Abstract · Web view2020. 6. 12. · An Agent-Based Simulation of How Promotion Biases Impact Corporate Gender Diversity. Chibin ZhangAleria PBC. Paolo GaudianoCity College of New

1AGENT-BASED SIMULATION OF CORPORATE GENDER BIAS

An Agent-Based Simulation of How Promotion Biases

Impact Corporate Gender Diversity

Chibin Zhang

Aleria PBC

Paolo Gaudiano

City College of New York

and

Aleria PBC

Corresponding Author: Paolo Gaudiano, c/o Aleria PBC, 261 Madison Ave, 10th Fl, New York,

NY 10016 USA

Email: [email protected]

Note: A shorter version of this paper with partial, preliminary results was presented at the

Future Technologies Conference in September of 2019, and appears in Zhang, C. & Gaudiano,

P. (2019). An agent-based simulation of corporate gender biases. In K. Arai et al. (Eds.): Future

Technologies Conference, AISC 1069: 90–106.


ABSTRACT

Diversity & Inclusion (D&I) is a topic of increasing relevance across virtually all sectors of our

society, with the potential for significant impact on corporations and more broadly on our

economy and our society. In spite of the fact that human capital is typically the most valuable

asset of every organization, Human Resources (HR) in general and D&I, in particular, are

dominated by qualitative approaches. We introduce an agent-based simulation that can quantify

the impact of certain aspects of D&I on corporate performance. We show that the simulation

provides a parsimonious and compelling explanation of the impact of hiring and promotion

biases on the resulting corporate gender balance. We show that varying just two parameters

enables us to replicate real-world data about gender imbalances across multiple industry sectors.

In addition, we show that the simulation can be used to predict the likely impact of different D&I

interventions. Specifically, we show that once a company has become imbalanced, even

removing all promotion biases is not sufficient to rectify the situation, and that it can take

decades to undo the imbalances initially created by these biases. These and other results

demonstrate that agent-based simulation is a powerful approach for managing D&I in corporate

settings, and suggest that it has the potential to become an invaluable tool for both strategic and

tactical management of human capital.

Keywords: Diversity/Gender, Simulations and Agent-Based Modeling, Labor and Workforce

Dynamics, Strategic Human Capital


INTRODUCTION

In spite of the growing body of evidence showing that companies with greater gender

representation in leadership roles tend to outperform companies with fewer women (Dezso et al.,

2012; Flabbi et al., 2014; Hunt et al., 2018), many industries continue to exhibit a sharp gender

imbalance, with senior and executive levels being dominated by men. These imbalances

contribute to some of the severe problems we see across a variety of industries, ranging from

gender pay gaps (Biagetti et al., 2011; Blau et al., 2007) and high churn rates (Becker-Blease et

al., 2016; Shaffer et al., 2000) to discrimination lawsuits (Hirsh et al., 2018; Murphy, 2004). In

turn, these problems lead to high costs and internal instabilities, and expose companies to

significant reputational risk. Beyond the private sector, gender imbalances also impact academia

and the public sector (Bain et al., 2000; Jokinen et al., 2017).

Given the extensive studies showing that greater gender inclusion can lead to corporate,

economic and societal benefits, given the tangible negative implications of gender imbalances,

and given the ongoing efforts ranging from individual activism to legislation, why are there still

such significant gender imbalances across virtually all industry sectors?

We believe that the relative lack of progress is due primarily to the sheer complexity of the

problem, and the lack of tools that can deal with this degree of complexity. Today, HR

management is considered a “soft” skill; workforce analytics platforms rely on measurements

and statistical analysis, but are unable to quantify the myriad activities, interactions, attitudes and

subjective preferences of employees.

The complexity that so challenges workforce analytics, we believe, is also the reason why certain

D&I initiatives that seem to work within one organization, often fail to produce results – or even

backfire – at other organizations: each organization is a unique “ecosystem” whose macroscopic


behavior emerges from the complex web of interactions among its staff, leadership, customers,

suppliers and partners. Borrowing a D&I initiative from another company and hoping that it will

have a positive impact on our company, is analogous to copying a specific advertisement that

was successful for another company in a different sector, and expecting it will sell our products.

When you also consider that the impact of personnel initiatives can take months or years to be

observed, and that missteps can be extremely costly, it’s no wonder that leaders are reluctant to

take decisive action. What is needed is a quantitative approach that can capture and analyze the

behavior of complex systems.

We have successfully begun using agent-based simulation, one of the primary tools of

Complexity Science, to replicate the complex behaviors of people within organizations. In this

paper, we show the results of applying agent-based simulation to a particular aspect of corporate

gender imbalance: by simulating the hiring and career advancement of employees at typical

companies, we can analyze the impact of introducing gender biases.

Under reasonable assumptions, we find that gender biases in promotion can yield the kinds of

gender imbalances that are typical of many companies, with decreased representation of women

at higher corporate ranks. We also find that by adjusting gender biases in hiring as well as

promotions, it is possible to develop gender imbalances that match the patterns observed in

different industries.

Because they capture the causal relationships that link individual behaviors and interactions to

the resulting system-level behaviors, agent-based simulations can be used to predict the outcome

of different initiatives. Here we use our simulation to test the likely impact of removing all

promotion biases in a company that is already gender-imbalanced. Under a variety of scenarios,


we find that simply removing biases is not a very effective strategy, as it can take much longer to

eliminate the gender biases than it took to establish them in the first place.

Lastly, we use the simulation to explore how company-level biases lead to different individual

day-to-day experiences for employees based on their personal characteristics, and discuss how

these experiences can impact employee satisfaction and productivity.

Our findings, in line with other studies, show that agent-based simulation is a powerful tool for

workforce analytics, and that this approach holds great promise for theoretical and applied

research into D&I – a topic of great current interest with significant economic and societal

implications.

After introducing some background materials, the remainder of this paper describes the

simulation we have developed, and then presents several results we obtained with the simulation.

The paper is brought to a close with some conclusions and suggestions for future opportunities to

expand this line of work.

BACKGROUND

Gender biases in the workplace

Although female labor force participation is increasing, women still are severely

underrepresented at the top levels of organizations: according to the U.S. Department of Labor,

women account for almost half of the total labor force in the U.S., and more than 40 percent of

those have college degrees; however, in 2018, women only held 26.5% of executive and senior-

level management positions, and only 5% of chief executive officer positions in S&P 500

companies (Catalyst, 2019).


