markets leverage the simple mathematics of diversity of knowledge, which, when applied with a little care, can turn a crowd of otherwise unremarkable individuals into a comparative genius. “If you ask a large enough group of diverse, independent people to make a prediction or estimate a probability, and then average those estimates, the errors each of them makes in coming up with an answer will cancel themselves out,” Surowiecki explains. “Each person’s guess, you might say, has two components: information and error. Subtract the error, and you’re left with the information.”
The house-hunting bees demonstrate this math very clearly. When several scouts return to the swarm from checking out the same perfect tree hollow, for example, they frequently give it different scores—like opinionated judges at an Olympic ice-skating competition. One bee might show great enthusiasm for such a high-quality site, dancing fifty waggle runs for it. Another might dance only thirty runs for it, while a third might dance only ten, even though she, too, approves of the site.
Scouts returning from a less attractive site, meanwhile, like a hole in a stone wall, might be reporting their scores on the swarm cluster at the same time, and they could show just as much variation. Let’s say these three bees dance forty-five runs, twenty-five runs, and five runs, respectively, in support of this mediumquality site. “You might think, gosh, this thing looks like a mess. Why are they doing it this way?” Tom Seeley says. “If you were relying on just one bee reporting on each site, you’d have a real problem, because one of the bees that visited the excellent site danced only ten runs, while one of the bees that visited the medium site did forty-five.” That could easily mislead you.
Fortunately for the bees, their decision-making process, like that of Olympics, doesn’t rely on the opinion of any single individual. Just as the scores given by the international judging committee are averaged after each skater’s performance, so the bees combine their assessments through competitive recruitment. “At the individual level, it looks very noisy, but if you say, well, what’s the total strength of all the bees from the excellent site, then the problem disappears,” Seeley explained. Add the three scores for the tree hollow—fifty, thirty, and ten—and you get a total of ninety waggle runs. Add the scores for the hole in the wall—forty-five, twenty-five, and five—and you get seventy-five runs. That’s a difference of fifteen runs, or 20 percent, between the two sites, which is more than enough for the swarm to choose wisely.
“The analogy is really quite powerful,” Surowiecki says. “The bees are predicting which nest site will be best, and humans can do the same thing, even in the face of exceptionally complex decisions.”
The key to such calculations, as we saw earlier, is the diversity of knowledge that individuals bring to the table, whether they’re scout bees, astronauts, or members of a corporate board. The more diversity the better—meaning the more strategies for approaching problems, the better; the more sources of information about the likelihood of something taking place, the better. In fact, Scott Page, an economist at the University of Michigan, has demonstrated that, when it comes to groups solving problems or making predictions, being different is every bit as important as being smart.
“Ability and diversity enter the equation equally,” he states in his book, The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies. “This result is not a political statement but a mathematical one, like the Pythagorean Theorem.”
By diversity, Page means the many differences we each have in the way we approach the world—how we interpret situations and the tools we use to solve problems. Some of these differences come from our education and experience. Others come from our personal identity, such as our gender, age, cultural heritage, or race. But primarily he’s interested in our cognitive diversity—differences in the problem-solving tools we carry around in our heads. When a group is struggling with a difficult problem, it helps if each member brings a different mix of tools to the job. That’s why, increasingly, scientists collaborate on interdisciplinary teams, and why companies seek out bright employees who haven’t all graduated from the same schools. “When people see a problem the same way, they’re likely all to get stuck at the same solutions,” Page writes. But when people with diverse problem-solving skills put their heads together, they often outperform groups of the smartest individuals. Diversity, in short, trumps ability.
The benefits of diversity are particularly evident in tasks that involve combining information, such as finding a single correct answer to a question. To show how this works, Page takes us back to the quiz show Who Wants to Be a Millionaire? Imagine, he writes, that a contestant has been stumped by a question about the Monkees, the pop group invented for TV who became so popular they sold more records in 1967 than the Beatles and Elvis combined. The question: Which person from the following list was not a member of the Monkees?
(a) Peter Tork
(b) Davy Jones
(c) Roger Noll
(d) Michael Nesmith
Let’s say the studio audience this afternoon has a hundred people in it, Page proposes, and seven of them are former Monkees fans who know that Roger Noll was not a member of the group (he’s actually an economist at Stanford). When asked to vote, these people choose (c). Another ten people recognize two of the names on the list as belonging to the Monkees, leaving Noll and one other name to choose from. Assuming they choose randomly between the two, that means (c) is likely to get another five votes from this group. Of the remaining audience members, fifteen recognize only one of the names, which means another five votes for (c), using the same logic. The final sixty-eight people have no clue, splitting their votes evenly among the four choices, which means another seventeen votes for (c). Add them up and you get thirty-four votes for Roger Noll. If the other names get about twenty-two votes each, as statistical laws suggest, then Noll wins—even though 93 percent of the audience is basically guessing. If the contestant follows the audience’s advice, he climbs another rung on the ladder to the show’s million-dollar prize.
The principle at work in this example, as Page explains, was described in the fourth century B.C. by Aristotle, who noted that a group of people can often find the answer to a puzzle if each member knows at least part of the solution. “For each individual among the many has a share of excellence and practical wisdom, and when they meet together, just as they become in a manner one man, who has many feet, and hands, and senses, so too with regard to their character and thought,” Aristotle writes in Politics. The effect might seem magical, Page notes, but “there is no mystery here. Mistakes cancel one another out, and correct answers, like cream, rise to the surface.”
This does not mean, he cautions, that diversity is a magic wand you can wave at any problem and make it go away. It’s important to consider what kind of task you’re facing. “If a loved one requires open-heart surgery, we do not want a collection of butchers, bakers, and candlestick makers carving open the chest cavity. We’d much prefer a trained heart surgeon, and for good reason,” Page writes. Nor would we expect a committee of people who deeply hate each other to come up with productive solutions. There are limits to the magic of the math.
You have to use common sense when weighing the impact of diversity. For simple tasks, it’s not really necessary (you don’t need a group to add two and two). For truly difficult tasks, the group must be reasonably smart (no one expects monkeys banging on typewriters to come up with the collected works of Shakespeare). The group also must be diverse (otherwise you have nothing more to work with than the smartest expert does). And the group must be large enough and selected from a deep enough pool of individuals (to ensure that the group possesses a wide-ranging mix of skills). Satisfy all four of these criteria, Page says, and you’re good to go.
Surowiecki would emphasize one point in particular: If you want a group to make good decisions, you must ensure that its members don’t interact too much. Otherwise they could influence one another in
