CHAPTER TWO

COGNITIVE REPERTOIRES

People throw around the word “diversity” like it’s a tip at a restaurant. But really, having people who have different mental perspectives is what’s important. If you want to explore things you haven’t explored, having people who look just like you and think just like you is not the best way.

—ASTRO TELLER

The first step in unpacking the logic that explains diversity bonuses involves making formal definitions. Specifically, I need to define what I mean by diversity before I can derive logical claims that sketch out the boundaries for when diversity produces bonuses and when it does not. The focus of this chapter, therefore, will be to define what I call cognitive repertoires. Repertoires consist of five components: information, knowledge, heuristics or tools, representations, and mental models and frameworks. In the next chapter, I link these repertoires to better outcomes.

My use of repertoires is not traditional. I rely on repertoires and not dimensional evaluations like IQ scores because IQ scores lack sufficient granularity to reveal how diversity bonuses arise. This limitation becomes apparent when trying to determine the ability of a team. Suppose that one person has an IQ of 120 and another has an IQ of 110. Any composite IQ for the team of both people will be idiosyncratic. The team’s IQ will not equal the sum of their individual IQs. It will not be 230. Nor will the team’s IQ equal the maximum of their IQs. That would make the pair only as smart as the smarter member—an equally implausible assumption. We could rely on some ad hoc rule—the average of the maximum ability and the sum of the abilities, or the square root of the sum of the IQs. If we did so, we would bake in whatever results we derived.

Put in mathematical terms, we lack an algebra of IQs. The algebra problem remains even if we decompose intelligence into multiple dimensions, such as Howard Gardner’s nine dimensions: linguistic, mathematical, musical, spatial, interpersonal, existential, intrapersonal, naturalist, and bodily.¹ While nine dimensions can embed more information than one, they do not overcome the algebra problem. If anything, they exacerbate it. We now need a method for adding vectors of abilities. Instead of one ad hoc rule, we need nine.

In contrast, using repertoires makes aggregation straightforward. The repertoire of a group of people equals the union of their individual repertoires. If one person knows double-entry accounting and a second knows linear regression, the group knows both. In this way, a group resembles a person with a large repertoire. High-ability teams, like high-ability people, will have large collective repertoires. One way for a team to have a large repertoire is if the members of that team possess different repertoires. That straightforward logic underpins many of the results that follow.

The use of repertoires also allows for intuitive measures of both diversity and ability. A team’s diversity can be measured by the lack of overlap in members’ repertoires. A person’s ability on a task can be measured by how well a person’s repertoire performs on that task, not on a general intelligence test. Given these measures, increasing the diversity of a team or the ability of a member will add tools to the team’s repertoire and improve the team.

This formulation also allows for a person to be intelligent on some problems and less so on others. Someone with a PhD in mathematics may have a large repertoire, but it may not be well suited for formulating a health care policy, developing a marketing plan, or designing a fall fashion line.

I constructed my characterization of repertoires as consisting of information, knowledge, heuristics or tools, representations, and mental models and frameworks with an eye toward elaborating the conditions in which diversity does and does not produce bonuses. In this chapter, I develop the components of that categorization at length. Before I dig into the details, I should note that this is not the only possible categorization of cognitive diversity. One alternative categorization of diversity distinguishes between acquired and inherent diversity.² Acquired diversity consists of experiences, along with learned behaviors and traits. We choose some acquired differences. Others we obtain by chance. Inherent diversity consists of immutable attributes: race, age, physical qualities, gender, ethnicity, and sexual orientation.

Another framework distinguishes between social category diversity, informational diversity, and value diversity.³ Social category or identity diversity refers to differences in age, race, gender, ethnicity, physical qualities, sexual orientation, and religion. This differs from inherent diversity in that some types of social diversity, notably religion, can be acquired. Informational diversity refers to differences in knowledge and perspectives—two of the components of my repertoires. Value diversity corresponds to differences in principles and standards.

Other scholars add personality and behavioral diversity. Both of these have been shown to affect team performance. Teams with a mix of introverts and extroverts may reach better solutions to problems than teams of all introverts or all extroverts.⁴ Behavioral diversity also matters for team success. Differences in norms and expectations can be detrimental to team performance.

