Modeling Work Promotion Bias in NetLogo

Introduction

According to the Women in the Workplace 2018 survey, people of color are far less likely than others to be promoted in the workplace. In a study of nearly 300 companies with over 13 million employees, researchers found that only 60 black women are promoted for every 100 men (McKinsey & Company, 2018). Although this study focuses on women in the workplace, black men are also discriminated against in the work promoting process.

The underrepresentation of black employees in senior positions represents a key issue of inclusion in the workplace. In the topic of Diversity & Inclusion (D&I), there has often been little focus on issues specific to inclusion. Although companies can present statistics of employee demographics to show equal representation, these numbers can often hide the lack of representation in leadership roles. Furthermore, studies show that inclusion in leadership roles can increase the performance of companies, so it would benefit both the equity and economic efficiency of the workplace (Zhang & Gaudiano, 2020).

There is a lot of research on the factors that contribute to discrimination in the workplace. The social scientific theories relating to biases are not the focus of this model. Instead, this initial model aims to show how promotion biases in a firm with equitable hiring practices lead to significant disparities between black and white employees in managerial and leadership roles. In the real world, discrimination in the workplace affects both promotion and hiring processes. For the sake of simplicity, only promotion bias will be modeled here. The resulting proportion of black and white employees in the different work positions will be measures for differing levels of promotion bias. The goal of this model is to understand how the presence of even slight promotion biases in lower and higher work levels can lead to the significant underrepresentation of black workers in senior positions.

Agent Properties

My model consists of two kinds of agents to represent workers, one type representing black and white workers. These agents are in the shape of people and have different colors, black for black workers and yellow for white workers. There is a third type of agent that is not visible on the patches. These are the promoter agents and determine which worker agents have the opportunity to be promoted. Each worker agent also has a promotion score that goes up by one when the agent is promoted to the next level. The world of agents represent one company or firm. The world does not wrap horizontally nor vertically. The patches in the world are split into three levels to represent the work level positions:

1. Bottom level - white patches - entry positions

2. Middle level - teal patches - manager positions

3. Top level - dark green patches - executive positions

The number of worker agents and the proportion of white to black worker agents are determined by the user. All worker agents are assigned to the entry positions at the start of the model. Promoter agents are placed in the entry and managerial positions. The number of these 'invisible' promoter agents is determined by the total number of workers set by the user. The model code is set up so that there are promoter agents equal to 15% of the total number of agents in the entry level and 5% for the manager level. The entry promoter agents promote workers to the manager level and the manager promoter agents promote workers to the executive level.

Interaction Rules

In this model, the worker agents do not interact with each other. As mentioned above, all worker agents begin in the entry level (white patches' section of the model). A worker agent is then selected for the opportunity of promotion by its proximity to a promoter agent in the entry level. The process of promotion in this model is different for white and worker agents. If a white worker agent is within a specified radius of a promoter agent, that worker is promoted to the manager level and moves to one of the middle, teal-colored patches. The worker agent's promotion score also increases by one, from 0 to 1.

To model promotion bias, my model uses two parameters of biases, a manager bias and an executive bias (both set initially by user). Both variables have a range of 0 to 1 and represent the likelihood that a black worker agent is promoted to the next working level. For instance, if the manager bias is set to 0.8, then each black worker agent in the entry level has an 80% likelihood of being promoted to manager after a chance encounter with a promoter agent. The user-determined biases only apply to black workers. By default, these biases do not apply to white worker agents (assume that these biases are set to 1).

If a black worker agent is not promoted, then their individual patch color turns pink and their promotion score is set to the promotion bias level. If this occurs, then this black worker agent is 'passed over' for promotion and is unable to get a second chance at promotion. In other words, they are left behind.

There are two major rules to determine the model's execution. Once 35% of the total number of workers have been promoted to management, the model will no longer promote entry level workers. Finally, once 15% of workers have been promoted to the executive level, the model stops totally. As such, this is a quick model and usually finishes within around 10 ticks.

NetLogo Initial Setup

The model begins with all workers in the entry level. The user sets the number of total workers, the proportion of white to black workers, and the level-specific biases for black worker agents.

Worker and promoter agents are randomly placed in the entry level patches (see image below). The default value for total number of workers is 300 with an equal proportion 50/50 of white and black workers. The manager promotion bias is set to 0.8 (80% likelihood that a black worker, if in radius of a promoter agent, is promoted to manager level) and the executive promotion bias has a default value of 0.6.

