The Power of Diversity

A different way to think of differences that can benefit problem solving and predictive tasks in education by Scott E. Page

Where do you store your ketchup?’’

That’s the question I posed to the entire student body of Greenhills High School in Ann Arbor, Mich., when I spoke at their Diversity Day. I raised this question for two reasons — to get students to think about differences using logic and to inject a little levity into what can be a heavy political topic.

As I had expected, most students’ families stored their ketchup in the fridge, but a few kept it in the cupboard. The cupboard students’ parents were mostly drawn from three distinct cultural groups: immigrants from the British Empire, African Americans from the South or former residents of Berkeley, Calif.

I followed up this question with a picture of DNA. I asked the students if they thought one of them might one day become a medical researcher and locate the “ketchup-in-the-cupboard gene” — that specific subsequence of human DNA that could explain this behavioral variation. Laughter ensued. The students recognized the ridiculousness of the question. I then asked about the “greeting gene’’ — the gene that determines whether we greet friends with a bow, a shake of the hands, a fist bump or a kiss on the cheek. Surely, once we find that, the “head scarf gene’’ and the “men who wear plaid kilts gene’’ should only be a chromosome or two away at most. More laughter.

The students got my central point. Most differences that we see across identity groups are not essential. They’re not hard coded into our genes. They originate in communities and in cultures and are reinforced by daily practice. People act the ways they do because they’re conforming to the people around them.

The ketchup question was just a warm-up (pun intended). My real intent was to introduce students to a new way to think about differences, based not on tolerance or appreciation, but on collective perform-ance and on the necessity of diversity to a well-functioning school, organization or nation. I am not saying tolerance isn’t important. It’s crucial. I’m saying that our collective ability to solve the world’s problems requires that we leverage our differences. Once we see that, achieving tolerance should be child’s play.

Nadine Hall, the diversity coordinator at Greenhills, recognizes the value of this message. In constructing a diversity curriculum, she not only wants to teach students to understand, appreciate and tolerate differences, she wants them to understand the central roles diversity plays in a robust, innovative society. Being a good citizen requires engaging difference so that the capabilities of the whole can exceed that of the parts.

Toolbox Concepts
To understand the value of diversity, we first have to reconceptualize how we think about ability. Students take a variety of tests that purport to measure what is variously called ability or aptitude. These tests spit out numerical scores, sometimes in one dimension (“your IQ is 107’’) and sometimes in two or three (“I got a 630 verbal and a 710 on math”). These tests identify specific cognitive skills and have some degree of predictive and explanatory power.

I come neither to praise or bury these tests, but to offer an alternative perspective, that of the toolbox. Rather than think of a student’s ability as a one- or two-dimensional score, we can instead think of each student as having ownership of a collection of tools. Tools might include the ability to solve trigonometric problems, an understanding of basic chemistry and the capacity to remember 11 randomly generated numbers in sequence.

The toolbox conceptualization is more than just a metaphor. It changes how we think about a student’s ability to contribute. First, it highlights how much students differ in a formal way. If there are just a few hundred possible tools and if each student possessed only 20 or 30 tools, the number of possible tool combinations dwarfs the number of people who have ever lived. Therefore, the idea that everyone is unique and potentially has something to share is not a sappy feel-good saying but a mathematical fact. It’s a mathematical fact that should instill confidence in students that each of them is an important part of the collective.

Second, if we think in terms of toolboxes, ranking students becomes much more problematic, if not impossible. If one student is told she has an SAT score of 1340 and another that he has an SAT score of 1270, the first cannot but help think of herself as smarter. If instead, the first student sees herself as having tools A thru T and sees her classmate as having tools G through W, she will be able to see the value of her classmate. True, the first student has more tools — 20 to 16 — but she lacks tools the second student has, namely U, V and W. Those tools may be useful.

Third, and most important, the toolbox conceptualization enables us to see the value of diversity in the classroom and in democracies. To make that link requires enlarging what we consider to be tools to include students’ representations of problems and situations.

This last point requires more unpacking. My central claims are that cognitive diversity drives understanding and fuels innovation and that without diversity democracies won’t function and innovation ceases. By cognitive diversity, I mean differences in how people think, not differences in identity, gender, race, ethnicity, culture or physical ability. To make clear to students (and to administrators) that I am considering differences in how people think, differences inside our heads, I often refer to them as being “inside-the-pumpkin” differences. That said, identity differences often correlate with and directly cause differences in how people think about and perceive problems. Psychological research on cognition shows that people reason from past experiences, draw on previous narratives and invoke rules and routines learned in other contexts. Thus, identity diversity can be a key driver for cognitive diversity, though it’s not the only one. Students who take chemistry acquire distinctly different tools from those who enroll in world history.