When compared to these other categorizations, my cognitive repertoire approach stands out as the one most naturally suited to analyzing diversity bonuses. Modeling how a person applies knowledge to a problem, a model to a predictive task, or information to an evaluation will be straightforward. It is less clear how someone could apply her identity, her integrity, or her goals to a prediction or to a problem-solving task. However, as I discuss, a person’s identity can shape her repertoire, and, thus, have an effect.

The cognitive repertoire framework is not without shortcomings. It fails to capture the full range of human cognitive differences, as people differ in their short- and long-term memory, in their visual and auditory abilities, and in their reaction speeds. It also muddles distinctions between fluid and crystallized intelligence and between slow and fast thinking.⁵

Figure 2.1  The Double Unpacking and the Logical Links

Some foreshadowing will be helpful in interpreting the influence of various parts of cognitive repertoires. In the next chapter, I link those parts to diversity bonuses on six types of tasks: innovating, problem solving, predicting, evaluating, verifying, and strategizing. What constitutes a better outcome, and a bonus, depends on the task. Better predictions are more accurate. Better solutions to problems have higher values.

That process of mapping repertoires to outcomes requires a double unpacking of the type shown in figure 2.1. The drawing is meant to be illustrative only. Each line represents a connection between a component of a repertoire and a task. As drawn, not every component applies to each task. Diverse heuristics apply to problem solving and not to verifying truth. Diverse representations improve performance on creative tasks, prediction, and problem solving. In practice, which parts of a person’s repertoire matter for a given type of task may vary.

I make no claim that this is a complete characterization of how cognitive diversity can produce bonuses. The connections implied by the omitted lines may also exist and be of greater significance and magnitude than those drawn. The figure drives home the point that to identify the conditions necessary for diversity bonuses to exist, one must first define repertoires, then define tasks, and then connect repertoires to tasks.

INFORMATION

The first component of cognitive repertoires is information. Information consists of facts about the world and can be represented as pieces or objects. The fact that the city of Dayton, Ohio, occupies fifty-six square miles is a piece of information, as is the fact that Susan B. Anthony was arrested in 1872 for voting in Rochester, New York.

Using tools from information theory, we can assign an information content to any raw data, be it a collection of pixels on a computer screen or numbers on a spreadsheet. Those data need have no meaning to a human observer. When those pixels combine to form the letter C, they take on meaning and become what I call information. The same goes for numbers on a business spreadsheet. They become information when we know that they describe sales figures and inventories.

Information: Interpretable, meaningful data.

Throughout our lives, we accumulate information. We learn it in school, acquire it at work, and absorb it at the knees of our parents and grandparents. No two people possess the same information. Our educations, experiences, and identities all influence the information we possess, as do our interests, motivations, and capacities. People who study anthropology know different information from people who study English literature. Accountants know different information from event planners. Given that people who belong to different identity groups read different books, watch different movies, and confront a different set of challenges and opportunities, then identity diversity will also correlate with information diversity.

With the Internet, we can pull up incomprehensible amounts of information in an instant. If we do not know the primary causes of ulcers, we can go to the World Wide Web, and it provides the answer: the bacterium Helicobacter pylori and overuse of anti-inflammatories. We might then think that technology renders informational diversity of little value. That is not true. Even though we have a world of information at our fingertips, having relevant information front of mind remains of value. A chemist would never mix ammonia and bleach to create a cleaning solution. A college student majoring in philosophy might. He would then have to contend with a noxious array of toxic chemicals and gasses.

KNOWLEDGE

Knowledge of a subject or domain of inquiry consists of a working or practical understanding. A person who knows German can speak, write, and understand the German language. A person with knowledge of biology can define the terms in the glossary of an introductory textbook and explain the main concepts. A person who knows accounting can read a balance sheet and perform double-entry accounting.

Knowledge: Theoretical, empirical, or practical understanding of patterns, literatures, or domains of inquiry.

