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# Modeling Bias and Self-Segregation in Promotion

Although such incidents occur less frequently as time progresses, many women in science, technology, engineering, and mathematics (STEM) can recall at least a few uncomfortable realizations that they are the only females in the room. Whether conscious or unconscious, these awkward moments have pushed women away from traditionally male-dominated fields.

Women who choose to pursue careers in STEM despite these feelings of not belonging often face discrimination. Studies consistently show that equally-qualified candidates are less likely to be promoted (or are offered lower salaries) if they are female. This is a societal issue, as both men and women display equal bias against females in male-dominated fields. With this research widely available, it makes sense that young women may not wish to pursue careers where they do not feel especially welcome.

Women who pursue careers in science, technology, engineering, and mathematics often face discrimination. Stock photo, Creative Commons.
Hiring committees, with the best of intentions to encourage diversity, lament that they cannot hire women who do not apply. To fight this vicious cycle, those with the power to influence hiring decisions would benefit from knowing where to aim their good intentions. Should they target their efforts towards training hiring committees to avoid gender-based discrimination? Or should they encourage more women to apply for positions in male-dominated fields? If they had to choose one, which would give the greater effect?

In a recently-published paper in Chaos, we set out to answer this question using a minimal model for promotion within hierarchically-structured fields (e.g., undergraduate students $$\rightarrow$$ graduate students $$\rightarrow$$ postdocs $$\rightarrow$$ tenure-track faculty $$\rightarrow$$ tenured faculty $$\rightarrow$$ full professor). Many fields—from medicine and law to academia and business—exhibit a clear promotional pipeline. We designed a compartmental decision-based model of promotion between different levels in a professional hierarchy to understand the so-called leaky pipeline effect present in many hierarchical professions.

We assume that all candidates in the model are equally qualified, meaning that any discerning differences are based on gender alone. In our model, the hiring process is broken into two stages: a person must first decide to apply for a promotion the level above his/her current position, and then those in that level must decide to hire this person. When gender is the only salient factor in a person’s decision to apply, we call that homophily — the tendency to seek out people like oneself. We assume that candidates are increasingly likely to pursue a promotion based on the number of same-gendered people they see in the next level. Bias—the tendency to elevate one candidate over another based on characteristics that are inessential to the position—occurs when gender is the only salient factor in a hiring committee’s decision.

While researchers previously explored the construction of a compartmental model for advancement within an academic hierarchy, the model stopped short of predicting the time required to reach parity in each field. A more recent model assumes that gender parity is inevitable, and uses this assumption to estimate the time to parity in a variety of academic fields.

Adding to these foundational studies, our model examines a wider variety of professions, including nursing, law, and journalism. It also extracts the relative impact of the two major stakeholders—the applicants and employers—on the progression of women through hierarchies. The resulting model is an $$L$$-dimensional system of ordinary differential equations representing the fraction of women in each $$L$$ level in a professional hierarchy.

The model exhibits surprisingly rich dynamics, even when there are $$L=3$$ levels. Focusing on the gender fraction at each level, we observe that the hierarchy tends toward gender parity for low homophily and low bias. On the other hand, the hierarchy strays from sustained gender parity for strong homophily and strong bias. Bias and homophily have distinct qualitative effects on the system in most circumstances, making it possible to distinguish each phenomenon’s degree in our data sets.

We gathered data on the gender fractions within 16 professional hierarchies, from male-dominated engineering to female-dominated nursing. We fit our model to each dataset (see Figure 1), then estimated the bias and homophily in each field based on this fit. The degrees of bias and homophily both vary significantly (see Figure 2).

Figure 1. Data (circles) and model fit (curves) for clinical academic medicine (left) and academic psychology (right).

Unlike with previous models, we found that gender parity may not be inevitable in all fields, especially in the highest levels of leadership. While some fields—like medicine and law—appear to be heading towards parity as quickly as turnover permits, other fields—like computer science and mathematics—may never reach parity at the highest levels of leadership without intervention.

Figure 2. Bias and homophily best-fit parameters for each hierarchy data set. Bias below 0.5 indicates that men are preferred, and bias above 0.5 indicates that women are preferred. Colors are the predicted long-term (equilibrium) female fractionation in the highest level of leadership.

Because our model disambiguates the relative impact of applicants and employers on the so-called leaky pipeline effect, we hope these insights will inform those in positions of power to target interventions in the most productive directions.

While this simple model’s predictions are not intended for direct implementation, the results suggest that gender parity might not be inevitable in all fields and may require deliberate intervention. As a society, we cannot be complacent if gender equity in the workplace is a desired outcome.

Kaitlin Hill is a MathCEP postdoctoral researcher in mathematics at the University of Minnesota, Twin Cities. Sara M. Clifton is a J.L. Doob postdoctoral researcher in mathematics at the University of Illinois, Urbana-Champaign.