Assessing Racial Bias and Homophily in Professional Hierarchies

By Lina Sorg

Professional hierarchies—such as business, academia, and medicine—routinely experience disproportionately low levels of demographic diversity at higher ranks. Members of the general population enter hierarchies in nearly every field through entry-level positions, then ascend the ranks with the goal of reaching the uppermost level. “As we go up the hierarchy, we see increasing power in terms of decision-making and things like hiring processes,” Laurie Balstad of St. Olaf College said. “We also tend to see things like decreasing diversity in terms of race and gender.” During a minisymposium presentation at the 2021 SIAM Conference on Applications of Dynamical Systems, which is taking place virtually this week, Balstad utilized a mechanistic model to examine racial diversity within professional hierarchy structures.

Balstad first introduced a mechanistic model by Sara Clifton that uses bias and homophily—individuals’ self-sorting tendency to associate with those who are similar to them—to explore how various levels of hierarchies gain or lose diversity. This model suggested that different fields vary widely in terms of gender bias and homophily, thus identifying a need for field-specific interventions to increase diversity within the hierarchies. Balstad aimed to adapt Clifton’s mechanistic model to accommodate multiple racial groups.

To do so, she considered the two mechanisms at play. Homophily manifests itself when people who are applying for promotions look to upper levels of the hierarchies and ask themselves if they belong there. In contrast, bias is more of a top-down mechanism wherein individuals at the top of the hierarchy selectively choose promotional candidates from a group. The presence of these two mechanisms in the promotion process can create skewed demographics, and Balstad presented a toy example to demonstrate this point (see Figure 1). She considered a cohort that is eligible for promotion; 25 percent of the people are part of group one, 25 percent come from group two, and 50 percent fall within group three. Due to homophily, only some of these employees will apply for a promotion. In Balstad’s model, members of group 3 are much more likely to apply than those in groups one or two. The presence of bias further complicates the situation, as individuals in group one and three are more likely to be promoted than group two. “By the time that we actually see the group that’s promoted, we’ve heavily skewed in favor of group three,” Balstad said. “Group two is quite underrepresented compared to the past level of the hierarchy.” 

Balstad then implemented these findings in the actual professional hierarchy, which includes many different levels. She began with the general population and included changing demographics that match U.S. demographics and predictions. Once employees enter their fields, they either choose to exit the system or undergo promotional processes multiple times until they reach the top. All groups leave any given level of the hierarchy at the same rate. Balstad applied a continuous time ordinary differential equation model to understand this process.

Next, she shared the results of the null model to confirm its functionality. In a bias- and homophily-free system, bias equals 1 over the number of racial groups in question and homophily equals 0. When these mechanisms are in place, the model trends toward matching the general demographic at each level of the hierarchy — regardless of the initial conditions. However, increasing levels of bias and homophily yields some nonintuitive and unpredictable results of diversity (or lack thereof) within the hierarchy. This understanding is important because different fields experience different types of bias and homophily, and field-specific interventions will likely be necessary to achieve gender parity. 

Balstad presented three cases studies that utilized racial data. First, she employed data from the Department of Defense to examine the breakdown of minority groups and White individuals in the military. In this scenario, the bias is relatively close to 1/2 (the level of a bias-free system) and the homophily is near 0. As such, the long-term behavior trends towards the general population demographic. “This makes quite a bit of sense when we think about how promotions in the military work, especially for enlisted individuals,” Balstad said. “They tend to be more time-based than applicant-based.”

Balstad also looked closely at academic medicine and divided race into the following three groups: Black Americans, Hispanic Americans, and “other.” In this case, a bias-free system would have a bias of 1/3. However, Balstad observed a high level of homophily and a high level of bias against Black and Hispanic Americans in this scenario (see Figure 2). “In this system, we don’t see any sort of achievement of parity in the long term,” she said. “We see kind of a flattening out of representation in these two groups across the hierarchy. We also see decreasing representation at increasing levels of the hierarchy.”

The third case study pertained to academic physics and relied upon data from the National Science Foundation that categorized individuals as Asian, underrepresented minorities, or White. As with the previous example, a bias-free system would have a bias of 1/3 and a homophily-free system would have a homophily level of 0. Yet in addition to a high homophily, this data displays a bias towards Asian Americans and against underrepresented minorities in the hiring process. The combination of parameters yields non-intuitive random happenings in terms of representation across the different academic tiers.

In addition to these three scenarios, Balstad analyzed several other different fields. To compare them, she took the standard deviation of the bias and plotted it against the homophily. The resulting chart revealed a wide range of bias and homophily across numerous fields (see Figure 3). “This suggests that we want to have targeted interventions to help address these issues,” Balstad said. In the case of strong bias, for instance, employers could think about changing the hiring process and encouraging hiring managers to choose applicants in a way that reflects the ratios of their hiring pool. If the homophily level is high, one might adjust recruitment processes and encourage applications from underrepresented populations.

Balstad concluded her presentation with a quick discussion of her model’s limitations. She uses a strict hierarchy, which assumes that everyone experiences each hierarchal stage. This is not always true in academia, for example, since not every graduate completes a postdoc. Her work also assumes that all members of the general population are equally qualified to enter the hierarchy, neglecting to account for educational disparities at the high school level. Furthermore, a general absence of data on racial groups—or data that is lumped together in awkward ways—makes it difficult for Balstad to fit her model to existing data sets.

In the future, Balstad plans to examine additional nonacademic hierarchies and consider nonuniform group behavior (different retirement rates at each level, varying homophily tendencies, etc.). She would also like to explore the mentorship model, wherein people look at the uppermost level of a hierarchy—i.e., when students look to their professors—to determine whether they feel they belong. 

Lina Sorg is the managing editor of SIAM News.