Knowledge differs from information. Information consists of facts that can be represented in bits and pieces and can be thought of like the items in a junk drawer. It includes the capital of Oregon (Salem), the name of the tallest person who ever lived (Robert Pershing Wadlow), and the middle name of Venus Williams (Ebony Starr). It also includes the preamble to the United States Constitution: We the people, in order to form …

Knowledge structures information. Recall the diagram of mathematical knowledge from the previous chapter and how different bodies of knowledge depended on other bodies of knowledge. Knowledge also assumes coherence. Knowledge of the Constitution consists of more than memorizing the preamble and the twenty-seven amendments. Knowledge requires an understanding of how the Constitution defines the branches of government, delineates and separates their powers, and describes amendment procedures.

HEURISTICS OR TOOLS

Heuristics are methods or techniques for generating new ideas. That new idea could be a solution to a problem, a strategy, or a psychological experiment to test a theory. This definition encompasses formal heuristics such as mathematical techniques and rules of thumb for making it through the day. It includes scientific techniques such as the ability to isolate chemical compounds. It includes opening moves in a chess match.

Heuristics: Methods for finding solutions or generating new ideas.

Heuristics include rules learned in math class like Newton’s method to find roots and Euler’s method to solve differential equations. They include the trick to solve an easier related problem. Heuristics also include the rule of thumb to save ten times your annual income for retirement and tricks for solving Sudoku puzzles. A glimpse of the vast array of informal heuristics can be seen by typing “rules of thumb for ____” into a search engine.

Home Decorating: Your rug should be no closer than eighteen inches to the wall.

Negotiating: Ask for more than you need initially.

Grilling Steaks: Rule of threes: three minutes direct heat on each side, followed by three minutes indirect heat on each side.

Meeting People: Never make a joke about someone’s name at a first meeting.

We learn heuristics from textbooks (Newton’s method), from novels (E. M. Forster’s “only connect”), and through interactions with friends, family, and coworkers (measure twice, cut once). Any one person’s collection of heuristics will be an idiosyncratic mixture of purposefully acquired techniques—a computer scientist, architect, or tax accountant will learn hundreds of domain-specific heuristics—and a smattering of tricks encountered and absorbed by chance. That small collection will come from a vast set.

Three features of heuristics make them a likely source of diversity bonuses. First, any given heuristic fails on a large set of problems. All human problem-solving heuristics have blind spots and biases. Even a sophisticated mathematical heuristic can be misled by a deceptive problem. A second heuristic, even a less effective one, may be misled on a different set of problems. If so, it produces a diversity bonus—not by being better but by being different.

Second, in well-developed fields, we need not learn heuristics in a specific order. This creates diversity bonuses. For example, heuristics for the traveling salesperson problem, a canonical optimization problem, try to improve on a route connecting a collection of cities by reducing total travel time. These heuristics fall into categories, like the exhibits at a zoo. One class of heuristics chooses a city at random and adds cities. In a second class, the heuristics improve on a randomly chosen initial route by switching pairs of cities or inserting others. In a third class, the heuristics create and winnow a population of possible routes. A person could learn the heuristics within these classes in any order.

Third, heuristics can traverse domains. Physician and author Atul Gawande describes how hospitals adopted a checklist heuristic used by airline pilots to reduce medical errors.⁶ The transferability of heuristics, particularly rules of thumb, can also produce bonuses. Those might be called cross-disciplinary bonuses.

REPRESENTATIONS: PERSPECTIVES AND CATEGORIZATIONS

Representations, or perspectives, are the most often mentioned and vaguely defined component of cognitive repertoires. Many businesses, universities, nonprofit organizations, and government agencies sing the praises of diverse perspectives on their web pages, in their recruiting documents, and in their mission statements. They use perspective to mean “a way of thinking or representing.” This use of perspective differs from both dictionary definitions, in which perspective means “a point of view,” and formal definitions in art, in which the term perspective refers to the representation of three-dimensional objects in two dimensions.

Here, I distinguish between two types of representations: perspectives and categorizations. Perspectives assign a unique name to each object. Categorizations do not. They group the possibilities into disjoint sets. Identifying each element by an atomic number creates a perspective. Partitioning the elements based on their state at room temperature—gas, liquid, or solid—creates a categorization.

Perspective: A representation that assigns a unique identifier to each member of a set of possibilities or alternatives.

Mathematicians and engineers represent points in physical space using numerical perspectives. In two dimensions, the Cartesian coordinate system represents points by their horizontal and vertical displacements from the origin. A second perspective, the polar coordinate system, represents those same points by a radius (a distance from the origin) and an angle. Figure 2.2 shows a point on a plane represented within the Cartesian perspective as x = 3 and y = 4 and in the polar perspective as an angle of 53.1 degrees and a radius of 5.