To understand the causes of these types of gender imbalances, Bielby et al. (1986) categorized

the causes of the gender gap in upper management positions into supply-side and demand-side

explanations. According to supply-side explanations, the divergence in employment outcomes

between women and men is mainly due to differences in gender-specific preferences and

productivity (Matsa et al., 2011), therefore individual attributes determine the gender inequalities

in the workplace (Olsen et al., 1983). For example, some believe that balancing work and family

life lowers women’s promotion rate as women need to take on a larger share of domestic and

parental responsibilities (Kossek et al., 2016); others hypothesize that women, in general, are less

competitive than men so they may be reluctant to compete for promotion (Niederle et al., 2007).

In contrast, demand-side explanations suggest that gender stratification in the workplace is

primarily due to gender-specific barriers; demand-side explanations focus on the institutional

constraints and managerial biases faced by women in climbing the career ladder. For example, a

male-dominated board of directors may prefer to hire male executives (Matsa et al., 2011);

women must meet higher performance standards for promotion than their male colleagues

(Gjerde, 2002; Lyness et al., 2006); and stereotypes of leadership style differences favor men in

advancing to leadership roles (Vinkenburg, et al., 2011).

In this paper, we introduce a quantitative methodology that provides indirect but compelling

evidence for a demand-side explanation. Specifically, we simulate the typical career

advancement of employees in an organization, and test the hypothetical impact of introducing

gender biases in the promotion process. We find that, under a range of simple and realistic

assumptions, it is possible to replicate the levels of gender disparity that are observed in typical

companies across a variety of industries, with increasing male dominance at increasingly senior

levels. Hence, while we cannot conclusively prove that gender imbalances are due to gender-


specific barriers, we demonstrate that the existence of gender-specific barriers yields the kinds of

imbalances that are observed empirically.

Another gender-specific barrier that we examined is bias in hiring. As suggested in a recent

report by McKinsey & Company (Krivkovich et al., 2018), in some industries women may

remain underrepresented at manager levels and above because they are less likely to be hired into

entry-level jobs, in addition to being less likely to be promoted into manager-level positions. To

test this hypothesis, we extended our simulation to capture a simple form of hiring bias, and

found that by adjusting the hiring and promotion biases simultaneously we are able to replicate

industry-specific gender balance patterns across various industry sectors, as reported in the

McKinsey study.

Simulating Corporate D&I

A majority of the research on gender inequality in the workplace is conducted by applying

statistical methodology on collected data. These statistical approaches have significant

limitations, including the fact that they hide details about individuals and cannot capture dynamic

interactions; in general, statistical approaches capture population-level outcomes but cannot

capture the underlying causal relationships and time-dependent interactions that lead to those

population-level outcomes.

The human behaviors and interactions that drive the performance of an organization – including

the impact of personal interactions that are influenced by D&I – are exactly the types of complex

relationships that cannot be captured through statistical, population-based analyses.

A more fruitful approach to analyzing the impact of D&I is to apply methodologies that are

designed specifically to analyze complex systems. In this paper we draw from Complexity

Science, a discipline that first took shape in the late 1960s with the seminal work of Thomas


Schelling on the emergence of segregation (Schelling, 1969), and became a full-fledged area of

academic inquiry in 1984 with the creation of the Santa Fe Institute. Complexity Science is a

broad field that encompasses a variety of technologies for studying complex systems, i.e.,

systems whose behavior depends in complex and often unpredictable ways on the behaviors of

many individuals interacting with one another and with their environment (Waldrop, 1992).

One of the primary tools for the analysis of complex systems is agent-based simulation, a

methodology that combines behavioral science and computer modeling (Bonabeau, 2002).

Agent-based simulations capture the behaviors of individuals, as well as their interactions with

other individuals and with their environment, to simulate the way in which the overall behavior

of a system emerges from these complex chains of interactions.

Agent-based simulations are ideally suited to analyze and predict the performance of human

systems such as companies (Fioretti, 2013; Wall, 2016), because they capture the mutual

relationship between individuals and the organization in which they belong: in the case of a

company, the behaviors of individual employees combine to determine the success of an

organization and, conversely, the environment created by the company influences the

performance of the individual employees. This sort of “feedback loop” is part of what makes

workforce management so complex, and it is exactly the type of problem that lends itself to

analysis using agent-based simulation.

In this light, agent-based simulation promises to be a valuable tool specifically to capture the

impact of D&I on corporate environments: to the extent that a company influences people’s

experiences differently based on personal traits, the company’s performance will in turn be

impacted by how those people are treated. In fact, the connection between D&I and complexity

science has been proposed by others (Page, 2017), and agent-based simulation has already been


used to analyze issues related to corporate D&I. For example, the simulation developed by

Bullinaria (2018) shows how ability differences and gender-based discriminations can lead to

gender inequality at different hierarchical levels within an organization; Takacs et al. (2012)

found that discrimination can emerge due to asymmetric information between employer and job

applicants, even without hiring biases; Robison-Cox et al. (2007) used agent-based simulation to

test the possible explanations of gender inequality at the top level of corporations, and found that

giving men favorable performance evaluations significantly contributes to the gender

stratification of top-level management.

Our agent-based simulation takes a step further and simulates ongoing activities and transitions

within a typical company, to show the dynamics of how corporate gender imbalances arise at

each level of the hierarchy as a result of biases in hiring and promotion processes. Our

simulation replicates the day-to-day operations of a typical company with men and women

distributed across four levels: entry-level employees, managers, vice presidents (VPs) and

executives. In a pilot project, we were able to simulate the impact of gender biases in the

promotion process, which leads to the kinds of gender imbalances seen in real companies, with

increasing representation of men in higher levels of the company (Zhang & Gaudiano, 2019). In

this paper we report a more complete set of results and provide a direct comparison to industry

data. In addition, we provide additional results showing that removing biases in a company that

is already imbalanced is not a very effective strategy, as gender inequalities can persist for

significant periods of time. Our findings are in line with those of Kalev et al. (2006), who found

that programs targeting lower levels of management, such as diversity training and performance

evaluations, do not help to increase diversity at higher corporate levels, and that imbalances

persist after organizations adopt these diversity management programs.