Diversity’s Logic
The power of diversity can be illustrated through two simple models, one covering problem solving and the other dealing with prediction. Full explication can be found in my 2007 book, The Difference (Princeton University Press). The essence of my research is this: Logic shows the value of diversity. Demonstrating that logic requires a few formal definitions and calculations, but nothing more complicated than F = MA.

Let’s first look at problem solving. When solving a problem, a student, a scientist or a school administrator first represents that problem using a perspective or an encoding. Each solution in that perspective has some value. For example, suppose my problem is to find the heaviest textbook. I could encode them according to their thickness. My logic here would be that thicker books should weigh more. That, of course, may not be true because not all paper stock has the same weight.

Mapping each solution in a perspective to its value creates what can be thought of as a problem-solving landscape, where the value of each point corresponds to its elevation. In my textbook example, the elevation would correspond to the weight. Because thickness would not perfectly correlate with weight, while the landscape would slope upward, it would exhibit some ruggedness. The ruggedness in our problem-solving landscapes makes finding the best solution to a problem difficult. As we search for answers, we get stuck on local peaks, points at which neighboring points have lower values.

This same process occurs when governments, schools or firms try to construct new policies. People can be thought of as crawling around on rugged landscapes. Someone proposes a new idea. If that new idea improves on the status quo- — that is if it’s a higher point on the landscape- — we all head toward it.

The rugged landscape model, which is borrowed from theoretical biology, makes the contribution of diverse perspectives obvious: Diverse perspectives create landscapes with different local peaks. If one person gets stuck, another person who sees the problem in a different way may be able to make an improvement. Thus, two heads, as long as they are different, really should be better than one at solving problems (provided, of course, that people listen to one another).

To test this intuition, Lu Hong, a mathematical economist, and I constructed a mathematical model that relies on both perspectives and ways of searching for solutions. We proved that teams of intelligent but diverse problem solvers outperform teams composed of the best individuals.

This theorem, what we call the Diversity Trumps Ability Theorem, relies on rather modest assumptions. The logic of the theorem can be traced back to the toolbox concept. The best problem-solving team has the most tools. On any given problem, the best individuals tend to have lots of tools, to be sure, but they also tend to have similar tools. Why? Because the best problem solvers possess the tools that allow them to do well on that problem.

Biologists do best on biology problems. Physicists do best on physics problems, and so on. School administrators do best on problems related to curriculum development. However, when putting together a team to solve a problem related to curricula, diversity will trump ability. A team of administrators will be outperformed by a diverse team that includes academic researchers, psychologists, teachers and students. I might add that this logic extends to the research lab, as well. As described in Daniel Goleman’s best-selling book Emotional Intelligence, the best individuals tend not to be those with the highest test score but those who have the richest network of collaborators who can provide the diverse tools necessary to solve hard problems.

Predictive Models
The power of diversity can be seen even more cleanly in the context of predictive tasks, where the value of diversity can be quantified. In a predictive task, a group of people is trying to estimate some current or future outcome. Voting in a democracy, at its core, is a predictive task.

To set the stage, let me give an example from Jim Surowiecki’s book The Wisdom of Crowds. At the 1906 West of England Fat Stock and Poultry Exhibition, 787 people guessed the weight of a steer. Francis Galton collected the data and found the average guess was 1,197 pounds. The actual weight of the steer was 1,198 pounds.

We can sit back awestruck by examples such as this or we can unpack the logic behind where the wisdom of the crowd originates. Without that logic, we cannot construct conditions under which the wisdom of crowds emerges. Attempts to produce collective wisdom might then be as likely to result in the madness of crowds — tulip crazes and all that.

In the predictive case, we can do a little math to show the power of diversity. It has been shown that the collective squared error (the error of the group) equals the average error of individuals in the group minus the group’s diversity, where diversity means the variance in the individuals’ predictions. If we define accuracy to be the negative of the squared error, we get the following equation: Collective Accuracy = Average Accuracy + Diversity.

I refer to this as the Diversity Prediction Theorem. In the case of Galton’s steer, the collective accuracy was approximately -1, the average accuracy was -2,956 and the diversity was 2,955. This means that individuals missed by about 55 or 60 pounds each. In this example, the -fairgoers owe their collective accuracy more to their remarkable diversity than to the prescient individual abilities. The same might be said of effective schools and effective democracies. Their success depends as much on the cognitive diversity as on the individual abilities of the people within them.

The Diversity Prediction Theorem states that diversity matters as much as average ability. Political and moral implications aside, diversity should be promoted because it helps us collectively make sense of the world. From a pragmatic standpoint, we should be as concerned with creating diverse thinkers as we are with creating high general-ability thinkers.