The choice between these two geometric perspectives influences the points that we think of as near an existing point. Imagine that figure 2.3 represents the possible location of a windmill on a large field. Two engineers might be seeking a location that maximizes the power the windmill generates.

Figure 2.2  Cartesian and Polar Representations of the Same Point

Figure 2.3  How Perspectives Influence the Adjacent Possible

If one engineer searches for locations using the Cartesian perspective, she will vary the horizontal and vertical positions of the windmill. The neighboring locations consist of a square. Complexity scholar Stuart Kauffman refers to these points as the adjacent possible.⁷ If the other engineer applies a polar perspective, the points in the adjacent possible lie within a given angle and radius. The polar perspective creates a wedge on the field.

The two perspectives create distinct adjacent possibles. Engineers who use polar coordinates will think of different solutions from engineers who use Cartesian coordinates. These different sets of possible answers create a potential diversity bonus.

Perspectives need not be geometric. Each of the following creates a perspective on the one hundred largest cities in the United States: rank by population size, rank by area in square miles, longitude and latitude of city center, alphabetical order, and order by date of founding. Each arranges the cities differently and creates a different adjacent possible. If I say “Detroit,” a person using an alphabetical perspective might think of Des Moines. A person thinking of population size might think of Seattle. As with the earlier example of Cartesian and polar coordinates, here diverse perspectives create distinct adjacent possibles that can result in diversity bonuses.

Perspectives uniquely identify alternatives. Often, we choose to be less precise and lump possibilities into categories. We say, “I saw Tonya at a coffee shop. She just bought a new pickup that is the same color of red as her sunglasses.” The lumpy categories—car, red, and coffee shop—suffice. We need not add more detail to communicate the main ideas.

Categorization: A partition of the possibilities or alternatives into disjoint sets.

Categories enable us to navigate, predict, and understand our world. We use categorizations to make statements and inferences. Rada writes poetry. Maia excels at wrestling. Cooking in a broiler leads to undercooked centers.

To make precise inferences requires fine categorizations. This is why experts use more categories than nonexperts. A master gardener might classify daffodils according to their growing zone, color, and time of bloom.⁸ A weekend gardener wandering in the nursery might classify all the varietals, including the delicate Canaliculatus, into a single category called “daffodils.” A teenager might place them all in an even lumpier category called “flowers” or “plants.”

Crude categorizations by novices offer fewer prospects of diversity bonuses. For a categorization to produce a diversity bonus, one of the categories must refine or only partly intersect with existing categories. The new category must organize the world differently.

Distinct categorizations also create different adjacent possibles. Figure 2.4 shows a categorization of ten cities by an American undergraduate. She places the four foreign cities in one pile, the three cities on the East Coast in a second pile, and the three western cities in a third pile.

Figure 2.5 shows a possible categorization of the cities by a European. She classifies New York, London, and Paris as cosmopolitan cities; Los Angeles, Sydney, and Barcelona as beach cities; and the other four cities as regional, American cities.

Figure 2.4  An American Categorization: East Coast, Western, and Foreign Cities

Figure 2.5  A European Categorization: Cosmopolitan, Beach, and US Regional Cities

If a conference organizer had planned a meeting in New York but a lack of hotel space forces her to consider other locations, the American student might recommend Philadelphia or Boston. These are her adjacent possibles. An adviser with the European categorization might suggest London or Paris instead. The distinct categorizations create different adjacent possibles and, perhaps, a diversity bonus.

MENTAL MODELS AND FRAMEWORKS

Models are simplifications that identify key features. Models take many forms. Some models consist of a set of assumptions. Given those assumptions, the modeler then derives results. Other models are built to resemble the real world. Still other models fit data to functional forms. All models simplify. They leave out variables, lump distinct objects into different categories, and omit causal relationships.

Models also differ in their complexity. Laypeople apply intuitive mental models to make predictions and draw inferences. Economists construct sophisticated mathematical models that often rely on only a small number of variables. Climate scientists build elaborate models with thousands of variables that they calibrate to data.

