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CHAPTER 1

DIVERSITY BONUSES: THE IDEA

The power of a theory is exactly proportional to the diversity of situations it can explain.

— Elinor Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action

On April 8, 1865, one week before his assassination at Washington's Ford's Theatre, Abraham Lincoln visited a field hospital near Petersburg, Virginia. To raise morale among the wounded troops, Lincoln picked up an ax and began chopping wood. As a youth, he had split thousands of fence rails to earn money or goods in kind — he was once paid in dyed brown cloth sufficient to make him a pair of trousers. On the day of his visit to the field hospital, he demonstrated to all assembled that the famed "Rail Splitter" could still "make the chips fly."

Suppose that you had to hire a team of people to split rails. You would look for strong, tall people like Lincoln who are best at splitting rails. The logic borders on the tautological: the best team of rail splitters consists of the best individuals.

That logic makes sense because splitting rails is a separable task. The number of rails split by the team equals the sum of the rails split by each person. That logic does not apply for teams of people who work on the complex tasks we confront in our modern, information-rich society. In those settings, a team's performance depends on the diversity as well as the ability of its members. As a result, a policy of hiring the best does not make sense on high-dimensional tasks. The best team will not consist of the "best" individuals. It consists of diverse thinkers.

The idea that diverse ways of thinking can lead to deeper insights is not new. It can be found in the writings of Aristotle. Lincoln himself applied a logic of diversity when appointing his cabinet. He did not create an echo chamber of like-minded people. He chose a diverse cabinet, the famed team of rivals. He opted for diversity partly to build political consensus but primarily because he faced complex problems. As he wrote in his December 1862 message to Congress, "The occasion is piled high with difficulty, and we must rise with the occasion. As our case is new, so we must think anew and act anew. We must disenthrall ourselves."

We too must disenthrall ourselves. We now operate and interact in a complex world in which we work with our minds, not our backs. We must therefore also think anew. We must abandon the narrow and demonstrably false belief that we should admit, hire, and promote those who perform best according to a common standard. As I show later in this book, those who score highest will tend to be similar. Hiring "the best" will reduce the diversity of our scientific teams, our planning commissions, and our boards of directors, and with it their collective potential.

On the complex tasks we now carry out in laboratories, clean rooms, boardrooms, courtrooms, and classrooms, we need people who think in different ways. And not in arbitrarily diverse ways. Effective diverse teams are built with forethought. Not all teams of rivals will succeed. Not all multitudes possess wisdom. To realize the benefits of diversity, we need logic and theory to identify the types of diversity that improve outcomes and to understand the conditions under which they do so. And then we need practice.

Getting the logic correct takes precedence. Otherwise, we cannot compose the best possible teams, and we limit what we can achieve even with practice. That is the main reason for this book: to help us get the logic right. To get us to embrace the contrary assumption and to make our world better.

In this chapter, I sketch the core logic for how diversity produces bonuses. That logic relies on linking cognitive diversity, which I define as differences in information, knowledge, representations, mental models, and heuristic, to better outcomes on specific tasks such as problem solving, predicting, and innovating. Cognitive diversity differs from identity diversity — differences in race, gender, age, physical capabilities, and sexual orientation. That said, identity diversity, along with education and work and life experience, will be a contributor to those differences. For the moment, we will keep them separate.

DIVERSITY BONUSES ON COMPLEX TASKS

To sketch the core logic, I borrow a stripped-down model that I developed with Jon Bendor. This model reduces cognitive repertoires to collections of tools. Think of these tools as analytic analogues of a carpenter's tools. A carpenter has a chainsaw; a mathematician knows the chain rule. A carpenter attaches boards with a nail gun; a plant biologist inserts DNA with a gene gun.

I use that model to show the logic of how diversity bonuses arise. I then connect assumptions about the diversity of tools that people possess to the complexity of the challenge or opportunity at hand. That second step includes two purposefully incomprehensible graphs.

In the tool-based model, I assign a unique letter to each tool. Figure 1.1 shows three people and their cognitive tools. Define ability of a person to equal the number of tools she knows. Ann possesses five tools, so she has an ability of five. Barry, in the center, has ability four, and Cam has ability three. Ann is the best.

Similarly, define the diversity of the team to equal the number of unique tools collectively known. If two team members know the same tool, that counts as a single tool. Next, define the diversity of a team as the percentage of the team's tools known by a single person. Two people with no tool overlap have 100 percent diversity. Two people with the same tools have 0 percent diversity.