THE SIMULATION

One of the most powerful aspects of agent-based simulation is that it captures the way real-world

systems work in an intuitive, human-centric fashion. This means that anyone who has familiarity

with the problem can contribute to the design of the simulation. In a sense, agent-based

simulation democratizes analytics, because it does not require knowledge of advanced

mathematical or computational techniques.

Agent-based simulations allow domain experts to be closely involved both with the model design

and with the analysis of the results (Gaudiano, 2017), a key departure from more traditional

approaches to analytics, in which a data scientist analyzes large amounts of data using analytical

tools to look for patterns, and the domain expert is relegated to making sense of the identified

patterns. In fact, working closely with domain experts, our team has developed dozens of agent-

based simulations to solve complex problems across many sectors, including consumer

marketplaces (Gaudiano, 2016; Duzevik et al., 2007), energy consumption in commercial

buildings (Gaudiano, 2013), manpower and personnel management for the U.S. Navy (Garagic et

al., 2007), healthcare (Gaudiano et al., 2007) and computer security (Shargel et al., 2005). In all

these examples, the simulations were developed by asking domain experts to describe individual

behaviors and interactions, and translating them into software simulations. The knowledge of the

domain experts is retained in the simulation, which makes the “structure” of the simulation

intuitive to anyone using them. Running the simulation then replicates the complex interactions

over time that are impossible to grasp intuitively or mathematically.

This is one of the benefits of agent-based simulations: because they are literally trying to

replicate the individual-level behaviors, they are intuitive to domain experts; but because they

replicate the complex interactions over time that occur in real systems, they are able to reproduce


the outcomes observed in the real world. We now show how we applied this methodology to the

study of corporate D&I, and, more specifically, to corporate gender biases.

Core Elements of Our Simulation

The simulation we developed for the present study is based on simple assumptions about the

operations of a typical company. Because we are exploring gender biases, in our simulated

company there are two types of employees, men and women. And because our aim is to study

the impact of institutional barriers, our simulation assumes that men and women have identical

abilities and that their performance is also identical. While many other details could easily be

added, for the present study we wanted to focus exclusively on how gender biases in promotion

and hiring impact the overall behavior of a company. Figure 1 is a screenshot of the simulation,

which was developed with the NetLogo simulation platform (Wilensky, 2015). Employees fall

into one of four increasing ranks: entry-level employees, managers, VPs and executives. At each

rank there are men (in blue – or darker shade if viewed in grayscale) and women (in yellow –

lighter shade).

Insert Figure 1 about here

At the start of each simulation “run,” employees are distributed across ranks in a way that

mimics a typical company, with smaller numbers of employees at higher ranks.

The company is assumed to grow over time, creating vacancies within each rank. In addition,

employees may separate from the company, creating additional vacancies. Vacancies at the entry

level are filled through hiring from a hypothetical external pool of candidates, while vacancies at

all other ranks are filled by promoting individuals from the rank immediately below, which, in

turn, creates additional vacancies at the rank from which someone was promoted.


For this version of the simulation we do not simulate direct hiring into higher ranks, nor do we

allow promotions to skip levels. However, these and other details could be added if we were

interested in exploring the effects of such modifications.

While the simulation runs, the employees move back-and-forth across the floor of their rank as

time elapses. (This movement is not relevant to the results, but it helps to visualize the activities

unfolding over time.) Employees who separate from the company rise just above the other

employees, turn gray and gradually fade. Employees who are promoted are seen floating up to

the next level. These movements help to visualize the main activities that take place during each

simulation run.

In addition, to help visualize the gender balance for each employee rank, the floor of each level

of the simulation acts as a simple histogram, showing the percentage of men and women at that

rank, while the two vertical bars on the left of the screen show the overall gender balance across

the entire organization.

The company’s overall gender balance is an emergent behavior that results from three main HR

activities that take place as the company grows over time: hiring, promotion and separation. We

now describe each of these processes.

Simulating the Hiring Process

When a vacancy occurs at the entry level, the simulation assumes that a new employee will be

hired from a potentially infinite external candidate pool. By default, there is an equal chance of

hiring a man or a woman. Gender biases in hiring can be simulated by setting a hiring-bias

parameter, which changes the probability of men (or women) being hired.


When an employee is hired, the simulation begins to track their seniority, i.e., amount of time

they have been with the company. At the start of the simulation, employees are assigned a

random rank and seniority level.

Simulating the Promotion Process

When a vacancy appears at any rank above the entry level, promotions are simulated by

identifying a pool of “promotion candidates” from the rank immediately below, and then

choosing randomly one employee from that pool.

By default, the promotion pool is set as a percentage of the total number of employees at that

rank, and is based on the “promotion score” of each employee, a normalized value based on the

amount of time the employee has spent at the current rank (“rank seniority”), relative to the

amount of time spent by the most senior employee at that rank. In other words, in the absence of

a bias, promotions are based on rank seniority, with some randomness to reflect the fact that

seniority is not an exact indicator of merit. It is worth noting that seniority has been widely used

as a salient criterion for promotion in many industries, and it has been suggested that promoting

the most senior employee instead of promoting the candidate with best performance or ability,

can reduce possible psychological disturbances (Mills, 1985).

When an employee is promoted, its seniority at the new rank is set to zero, while the simulation

still tracks the total amount of time that the employee has been with the organization.

Gender biases in the promotion process are simulated by adding a promotion-bias parameter, a

value that is added to the rank seniority of each employee to calculate the promotion scores. The

promotion-bias parameter can be positive or negative to simulate biases that favor men or

women, respectively. The promotion-bias parameter is applied uniformly at all ranks.


It is important to note that we are not suggesting how promotion biases come into play; we are

simply interested in understanding how gender biases in the promotion process, if present, would

impact the overall outcomes for the company, regardless of their source or nature.

Simulating the Separation Process

In this simulation we do not distinguish between employees who quit and those who are fired,

referring simply to “separation” as the act of an employee leaving the company. While it would

be possible to capture the nuances of the different types of separations, for the purposes of this

study the key value of separations is to create turnover at a rate comparable to what we see in

real companies, so that the company’s employee pool is refreshed over time.

