What Are the Odds?

How cognitive and identity diversity can improve actuarial practice Scott E. Page

In this article, I describe a novel approach to rethinking the value of diverse teams. I describe how different ways of thinking produce “bonuses” when performing the complex cognitive tasks that actuaries perform. First, though, I want to tell a story about calculating the odds.

In 1994, after having just moved to Los Angeles, I attended a housewarming party in Long Beach. The hosts, first-time homeowners, made a big deal out of the fact that their house number, 7306, matched the final four digits of their new phone number. Everyone agreed that the numerical match portended powerful karma.

Someone asked, “What are the odds the numbers match, they must be one in a billion?” I immediately responded, “A little bit less than one in 10,000.” I then added that if everyone had four-digit house numbers, that about 10,000 other Americans had the same numerical karma.

As you might guess, my comments were not a hit, and the phrase “what are the odds” has become a bit of a family joke: What are the odds that we both wore green shirts? What are the odds of us not running into anyone papa knows in New York City? Or even, what are the odds that none of us is an actuary (at least not yet)?

Breaking Down the Odds

What are the odds? That question lies at the core of the actuarial profession and the assessment of risk. Twenty years ago, while studying decision sciences and game theory in graduate school, I learned of the bright line distinguishing risk—quantifiable, calculable or measurable probabilities—and Knightian uncertainty—unquantifiable future likelihoods. That clean dichotomy made sense to me. I could calculate the probability of six random tosses of a coin resulting in exactly five heads. But I could not, nor could anyone else, calculate the probability of an economically feasible fusion nuclear reactor by 2065. Too much is unknown to make a calculation.

In the intervening years, I became a scholar of complexity, and I have come to see Frank Knight’s century-old distinction as less compelling. Now, I think of the knowability or measurability of risk as arranged on a continuum, where the complexity of the domain or phenomenon determines—or at least correlates with—the degree of measurability.

I am not alone in that thinking. The complexity of risk assessment has necessitated a change in how actuaries practice. In the distant past, a risk assessment might have been expressed as a weighted linear combination of independent variables. The assumption of independence, though a stretch in some cases, was not seen as overly problematic.

The current models actuaries construct to measure the “odds” for morbidity, mortality, retirement, accidents and so on have become far more sophisticated. They include nonlinear and interaction terms. They consider correlation, kurtosis (more likely than normal extreme events) and heteroskedasticity (variation that changes as a function of a variable’s value). These newer models must accommodate non-normal, long-tailed distributions. Otherwise, the estimated reserves the models advocate would be insufficient to withstand increasingly common large events.

The Importance of Diverse Teams

The growing complexity of the world, along with increased access to data, has had consequences for actuaries. First, machine learning software packages may contain more than 100 algorithms that actuaries can tap into. When calculating odds, model diversity reduces error. Hence, to be at the cutting edge, you must be able to speak of model ensembles and random forests, and not just the analysis of variation.

Second, the variables the models include and the dimensions you manage span traditional and nontraditional disciplines. A risk assessment might require predicting the likelihood of flood, hurricane, political overthrow or a disruptive technology. Though obtaining an actuarial credential demonstrates a facility with mathematics, economics and statistics, it offers no guarantee of expertise in climatology, international politics, social movements or technological upheavals. Yet, the tasks that actuaries address require knowledge of those domains.

This is not meant as a critique of actuarial credentialing. Disciplines, by definition, narrow. Getting an M.S. in data science does not make you an expert in human behavior. Earning a Ph.D. in climatology does not guarantee a facility with hazard rate analysis.

My point is that the complexity of the tasks requires a diversity of minds, trained in diverse ways. That is why actuaries often find themselves working in diverse teams that include data scientists and climatologists. Actuaries may even consult political analysts to assess regime stability.

These two trends—the increased use of multiple models and the reliance on diverse teams as opposed to individuals—are not random occurrences. Both have logical underpinnings. Progress on high-dimensional complex tasks—creating, problem-solving, designing and predicting—depends on cognitive diversity. Different ways of representing problems, different heuristics and different models have fewer common blind spots. They also produce what I call diversity bonuses, in which the sum can be more than the parts only if the parts differ.

