new strategies to find out whether it is indeed possible to get a more accurate count of a teeming mass of humanity.
Crowd-Counting 101

Herbert Jacobs, a journalism professor at the University of California, Berkeley, in the 1960s, is credited with modernizing crowd-counting techniques. From his office window, Jacobs could see students gathered on a plaza below protesting the Vietnam War. The plaza’s concrete was poured in a grid, so Jacobs counted students in a few squares to get an average of students per square, then multiplied by the total squares. He derived a basic density rule that says a light crowd has one person per 10 square feet, a dense crowd has one person per 4.5 square feet, and Yip and Watson’s mosh-pit density would have one person per 2.5 square feet.

Fifty years after Jacobs, the tools for counting crowds have improved but the principle is the same: area times density. Steve Doig, a journalism professor at Arizona State University, used a photo from a GeoEye-1 military satellite to count people at President Barack Obama’s inauguration speech in 2009 (he estimated 800,000 people). The New York Police Department counts the people in the fenced crowd-control barricades that it places, then multiplies by the number of barricades. Yip and Watson applied the basic formula to the candlelight vigil in Hong Kong.

But a simple area times density calculation has its limits. Crowds are not uniform—they clump in some places and spread out in others. To account for this, estimation methods are becoming more sophisticated. Companies such Digital Design and Imaging Service are now adapting the formula for multiple densities. The firm has counted attendance at major events on the National Mall in recent years and claims it can count the crowd to within 10 percent. So CBS hired DDIS to count heads at Glenn Beck’s rally at the Lincoln Memorial in August 2010.

To get its figure for the Beck rally, the design firm first cased the venue, created 3D maps marked with probable high-density spots and cross-referenced those with historical photos of similar events. The result was a prediction of how people would congregate. “Our goal is to find out where we anticipate the crowds will gather. If it’s in the winter, we look for the wind breaks, and if it’s in the heat of summer, we look for the shade,” Curt Westergard, the company’s president, says. Crowds press toward the stage, but also toward the Jumbotron screens, and they shy from loudspeakers, he says.

Knowing what to expect, Westergard chose his observation point and launched a tethered balloon at the height of the rally. The balloon lifted a suite of remote-control cameras that, within seconds, had captured 360-degree crowd shots at various heights: 200 feet, 400 feet and 800 feet. The different heights allowed for shots of people under trees and in hard-to-see places. He laid a composite of the images over the 3D model and counted heads. His team counted heads in grid squares that represented different densities. Then, for each density (such as lightly populated or very heavily populated) they multiplied the number of people per square by the number of squares of that category, finally arriving at an estimate of 87,000 people for the Beck rally.

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