This simple model produces two types of diversity bonuses. First, a diversity bonus occurs if someone adds a unique tool. When this happens, we can add someone of less ability to a group and make the group smarter. That's a bonus. In addition, if teams can apply combinations of tools, then adding a person with a new tool produces new combinations, a second bonus.

Working through the example clarifies how bonuses arise. Figure 1.2 shows two possible teams and the union of their cognitive tools. The first team consists of the two highest-ability people, Ann and Barry. Ann has an ability of five. Adding Barry to the team adds one more tool, giving the team an ability of six. That's a bonus of one. The second team consists of Barry and Cam. Barry has an ability of four. The team of Barry and Cam has an ability of seven. Thus, when paired with Barry, Cam produces a diversity bonus of size three. If Cam were paired with Ann, he would only produce a bonus of size one. Thus, the bonus someone produces depends on the team.

As suggested, counting the number of tools understates the potential diversity bonuses if tools can be applied in combination. We will start with the team of Ann and Barry. Ann knows five tools, so she could apply up to ten unique pairs of tools. She and Barry know six tools, creating fifteen unique pairs. By adding Barry, she gets one new tool and five new pairs of tools.

Barry, on the other hand, knows four tools and therefore six unique pairs of tools. When Cam is added to Barry's team, Cam adds three tools, as well as three pairs of tools: {CD, CG, DG}. When combined with Barry's four tools, his three tools create twelve new pairs of tools. Thus, Cam adds fifteen potential pairs of tools. That is what is meant by a diversity bonus.

Note also that Barry and Cam are the best team of size two. That team jointly possesses the most tools and therefore has the most ability. In this example, as in many others that will follow, the best team does not consist of the two highest-ability people.

Complexity and Bonuses

This example would seem to create diversity bonuses without any reliance on complexity; that is, on the task being part of a context that is difficult to predict, explain, or design. That is not true. The assumptions that I made on the tools that the people possess imply multiple relevant knowledge bases and types of approaches to solving the problem. To see why requires a second example and then some assumptions on the structure of tools.

The second example consists of three people with the tool sets shown in figure 1.3. Notice that no diversity bonuses can arise in this example. The best person knows every tool of the second-best person, who in turn knows every tool of the third person. The best team will be any team that includes that best person.

A comparison of the tool sets in figures 1.1 and 1.3 reveals the key insight. The cognitive tools that people possess in the first example are idiosyncratic. The cognitive tool sets in the second example would come about only if people accumulate tools in the same order, that is, if a person had to learn tool A before tool B and tool B before tool C.

As an analogy, think of people riding on a train from Chicago to Los Angeles. At each stop along the way, the conductor tells the history of the station. If one person stays on the train longer than another, that first person learns about more stations than the second. She necessarily knows about every station that the second person knows about.

The cognitive tools shown in figure 1.1 do not satisfy that condition. Here, the person with the fewest tools knows tools the most talented person does not. For this configuration to occur, it must be that tools need not be acquired in a single order. Instead of a train trip, a trip to the zoo would be a more appropriate analogy. One person might spend a full day at the zoo and visit five exhibits (Alligators, Bears, Camels, Ducks, and Elephants). A second person might leave mid-afternoon after taking in only three exhibits (Camels, Ducks, and Gorillas). The second person learns less, but she gains knowledge of gorillas that the first person does not have. The first person does not know everything the second person knows.

Figure 1.4 represents these two possibilities in network form. Assume that a person must first learn a tool on the left edge and then can follow any path. The upper path corresponds to the train ride. Diversity doesn't matter. The best team consists of the best person. Ability rules.

The lower path represents the trip to the zoo. As shown in figure 1.5, the tool sets in the first example can be constructed within this network. Ann can follow a path that leads to A, B, C, D, and E. Barry can learn A, B, E, and F, and Cam can learn tools C, D, and G. The fact that a person can know fewer but different tools means that someone can have less measured ability than the people already in a group but still contribute.

The remaining step in the logic connects the value of diversity to complexity. The intuition will be straightforward: Our accumulation of knowledge, representations, techniques, and models produces elaborate networks of what I am calling tools. This allows people to construct distinct tool sets. That need not be the case for less developed bodies of knowledge, which often create linear orders.