We simulate separations by assuming a certain annual company turnover rate and apply that

uniformly at each rank at each time step. This means that, in a given year, the absolute number of

employees who separate is greatest at the entry level, and decreases with increasing rank. This

ensures that the ratios of the number of employees across ranks remains consistent (subject to

small fluctuations due to the timing of terminations and promotions) as the company grows over

time. Notice that this also means that the average “tenure” of employees is directly proportional

to rank: if there are twice as many entry-level employees than VPs, then, on average, the tenure

of a VP will be about twice as long as that of an entry-level employee.

To determine which employees separate at each rank, at each time step we determine the number

of employees who are likely to separate, and then we randomly select these employees from a

“separation pool,” a portion of the employees with the lowest promotion score at that rank; in

other words, the decision to terminate is influenced both by seniority (or lack thereof) and

gender.


Applying the same gender bias for separations as well as for promotions reflects two

assumptions: first, that the sources of bias that drive promotion decisions are also behind

termination decisions. This seems reasonable, given that typically the same manager is in charge

of both decisions. Second, if bias causes women to be held back, they are more likely to get

frustrated, which may increase the probability that they will separate voluntarily (i.e., quit). In

preliminary studies we have tried other separation processes, such as purely random selection.

Including gender bias in separation heightens and accelerates some of the results we report, but

does not alter our overall findings.

SIMULATION SETUP

Simulation Time Step and Duration

The simulation is time-based, meaning that we simulate the passage of time, with each time step

equal to one week of operations. The software is designed to allow any level of temporal

resolution, but we found that a weekly time step gives the best balance between capturing typical

fluctuations and being able to simulate sufficiently long operating periods to see meaningful

results. For all results reported below, we ran the simulations for the equivalent of either 10 or 40

years (520 or 2,080 time steps, respectively). Using a standard laptop, we can simulate four

decades of company operations in a few seconds. We have tested reducing the time step to one

day or even hours, and found no significant differences – other than taking proportionately

longer to run. All time-dependent variables described herein are specified as annual rates, and

then scaled automatically to the time-step size to ensure consistent behavior.


Randomness

At each time step, the simulation includes several operations that invoke a random-number

generator, which results in variance across simulations (e.g., in selecting promotion and

separation candidates). To ensure reproducibility of individual simulation runs, we have the

ability to select the seed for the random-number generator. Unless otherwise specified, each of

the results reported here was obtained by averaging the results from ten runs with different

random seeds at each parameter setting, and includes error bars corresponding to one standard

deviation. We found that results do not vary significantly as we increase the number of

simulations beyond ten.

Company Size and Employee Distributions

For all results reported here, the company begins with a total of 300 employees, 150 women and

150 men. The employees are distributed across the four levels in a way that roughly simulates a

typical company: 40% at the entry level, 30% at the manager level, 20% at the VP level and 10%

at the executive level. We have tested the simulation with other settings and found that the

overall company size and exact distribution across levels has no significant impact on the results.

However, the smaller the company, the more fluctuations will be seen across simulation runs

with different random seeds.

Company Growth and Separation Rates

As mentioned earlier, the simulation time step is set to correspond to a seven-day period. At each

time step, random numbers are drawn to determine whether separations, hires or promotions

need to take place. The frequencies of each of these occurrences are set so that, over the course

of a simulated year, the overall growth and churn rates are within a range that would be


consistent with a “generic” company: the company grows by 10% each year (linearly, meaning

that it will double in size in ten years, and triple in size in 20 years), while we target an annual

churn rate of 20%, which is in line with national average separation rates (Mercer, 2020).

Promotion and Separation Pools

For promotions, we set a candidate pool size of 15%: in other words, when someone needs to be

promoted to a higher rank, we select the 15% of employees with the highest promotion scores,

and then randomly choose one of them to be promoted. For separations, we set the candidate

pool size to 50%, meaning that someone is selected randomly from half of the employees at each

rank with the lowest promotion scores. We have tested different size candidate pools and found

that the results do not change significantly as these parameters are changed.

Employee Characteristics and Variables

Our simulation treats each employee as an “agent” with certain characteristics and variables. For

this study, at the start of each run every agent is assigned a gender value that remains unchanged

during the simulation. Each employee is also randomly assigned to an initial rank based on the

distributions given above, and is given a start date that is set randomly (proportional to the

starting rank). The start date is used to calculate the seniority of each employee.

All other agent properties are variables, such as seniority and promotion score, that are used to

track the state of each agent over time and to make decisions about promotions and separations.

Table 1 describes all the agent characteristics and variables we used.

Insert Table 1 about here


Scenario-Testing Parameters

To test the impact of gender biases, we varied certain parameters systematically to explore

scenarios of interest. Specifically, all of the scenarios reported here manipulated one or more of

the following three parameters:

Hiring Bias: this parameter determines the proportion of men and women that are

hired when vacancies occur at the entry level. A positive bias means men are favored,

and a negative bias means women are favored.

Promotion Bias: this parameter is added to the seniority of each simulated employee

to influence the probability that the employee will be included in the candidate pool

when a promotion takes place. A positive bias means men are favored, and a negative

bias means women are favored. The bias is expressed as a number between 0.0 and 1.0

that is added directly to the employee’s rank seniority.

Promotion Bias Duration: for some of the scenarios we tested, the Promotion Bias

was set to zero after a certain amount of time (typically 10 years) to simulate the

removal of all gender biases in promotions and separations.

A complete list of parameter settings used for all simulations (except as noted) is provided in

Table 2.



RESULTS

Experiment 1: the Impact of Gender Biases in Promotion

In the first set of experiments we wanted to establish a baseline and then test the impact of

systematically increasing the degree of gender bias in the promotion process. In all these

simulations, the hiring bias is set to zero.

Figure 2 shows the gender balance at each rank during a 40-year simulation when there is no

promotion bias or hiring bias. The figure shows that, in the absence of biases, the gender balance

stays at 50-50 throughout the simulation, with only small oscillations due to the inherent

randomness of the simulations.


Next, we tested the impact of increasing the promotion bias to 0.1, 0.3 and 0.5. As mentioned

earlier, in the absence of biases, each simulated employee’s promotion score is simply its

seniority relative to the most senior employee at that level (rank seniority). Hence all the

promotion scores prior to the application of a gender bias are between 0.0 and 1.0.