Abundant empirical evidence supports the existence of these bonuses on complex tasks. For example, half a century ago, most academic papers had one or two authors. Now, the model paper has six to 11 authors. Thirty years ago, individuals ran three-fourths of mutual funds. Now, three-fourths are run by teams. Why? Because in each case, teams win. Team-authored papers are four-and-a-half times more likely to earn 100 citations (a common benchmark). Team-run mutual funds outperform single manager funds by 60 basis points. Diverse teams outperform individuals just about everywhere you look—songwriting, patent development and economic forecasting.

Deeper empirical dives to search for the causes of team success, by Brian Uzzi, Melissa Schilling, Richard Freeman and others, show that the success of teams lies not in their size but in team members’ individual abilities and collective cognitive diversity—the differences in how they categorize, model and solve problems. 

Finding Relevant Cognitive Diversity

Abilities can be measured. For example, the requirements to obtain an actuarial credential establish a meritocratic competence threshold. If you are selecting from among people who pass that threshold, you want them to be different—to have different undergraduate majors and training. You want cognitive diversity.

But, how does one find relevant cognitive diversity? We must look to the relevant sources. Cognitive diversity comes in part from our education and training, and in part from our life experiences. And, because who we are affects the nature of our experiences and how we filter and categorize life’s events, our identities also matter. Thus, identity diversity correlates with cognitive diversity. Who we are influences how we think. The profession therefore wants to broaden the population from which it draws candidates.

How much identity diversity matters depends on the task—it likely matters more for developing health care plans, interpreting laws, investing money and writing songs than it does for sequencing genes and isolating molecules. And yet, an analysis of more than 14 million academic research papers finds significant positive correlation between ethnic diversity and both citations and impact, so we should be cautious not to constrain our ideas about how who we are influencing how we think.

The logical syllogism bears repeating. First, cognitive diversity improves performance on complex tasks. Complexity here is the key. We do not need diversity on easy tasks. Actuaries do not spend much time on easy tasks, which is why diversity is so central to the field. Second, identity diversity contributes to cognitive diversity. Identity does not contribute directly, but through differences in how we think. Thus, organizations hoping to create the most successful teams should hire people with diverse training, experiences and identities.

The Way to Increased Diversity Bonuses

Though the connection between diversity and inclusion policies and innovation requires just two logical steps, many people find it surprising. They associate innovation with continuous learning and outside-the-box thinking, and diversity and inclusion training with reducing discrimination and avoiding lawsuits.

Yet, the logic should be clear, as should the paths of inquiry. The question will be not whether cognitive diversity can produce bonuses, but how large those bonuses might be. The question will not be whether identity diversity correlates with cognitive diversity, but how to identify how and when identity diversity produces task-relevant cognitive diversity. Diversifying the pool of the actuarial profession will not only align with the normative ideal of a more integrated society, it should improve the profession and make teams of actuaries better at what they do.

The on-boarding of a more diverse population will not produce bonuses by magic. Even with the right team composition, organizational culture and routines will determine the benefit of diversity. If people sense that others validate their opinions and ideas, they will bring their whole selves to the table. If people feel disrespected, they will close up and share fewer ideas.

The one-minute elevator speech for actuaries might go like this:

  • Logic and evidence show that complex tasks require diverse models and diverse thinkers.
  • Diverse thinkers do not all look “just like you,” no matter how accomplished you might be.
  • Choose diversity wisely and create work environments where diverse people can flourish.
Scott E. Page is Leonid Hurwicz Collegiate Professor of Complex Systems, Political Science, and Economics at the University of Michigan and an external faculty member of the Santa Fe Institute. He is the author of The Diversity Bonus. His new book, The Model Thinker, will published in November 2018.

Copyright © 2018 by the Society of Actuaries, Schaumburg, Illinois.