Models have become ubiquitous. Organizational consultants, intelligence analysts, domestic policy advisers, and academics all use formal models to predict, design, explain, act, and explore. They also use models to get the logic right.⁹ The rise of models is not a mystery. Model thinking outperforms thinking without models. In head-to-head predictive contests, models outperform human experts.¹⁰

As we will be applying models to tasks, I define them in relation to some domain, such as investing in stocks, writing a health care plan, or investing in infrastructure.

Model: A systematic, simplified description that shares or captures relevant features of a domain.

We often rely on folk models that describe relationships between categories: red sky at night, sailors’ delight; defense wins championships; and so on. These models vary in their accuracy. When asked to make a prediction, we construct models. These models create a causal or correlative framework that connects what we know to what we expect to happen (see box).

The most accurate mental models satisfy the laws of probability and are logically consistent. They do not ignore disconfirming facts, and they respond to new information.¹¹

Models, along with categorizations, play a central role in prediction. Models relate information about the current situation to potential outcomes. People who are better at making predictions and forecasts employ many models.¹² Imagine an ensemble of models in a person’s head, each one competing for attention. Good predictors search among them and combine insights from the best models. The person comes to resemble a diverse team.

To be accurate, models need information. Formal models embed information within equations. Models that forecast the weather include barometric pressure, wind speed, temperature, and humidity and then map these into distributions over outcomes.

Mental models and frameworks tend not to be as sophisticated and rely on categorical information. The aforementioned phrase, “Red sky at night, sailors’ delight. Red sky at morning, sailors take warning,” categorizes morning and evening skies as red or not red and makes predictions. That model, though not as accurate as modern meteorological models, rests on scientific foundations. High barometric pressure holds particulates lower in the atmosphere. These particulates scatter the longer red light waves, producing red skies. A red sky at night, that is, to the west, correlates with high pressure and good weather coming the sailors’ way.

While model diversity can result from different categorizations, it can also arise from different causal structures applied to the same categories. Think of the categories as the nouns and causal structures as the verbs. One person’s model might be that the richest one-fifth vote Republican because they want lower taxes. Another person’s model might be that wealthy people vote Democratic because their financial security allows them to be empathetic to others. Though the two models use the same category (the richest one-fifth), they make different predictions.

These two mental models could be brought to data. The data would corroborate that the richest one-fifth have more often voted Republican in the past. If so, the empirical evidence would not be definitive. The data could be biased, or the future could differ from the past. Those caveats aside, data adjudicate between mental models. Useful mental models align with facts.

Different models can align with distinct facts. A realist model of international relations sees nation-states as self-interested actors and assumes that power dictates relations between states; a liberal model assumes larger, transnational interests. Realism assumes states in conflict; liberalism assumes coalitions with common purposes. These two models both compete and complement. Individually they might advocate different actions. Collectively, they lead to deeper understandings.

Neither model is right or wrong. One can find evidence for both models. Realists point to the failure of the League of Nations. Liberals respond with data on the rarity of wars between democracies.

THE GROUP AS THE UNION OF REPERTOIRES

In the best-case scenario, a group will have access to every component of its members’ repertoires. If so, the group could apply any heuristic, mental model, or categorization known by a member. It could access any piece of information or knowledge of a phenomenon. It could act as a single individual with an enormous repertoire.

The challenges of coordination and cooperation mean that a group is not the same as a person with a large repertoire. Furthermore, an individual’s repertoire may exhibit a coherence, a gestalt that a group’s lacks. A person gathers information and knowledge that plugs into her mental models. A person develops representations and heuristics in tandem. Pieces fit together.

When we combine the repertoires of two people, no gestalt need emerge. One person may possess deep knowledge of international human rights treaties. A second person may know advanced techniques for translating text into categories. When they combine repertoires, they may find that the first person’s categorization of treaties cannot be applied to the existing categories. The whole, in this case, may be less than the union of the parts. Had the person who categorized the treaties known how to apply translation techniques, she would have developed a tractable categorization.

Though a group may not apply its full repertoire ideally or may lack coherence in its repertoire, the fact remains that groups possess larger repertoires than the people who compose them. That largeness enables groups to produce diversity bonuses. The logic underpinning those bonuses is the focus of the next chapter.