Adding a promotion bias of 0.1 thus means that while women’s scores will still be in the range

[0.0,1.0], men’s promotion scores will be in the range [0.1,1.1]. Similarly, at the highest level of

bias reported here (0.5), men’s promotion scores will be in the range [0.5,1.5], while women’s

promotion scores will stay in the range [0.0,1.0].



As can be seen in Figure 3, a bias of 0.1 in promotions begins to show an interesting pattern:

while the entry and manager levels continue to stay roughly at 50- 50, the VP level (dashed line

with no symbols) is starting to show an imbalance in favor of men, and men now make up

roughly 60% of the executive level (solid line with diamond symbols).

The pattern becomes much more evident in Figure 4 and Figure 5, which show the gender

balance at each company level when the promotion bias is set to 0.3 and 0.5, respectively.

Several interesting phenomena are worth pointing out.

Insert Figure 4 and Figure 5 about here

First, we see that, even though the promotion bias is a single parameter that works uniformly at

each level, the successive promotions compound the effect, so that the gender imbalance is

greatest at the executive level: after several simulated years, the executive level shows an

imbalance of approximately 80% men when the bias is at 0.3, and exceeds 90% men when the

bias is at 0.5.

Second, increasing the bias has the effect of increasing the degree of imbalance, but also the

speed with which the imbalance spreads through the organization: notice that with a bias of 0.3,

the imbalance at the executive level builds gradually over a span of nearly 20 years; but when the

bias is 0.5, the proportion of men at the executive level crosses the 80% mark in less than five

years, and has essentially leveled off by year 10.

Third, there is a surprising effect at the entry level: the percentage of female employees goes up

as the promotion bias increases, even though there is no hiring bias, and even though women are

being terminated more often than men because the promotion score influences separations. We

can see in Figure 4 and Figure 5 that women make up an increasing percentage of the entry-level


population, reaching 60% when the bias is 0.5. The reason for this “reverse imbalance” is that

men are being promoted at a much higher rate than women, so that women are being left behind.

In reality, this is not uncommon in the real world: many industries have large numbers of women

in entry-level positions, and women often describe the negative experience of being “stuck”

while their male colleagues get promoted (e.g., Chamorro-Premuzic, 2019).

This last observation illustrates another great aspect of agent-based simulations: unlike typical

“black-box” models, with an agent-based simulation it is possible to dig into the detailed

activities to understand the origin of observed macroscopic phenomena, i.e., emergent behaviors.

Overall, the results of the first experiment show that, starting with very simple assumptions, we

can capture some qualitative phenomena that match our observations of real-world companies:

the presence of gender biases in promotions leads to increasing gender imbalance at higher

levels, and women being stuck in lower levels.

In the next section, we show how, by manipulating both hiring and promotion biases, we can

accurately replicate real-world data on gender imbalance observed for specific industries.

Experiment 2: Combining Promotion and Hiring Biases to Match Industry-Specific

Imbalances

While the patterns shown in Experiment 1 qualitatively look remarkably like those we observe in

real companies, we wanted to see whether, using a minimal set of assumptions, we could match

real-world data on gender imbalances for more specific cases. To this end, we used our

simulation to match data from McKinsey’s and LeanIn’s Women in the Workplace report

(Krivkovich et al., 2018).

We ran simulations for ten years, and measured the gender (im)balance at each rank. In all

simulations we modified two parameters from the baseline case: the promotion bias and the


hiring bias. In general, as mentioned earlier, higher promotion biases create larger imbalances at

higher ranks, and can lead to reverse-imbalance at the entry level. In other words, if we think of

the company’s gender balance as having the shape of a funnel going from the entry level up

toward the executive level, that funnel is straight in the absence of biases, it becomes a bit

narrower at higher ranks when promotion bias is low, and becomes dramatically narrower when

promotion bias is high. In contrast, the hiring bias has a direct impact on the number of women at

the entry level, which will have a uniform impact on all subsequent ranks; hence we expect that

increasing the hiring bias will make the overall funnel narrower.

In Figure 6, we show the comparison of ten-year gender balance data from our simulation and

from the McKinsey report. The McKinsey report uses six levels (entry, manager, director, VP,

SVP and C-Suite), so we selected the four levels that match the ranks used in our simulation:

entry, manager, VP and Executive (C-Suite).


Starting with Figure 6(A), we see that setting the promotion bias to 0.3 and high hiring bias of

0.4 results in only one third of women at the entry level, and less than 20% women in the top

ranks. This shape closely matches the gender imbalances observed in the Engineering and

Industrial Manufacturing sector in the McKinsey study.

In Figure 6(B), the promotion bias remains at 0.3, but hiring bias is lowered to -0.1 so that

recruitment at entry level favors women. As expected, the bias favoring hiring of women widens

the base of the “funnel,” leading to approximately 60% women at entry level; however, the high

promotion bias narrows the funnel, leading to only 20% women in the top ranks. These results

match closely the gender data reported by McKinsey for the Insurance sector.


In Figure 6(C), the promotion bias is lowered to 0.2. with the absence of hiring bias, women

make up more than half of the entry level, while the somewhat lower promotion bias leaves

nearly 25% of women in the top ranks. These results closely match the gender data reported by

McKinsey for the Banking and Consumer Finance sector.

Finally, Figure 6(D) shows a pattern that resembles the gender imbalances observed in the Retail

sector, which tends to be dominated by women at the entry level, but with only a modest female

representation at the top ranks. We obtained this graph by keeping the promotion bias to 0.2, but

setting the hiring bias to -0.2 so that women receive favorable treatment when hiring into the

entry level.

Accuracy of the Industry Simulations

To test the accuracy of our simulations of industry gender imbalances, we calculated the root-

mean-squared deviation (RMSD) between each simulation and the data provided from the

McKinsey study, given by the formula:

RMSDi=√ (LO D−LOS)2+(L 1D−L 1S)

2+(L 2D−L2S)2+(L3D−L3S)

2

4

Where RMSDi is the RMSD for a given industry i; each squared term captures the difference

between the gender balance data (subscript D) and the simulation (subscript S) at a given level

Ln (with n representing rank, from 0 for the entry level to 3 for the executive level); and the

division by 4 represents the fact that we are averaging the result across the four levels.