As an example, consider topics in mathematics. Figure 1.6 shows the relationships between the topics covered in elementary school mathematics. The topics build on one another in a linear fashion. You need to be able to count in order to add, to add in order to multiply and divide, to multiply and divide in order to understand fractions, and to understand fractions in order to define the trigonometric functions sine and cosine. These topics can be represented in a linear order.

In contrast, the advanced mathematical topics in figure 1.7 connect in multiple ways. This is the first incomprehensible graph. To approach a network of this complexity, ignore the technical terms and focus on the many boxes and arrows. Notice that there exist multiple paths a student could pursue. Parts of the network can be understood by anyone. For instance, in the middle of the figure, the integers (1, 2, 3, and so on) point to the rational numbers (1/2, 1/3, ...), which in turn point to the real numbers (π = 3.1415 ...). To know the real numbers, a person must first understand integers and fractions. That portion of the network looks like the linear elementary school network.

Making sense of other parts of the network requires deeper technical knowledge. The graph implies that a person could master Lie groups (in the upper left) without knowing Hilbert spaces, distributions, or quantum field theory (in the upper right). The implication is that the tool sets of professional mathematicians would look like those in our first example. And each mathematician would add diversity to the group.

Making breakthroughs in mathematics often involves combining different tools. A report by the National Academy of Sciences describes "an increasing need for research to tap into two or more fields of the mathematical sciences." Tapping into two fields implies a diversity bonus. Something that could not be proved using either field alone can be solved with tools from two fields.

That same report notes the growing connections between mathematics and other fields including defense, entertainment, physics, economics, computer science, linguistics, manufacturing, finance, and biology. These connections reflect a broader trend toward multidisciplinary inquiries. That can be explained by the complexity of modern challenges and opportunities.

Consider the rise of obesity. Some call it an epidemic. Fifty years ago, we might have placed the challenge of reducing obesity within the domain of nutritional sciences. We now understand that it has myriad causes that cross disciplines.

Figure 1.8 characterizes one attempt to explain the obesity epidemic with arrows denoting causal forces from the Foresight Group in the UK. It is meant to be overwhelming. (Yes, this is the second incomprehensible graph.) The disciplinary knowledge embedded in the graph crosses economics, nutrition, physiology, sociology, biology, media studies, advertising, transportation and infrastructure, and genetics.

No one person can understand all of the boxes and arrows in the full diagram, and no one person will find a cure for obesity. At best, the combined wisdom of a multitude of diverse people can march us toward less obesity through a constellation of interventions. The types of diversity necessary to find ways to reduce obesity differ from the types needed to advance mathematical knowledge. Though in each case, the fact that diversity in the background knowledge one acquires through education will be of central importance hardly needs explaining.

Aside: John Milton and TMI & TMK

The explosion of available information and knowledge creates a second reason we need diversity on complex tasks. On a simple task like building a tool shed, a single person might have sufficient knowledge, but that is not true for complex tasks like reducing obesity, calculating a supply chain, managing and investing a portfolio, or advancing the field of mathematics. In those domains, no single person can master all relevant knowledge. There exists too much information (TMI) and too much knowledge (TMK).

TMI and TMK imply the necessity of diversity. When Euclid was writing his axioms, a person could learn all of mathematics. That is not true today. Think back to the diagram of mathematical knowledge. There's too much to know.

The polymath John Milton might well be the pivotal person in the transition from all-knowing experts to a world of intelligent people with diverse repositories of information and knowledge. Born in 1608 in Cheapside in the city of London, England, Milton introduced more than six hundred words into the English language. He traveled the world, discussing ideas with luminaries from Galileo to Isaac Newton.

In 1640, at the peak of Milton's career, the British Library contained fewer than forty thousand books. A voracious reader in a dozen languages, Milton learned a substantial percentage of what was knowable. Reading two books a day, he could have read fifteen thousand books by age thirty and, by age fifty, could have made his way through the bulk of the British Library.

With nearly one and a half million books now published each year, a modern Milton could not make it through a week's production of knowledge. To finish the quarter million books published by traditional book publishers each year would involve reading fifteen books a day for fifty years, leaving little time to digest the more than one and a half million academic papers published annually.

A modern Milton can only know a thin slice of what's knowable. That observation holds true within academic disciplines, professions, and industry. The information and knowledge produced within organic chemistry, oncology, or economic sociology overwhelms the capacity of any one person. Hence, we need teams. And we need teams that include people with diverse information and knowledge.

(Continues…)

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Excerpted from "The Diversity Bonus"
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