Workplace Application
The Diversity Prediction Theorem and the Diversity Trumps Ability Theorem are not feel-good mantras intended to promote tolerance. They are mathematical truths that should change how we think about differences. They provide specific lenses on a fundamental truth that progress and innovation depend on leveraging differences. School administrators should therefore see diversity just as they see any other resource. Not only should they leverage what they have, they should also encourage its continued production.

There are three ways to apply the logic of diversity. The first relates to classroom instruction. The second concerns the functioning of school administration. The third deals with how students think about a democratic society.

Most schools teach students about diversity but that education focuses on tolerance, and not performance. A concurrent focus on the pragmatic benefits of diversity, perhaps taught in mathematics or science classes, would give students a reason beyond tolerance to engage people from different backgrounds.

How might this be done? Ironically, the benefit of perspective diversity is already taught in mathematics classes when instructors show the benefits of using different coordinate systems, such as polar coordinates. Though students learn why thinking of a point defined by an angle and a radius makes solving some problems easier, they do not make the link to why different cultural interpretations of a historical event might be equally useful. That point has to be driven home. To the best of my knowledge, few schools’ diversity days involve mathematics and science departments. They should. Doing so would demonstrate the benefits of diversity with the cold, hard austerity that only science can muster. The transference of those lessons to the social world could then be accomplished through dialogue.

By the way, I have nothing against bringing in multicultural drum teams or dancers. To the contrary, I think they’re an ideal way to break the boundaries of our cognitive boxes. But, as C.P. Snow argued long ago, we have to bridge the two cultures, we have to merge art and science if we hope to have a well-functioning society and vibrant intellectual communities.

Boards, Committees
School administrators don’t act alone. They report to school boards, and they form boards, committees and teams to solve district- and school-level problems. To the extent that administrators think of diversity in creating these teams, they tend to see it in representational terms, that is are all relevant communities included? Inclusiveness matters. If a group is not at the table, shared ideas within that community may be excluded.

That said, the benefits of diversity accrue from having people who think differently. Differences in how people think about problems have multiple sources: identity, experience, education, training and interests.

When forming teams or committees, administrators need to ask themselves, How differently do these people think? Equally important, administrators need to make clear the pragmatic reason for diversity on these teams and committees. Harvard researchers Robin Ely and David Thomas have shown that diversity brings benefits when people believe it will. Team members are more likely to be tolerant and validate the opinions of others if they believe diversity generates benefits.

When hiring faculty, school leaders should look at the full range of tools that a teacher brings to the community. What life experiences, understandings and skills will a potential hire add to the mix?

Here is where traditional identity concerns such as race and gender often come into play and can do so in important ways. People from underrepresented identity groups often bring diverse perspectives and tools. When that is the case, and it often is, then their diversity should be taken into account. I should add this is not because of affirmative action considerations but because of the collective benefits of diversity. Adding one more person who thinks the same way will not improve collective performance as much as hiring someone who thinks differently.

Diversity in Democracy
As Thomas Friedman describes in his book The World is Flat, today’s high school graduates will compete in a global economy. The world has become small and interconnected owing to technological advances, particularly in transportation and information. It’s even more true that not only will those students have to compete, they will have to learn to collaborate and cooperate in a global society.

Whether the world these graduates construct will allow their differences to symbiotically interact to produce new art forms, medicines, technologies and institutions, or whether it implodes in a Babel of misunderstanding, depends partly on how they think about differences. Do they see differences as something to fear and avoid, or do they see differences as beneficial and therefore something to be encouraged?

Randall Dunn, the head of the Roeper School in Birmingham, Mich., pursues the latter path. His mission is to have students pursue humanistic ideals but to think critically while doing so. The Roeper School accomplishes this by creating a culture where anyone can challenge anyone else’s ideas or opinions. This promotes diversity of thought. Students are encouraged to think outside of any boxes placed in front of them. All such challenges, though, must be done respectfully and in a way that separates the person from the ideas being discussed.

Teaching by Example
In effect, what I present is a logic of diversity. One byproduct of that logic will be changing attitudes about policies of inclusion and diversity that complement political and moral arguments. Students who learn how cognitive diversity plays a central role in scientific progress will likely be more tolerant of others. They will be energized to develop the unique and large toolboxes of skills that will help society tackle the problems that it confronts.

For this to happen, school leaders have to enlarge the current diversity curriculum to include the science of diversity. They also must modify their own actions, rhetoric and thinking so students see the power of diversity in action.

Scott Page is a professor of political science, complex systems and economics at the University of Michigan and the author of The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools and Societies. E-mail: scottepage@gmail.com