The analysis of the accuracy of the simulations shown in Figure 6 is summarized in Table 3. In

all cases, the RMSD was below 3%.


Take together, the results shown in Figure 6 and Table 3 show that, by changing just two

parameters – promotion bias and hiring bias – our simulation is able to replicate real industry

data with high accuracy.

Experiment 3: The Impact of Removing All Biases

Many companies nowadays have implemented diversity management policies in an attempt to

create an inclusive environment for women and members of underrepresented minorities. One of

the most important policies targeted at lowering managerial bias in promotion is diversity

training. However, most of the research that examines the efficacy of diversity training such as

seminars and workshops reveals that implementing diversity training as a single initiative will

not lead to a more diverse organization, at least not in the short run (Cavaleros, Van Vuuren, &

Visser 2002; Kalev, Dobbin, & Kelly, 2006). Some studies show that bias awareness training

could even cause bias to be strengthened after the training (Duguid & Thomas-Hunt, 2015).

We wanted to test what would happen in our simulation if we completely removed all biases

(hiring and promotion) for a company that was already showing significant gender imbalance. In

other words, we wanted to see whether creating equal hiring and promotion opportunities by

eliminating all bias is sufficient to undo the gender imbalances originally caused by the biases.

To test this, we repeated two of the same scenarios we tested in Experiment 1, but we set the

promotion bias to zero after 10 years of operations. Once the promotion bias drops to zero, the

promotion score is solely based on an employee’s seniority, meaning that advancement depends

only on how long an employee has been at a given rank, and not on gender.

The scenarios we chose for this Experiment used the same parameters from Table 2 that were

used to generate Figure 4 (promotion bias of 0.3) and Figure 5 (promotion bias of 0.5)


Figure 7 and Figure 8 show that even if all biases could be removed, it can take a very long time

to “undo” the damage done, especially at the upper levels.


Specifically, we can see in Figure 7 that, after ten years of operations with a gender bias of 0.3,

men occupy 80% of positions at the executive level, 75% at the VP level, 60% at the manager

level and 45% at the entry level. (As we mentioned earlier, the reason why there are more

women than men at the entry level is because more women are left behind as men have a higher

chance of being promoted to the manager level.)

When all biases are removed after ten years, we see that the entry level and the manager level

return to 50-50 within three years, as women are quickly promoted from entry level to manager

level. However, it takes nearly ten years for the VP level to return to approximately a 50-50

level. As to the executive level, we see a gradual decline over the two decades following bias

removal, but even after a full 30 years, men still maintain a 60-40 majority over women.


The results are similar when the promotion bias is initially set to 0.5: as shown in Figure 8, after

ten years the representation of men across the four levels is about 40% (entry-level), 70%

(manager), 85% (VP) and 90% (executive). As in the previous example, the two lower levels

return to 50-50 gender balance within about three years, the VP level reaches parity in just under

ten years, while the executive level takes about 12 years to drop from 90% to 70%, but then

declines only very gradually, and is still around 60% after three full decades without bias.


These results are relatively easy to understand when we think about the compounding effects of

two different factors. First, as explained in an earlier section – and as is generally the case in real

companies – the average tenure of employees is related to their rank, with employees at higher

rank staying longer than employees at lower ranks. Hence it simply takes longer to “flush out”

the imbalances at the higher ranks. Second, simply removing promotion biases does not cancel

the existing disparities; consider for example what happens at the manager level in Figure 8: just

when the biases are turned off in year ten, 70% of managers are male. If employees are promoted

“fairly,” then for every ten managers promoted to VP level, seven of them will be men, which

will continue to support gender disparity at the VP level. In fact, in our simulation, the women in

this scenario will get a temporary “boost,” because all of the women managers who were more

senior than their male peers but were not being promoted, will suddenly find themselves to be

the most senior managers, and will be much more likely to be promoted in the first few months

after the biases are turned off, a condition unlikely to occur in a real company.

This experiment leads us to a general conclusion about corporate gender biases, namely, that

simply removing biases is not an effective way to create equality. Put another way, when

systemic biases have created disparities, equal opportunity is not an adequate remedy. Our

results suggest strongly that some sort of affirmative action that favors the placement of women

into higher ranks – whether through more aggressive promotion or through external hiring – is

needed, if balance is to be restored.

Experiment 4: The Impact of Promotion Biases on Individual Employees

One of the great benefits of agent-based simulations is that they make it possible to analyze at

the same time the experiences of individuals and the overall company-level outcomes. This is

perhaps the most powerful argument for using agent-based simulation as a core tool in managing


talent in general: especially in the context of D&I, we tend to hear anecdotes about individual

experiences, but most of the data reported is based on statistics measured at the company level,

which hides the details of individual experiences. With agent-based simulation we can do both:

we can calculate population-level data just as we would in the real world, without losing any of

the information about individual experiences. This makes it possible to explore the causal

relationships that link individual experiences with company-level, emergent outcomes.

To illustrate this point, we conducted one final experiment to highlight how a company-wide

promotion bias manifests itself in terms of the lived experiences of individual employees. In

particular, while running simulations we noticed – not surprisingly – that women were often

stuck at each rank, while men with less seniority were getting promoted ahead of them.

Anecdotally, this is an experience that is often reported by women.

To quantify this phenomenon, we tracked how many times each simulated employee is passed

over for promotion, and how much time it spends at a given rank. Specifically, each time an

employee is promoted from a certain level, all other employees who are more senior increment a

counter that tracks how many times they have been passed over for promotion. When an

employee is promoted, we record the total amount of time it had spent at that rank (its “tenure-in-

rank”) and the number of times it was passed over, and then we reset the counter to zero before

heading to the higher rank. Note that, because there is no promotion beyond the executive level,

this analysis can only be done for the first three ranks (entry level, manager, VP).

Because the number of employees differs at different ranks, and because the simulation tracks

every promotion, entry-level employees were being passed over many more times than

managers, who in turn were being passed over more times than VPs. To correct this unrealistic

situation, we normalized the data by dividing the number of times passed over by the number of


people at that rank, and multiplying by ten. This roughly corresponds to assuming that, at each

rank, employees are only comparing themselves to a group of ten “peers.” We also normalized

the passed-over data by the average number of years that employees spend at each rank, to obtain

an average annual figure, which made comparison across ranks more meaningful.

Figure 9 shows the results of this analysis. The top row shows data for VPs, the middle row for

managers, and bottom row for entry-level. Within each row, the left chart shows the average

number of times passed-over in one year, while the right chart shows the average tenure-in-rank

in years. Within each chart, there are four pairs of bars, representing, from left to right, the level

of promotion bias (0.0, 0.1, 0.3, 0.5); each pair of bars represents data for men (dark grey) and

women (light gray). As with all other experiments, each data point was obtained by running the

simulation ten times with different random seeds, and error bars show one standard deviation of

the mean.


Several things are worth noting. First, when there is no promotion bias (the leftmost pair of bars

in each plot), we see that the results for men and women are very similar, as expected. Note also

that, because promoted individuals are selected randomly from a promotion pool (as described in

the section Simulating the Promotion Process), even in the absence of biases there will always be

some employees that are passed over, which is why the leftmost bars at all three ranks are non-

zero.

Focusing now on each rank, we see consistent patterns both in the passed-over data and in the

time-in-rank data. First, as the bias increases, all simulations show that women are passed over


more times per year than their male peers, as expected. Second, we see that the average tenure-

in-rank increases for women, while staying flat or even decreasing for men.

If we now compare the passed-over results across ranks, we notice another important trend:

while at the entry level the average number of times passed-over for women seems to grow in a

roughly linear proportion with the amount of promotion bias, for higher ranks this relationship

seems to grow more geometrically: at the entry level, raising the bias from 0.1 to 0.5 increases

the number of times passed-over for women from 0.63 to 1.91– a ratio of 3.0; at the manager

level, this ratio increases to 6.2 (from 0.5 to 3.1); at the VP level, the ratio further increases to

15.1 (from 0.32 to 4.83). This, in retrospect, makes sense, because being passed over is

compounded by the increasing proportion of men at higher ranks: the promotion bias gives each

individual man an increasing chance of being promoted over a female peer, and there are a lot

more men in each woman’s peer group – which means that even in the absence of biases, more

men than women would be promoted.

If we now focus on the tenure-in-rank data (the charts in the right column of Figure 9), we notice

that the average time spent at each rank increases for women with increasing promotion bias, but

this increase is fairly consistent across ranks. What is more interesting about the tenure-in-rank

data is to observe that, especially at the lower ranks, the average tenure-in-rank of men decreases

while that of women increases. This result, while not entirely surprising, further quantifies the

differences in individual experiences of men and women that result when gender biases exist in

the promotion process.

There is one aspect of our simulations that is unrealistic, and which makes it difficult to compare

our quantitative results to real-world data. Namely, in our current simulation employees only

separate from the company at random times. In contrast, being passed over repeatedly in real life


would likely cause a decrease in satisfaction, which would in turn lead to higher turnover rates

for women than for men (Stamarski & Hing, 2015). Hence the idea that women will remain stuck

at a level for a much longer time than men is somewhat unrealistic, because in real life, women

in those situations would be more likely to quit.

We are currently developing a version of this simulation in which each agent has an internal

“satisfaction” variable that is impacted by being passed over for promotion, and which, in turn,

increases the probability that an employee will voluntarily leave the company. In this case, we

expect to see lower retention rates for women and immediate changes in the organization’s

turnover rate (Holtom, Mitchell, Lee, & Inderrieden, 2005) – phenomena that are common across

male-dominated industries. We leave this additional analysis to future work, and simply point

out another advantage of agent-based simulation, viz, the ability to add details to the simulation

without compromising or invalidating the results obtained with a simpler simulation.

DISCUSSION

We have introduced an agent-based simulation that captures, albeit in simplified form, some of

the gender imbalances that are observed across a variety of industries, supporting a demand-side

explanation of observed corporate gender biases (Bielby & Baron, 1986). What is perhaps most

striking about our findings is that we are able to capture several phenomena through very simple

assumptions, and by varying only a small number of parameters.

Of course, the fact that our model is able to reproduce some of the observed phenomena does not

mean that we are accurately capturing the true causes of these phenomena: it is possible that the

mechanisms we hypothesized are not representative of real-world corporate functions, and that

the similarity between our results and real-world observations are purely coincidental.


However, what we have been able to show is that if a company has gender biases in the way it

promotes its employees, then, over time, the company will exhibit growing levels of gender

imbalance, and that this imbalance will be increasingly pronounced at higher ranks within the

organization.

Because our model is capturing the causal links between the behaviors of individuals and the

emergent behaviors of a company, and because our model is very parsimonious in its

assumptions, we are therefore confident that our model, while certainly simplistic, is capturing

fundamental aspects of corporate function that reflect real-world contexts.

There is another way in which our simulation offers indirect but strong support for a demand-

side explanation of corporate gender biases: as we discussed in our description of Experiment 2,

our simulation shows that reducing the number of women that are hired at the entry level (which

could result from a smaller supply of women or from hiring biases) would results in an overall

reduction in the representation of women that is consistent at all ranks. In other words, if we start

the simulation assuming that only 40% of applicants are women, over time there will be 40%

women at every rank. A supply-side hypothesis would have to explain the progressive reduction

in representation at higher ranks, and why this progressive reduction is observed so consistently

across every industry. Any single proposed factors, such as child-bearing or competitiveness,

would be unable to explain the observed results.

The Nature of Gender Biases

Our simulation treats gender bias as a single parameter. We are not making any claims about

what is actually causing this bias, or whether the bias results from a single factor or from

multiple factors. Rather, we believe that each company has a combination of individual biases


and structural biases that jointly impact the probability that women will be selected for

promotion.

At the individual level, studies have shown that managers often fall victim to a range of

unconscious biases, such as implicit prejudice based on stereotypes, group favoritism, or

overclaiming credit for their own achievements (Banaji , Bazerman, & Chugh, 2003). At the

structural level, a company may consider “face time” or other performance metrics that

implicitly favor men as part of their promotion criteria. The idea behind our use of a single

parameter is to show that, taken together, these kinds of biases combine to shape the experiences

of individual employees in a way that differs for men and women.

And although it is likely that, on one hand, certain forms of bias are wide-spread, and on the

other hand, each company may have unique forms of biases, the fact that different industries

exhibit different levels of imbalances suggests that certain types of biases may be endemic to

specific industries.

In the future, we hope that companies will be able to use agent-based simulations such as the one

we have used here to estimate the level of gender biases that are likely to exist in their

organizations, and then use that information as guidance to identify – and remove – specific

sources of bias that impact their employees.

Benefits of Agent-Based Simulation as a Management Tool

It is worth noting that most research on gender inequality in the workplace is conducted by

applying statistical methods to observed data. This common approach has a number of

limitations, including the fact that it is only capturing present conditions, it removes any

information about dynamics, it hides details about individual interactions, and, most importantly,

it tends to identify correlations that may or may not be due to causal relationships. As we


highlighted in Experiment 4, our agent-based simulation preserves the individual experiences,

and makes it possible to explore the causal relationships that link individual behaviors to the

emergent behaviors observed at the company level. This is one of the greatest benefits of using

agent-based simulation to study corporate workforce management in general, and D&I in

particular.

Another significant benefit of agent-based simulation as a management tool is that, because it

captures causal relationships rather than correlations, agent-based simulation can also be used to

explore the likely impact of different initiatives. In other words, agent-based simulation can

serve both as an explanatory tool and as a predictive modeling tool. For example, in this paper

we used the simulation to estimate the likely impact of removing all promotion biases. In fact,

we believe that the inability of corporations to predict the likely impact of different D&I

initiatives, and the risks that D&I missteps can create, are some of the main reasons why, almost

half a century after the passage of equal opportunity, corporate D&I across most industries has

made little, if any, noticeable progress (Newkirk, 2019).

Future Research Directions

We see this project as the beginning of a systematic study of the impact of D&I on corporate

performance. For instance, while the simulation we used in this paper focused only on

advancement, we can use a similar approach to simulate other aspects of workforce management,

including retention or recruitment. In fact, a former graduate student of one of the authors, for his

Masters thesis, developed an agent-based simulation that shows how job candidates are

influenced by the perceived level of inclusion and diversity of a company, and how this will

impact the talent pool available to any company and influence the cost of hiring (Naghdi Tam,

2017). We have also begun to simulate the impact of many other facets of D&I that impact the


day-to-day experience of individual employees, how these experiences impact the satisfaction

and productivity of individuals, and how this in turn impacts overall performance of the

company across a variety of performance indicators.

Even within the promotion model itself, there are many ways in which we could increase the

fidelity of the model to explore the impact of different assumptions and of different initiatives.

We already mentioned our plans to extend the simulation to track employee satisfaction and its

impact on retention and productivity. Similarly, we could also simulate how the presence of

managers of a different gender impacts satisfaction and career advancement, or we could test

alternative hiring practices, such as hiring people directly into higher ranks. In other words, this

model can serve as the basis to explore a large number of hypotheses about the sources of gender

disparities, and to test the likely impact of different interventions.

Finally, although in this paper we have focused on gender, and we treated gender only as a

binary (male/female) variable, it is possible to capture a more nuanced and realistic

representation of gender identity and to represent other personal characteristics that impact an

employee’s experience, such as ethnicity, race, religious beliefs, sexual orientation, physical and

cognitive abilities, and any other characteristic that may impact an individual’s experience within

an organization. We have actually begun to develop some agent-based simulations that include

other facets of diversity, and have already encountered some complex, fascinating issues that

suggest entirely different ways of thinking about D&I and its impact on employee satisfaction

and corporate performance.

In all, we are optimistic that our work can lead to a dramatic shift not only in how corporate

leaders think about D&I, but, more importantly, how they manage it.


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Table 1

List of employee agent variables tracked in the simulation

Variable name Variable Description

rank The level within the organization

start-date The date when the joined the company

start-date-in-rank The date when they first reached a certain rank

tenure-in-rank How much time they have been at a certain rank

seniorityA normalized variable [0-1.0] that reflects how long the employee

has been at this rank, relative to all employees at the same rank

promotion-score A score that combines seniority and promotion gender biases

times-passed-overThe number of times someone else from the same level with

lower seniority was promoted

hr-events A list of HR-related events such as being hired or promoted


Table 2

Parameter settings for our promotion bias Experiments 1 and 3

Simulation duration (in years) 40

Number of repetitions of each simulation 10

Initial company size 300

Initial gender balance (male-female) 50-50

Promotion Bias level 0, 0.1, 0.3, 0.5

Promotion Bias Duration N/A (exp. 1), 10 (exp. 3)

Hiring Bias 0

Promotion pool size 15%

Termination pool size 50%


Table 3

Bias parameters and simulation accuracy for the four industries simulated in Experiment 2

Promotion

bias

Hiring

bias

Industry simulated Variability

score

0.3 0.4 Engineering and industrial manufacturing 0.007

0.3 -0.1 Insurance 0.024

0.2 0 Banking and consumer finance 0.017

0.2 -0.2 Retail 0.015


Figure 1

Screenshot of the simulation


Figure 2

Fluctuations in gender balance across all four levels during a 40-year simulation. For this

figure the promotion and hiring biases are set to zero


Figure 3

Fluctuations in gender balance across all four levels during a 40-year simulation when the

promotion bias is 0.1


Figure 4




Figure 5




Figure 6

Simulating the gender imbalances of different industries by adjusting both promotion and hiring

biases.

(A) Promotion Bias 0.3, Hiring Bias 0.4 (B) Promotion Bias 0.3, Hiring Bias -0.1

(C) Promotion Bias 0.2, Hiring Bias 0.0 (D) Promotion Bias 0.2, Hiring Bias -0.2


Figure 7

Gender balance across all four levels during a 40-year simulation that starts with a promotion

bias of 0.3, which drops to 0.0 after 10 years

NO BIASBIAS


Figure 8

Gender balance across all four levels during a 40-year simulation that starts with a promotion

bias of 0.5, which drops to 0.0 after 10 years

NO BIASBIAS


Figure 9

Average number of times passed-over (left column) and average number of years in rank (right

column) for VP (top row), Manager (middle row) and Entry (bottom row) levels

VP level

Manager level

Entry level

Documents

Abstract · Web view2020. 6. 12. · An Agent-Based Simulation of How Promotion Biases Impact Corporate Gender Diversity. Chibin ZhangAleria PBC. Paolo GaudianoCity College of New