Here is a snapshot of the initial setup of the model in NetLogo:

At each tick, the process of promotion occurs. When workers are within a 1 patch radius of a promoter agent, agents have a chance of promotion. As mentioned before, the promotion biases do not apply to white worker agents. In other words, if a white workers is within a 1 patch radius of a promoter agent, they are always promoted. This process for black worker agents depends on the level of manager or executive bias set by the user.

These processes continue until the major stopping rules are reached.

Here is a snapshot of the model after 15% of total number of workers have made it to the executive position under the default parameter values:

Simulation Procedure

Using the BehaviorSpace feature in NetLogo, I swept three different parameters: proportion of black workers, manager promotion bias, and executive promotion bias.

For each promoter, the simulation runs multiple iterations at incremental levels of each parameter while the other variables are held constant. As such, there are three simulation experiments:

Experiment 1: Incrementally increase the proportion of black workers from 10% to 90%. Total number of workers is held constant at 300 and manager and executive biases are also held constant at default levels (0.8 and 0.6, respectively)

Experiment 2: Incrementally increase the manager promotion bias from 0.1 to 1. Total number of workers is held constant at 300 and the proportion of white and black workers is also constant at 50/50. Executive promotion bias is held at 1. In other words, if a black worker agent is within a designated radius of a promoter agent in the manager level, they are effectively promoted to the executive position.

Experiment 3: Incrementally increase the executive promotion bias from 0.1 to 1. Total number of workers is held constant at 300 and the proportion of white and black workers is 50/50. Manager promotion bias is held at 1. So, if a black worker agent is within a designated radius of a promoter agent in the entry level, they are effectively promoted to the manager position.

For each experiment, the proportion of black and white worker agents at each position is measured along with the number of black worker agents that are 'passed over' for promotion for Experiments 2 and 3.

Results

Experiment 1

As the proportion of white to black workers increases, the disparity between the workers in the leadership roles decreases. When there are fewer black workers, the white worker agents make up the majority of all positions. Around the 50/50 proportion, the leadership role disparity is clear. When there are equal numbers of black and white workers, the two types of agents equally make up the entry and manager positions. In the executive level, however, the proportion of white worker agents is at its highest (>60%). These results arise from the default promotion biases (0.8 manager bias and 0.6 executive bias). The two biases compound, resulting in the highest disparity between white and worker agents at the executive level. As the proportion of black workers increases over 0.5, the representation of black workers in each level increases. However, the increased representation in the executive level is the slowest to increase, further supporting the hypothesis that promotion biases significantly decrease the number of black workers in top leadership roles.

Experiment 2

Expectedly, as the manager promotion bias level increases, the proportion of black workers in the managerial position increases (the orange line tends to decrease). At low levels of bias, which means low likelihood of promotion to management, white worker agents make up the vast majority of both manager and executive positions (orange and grey lines begin near 90% when bias is 0.1). Because the manager and executive positions are made up of mostly the white workers, the proportion of white agents in the entry level is far below 50%. In other words, black workers agents are left behind in the entry level due to the restrictive promotion bias. Even though the executive promotion bias is 1 (no bias), black workers are too restricted to enter the manager position so they are still underrepresented at the top executive level.

The second figure shows the number of black workers who are passed over for promotion to the manager level. As the bias level increases (actual bias decreases), the number of passed over employees decreases. There seems to be a turning point around a bias of 0.2 when the number of black workers who are passed over declines less sharply. This result was found for only about 50 repetitions per bias level and needs to be repeated on more iterations to confirm this trend.

Overall, once the manager bias level has increased past 0.8, the proportion of white and black workers becomes more equal in each level.

Experiment 3

The first figure shows that, as executive promotion bias increases (likelihood of promotion for black workers also increases), the proportion of black workers in the executive level increases. In this simulation, the manager promotion bias is held constant at 1. This means that white and black workers are equally likely to be promoted to manager positions. However, the top figure shows that black workers make up the majority of those in the manager position throughout the experiment (orange line below 50%). This occurs because the executive promotion works to promote more white workers to the top leadership roles, leaving black workers behind in the manager positions. Once the bias goes past 0.7, this disparity reduces.

Similar to the second graph from Experiment 2, the number of black workers passed over for promotion to the executive level decreases as executive bias level increases. The trend seems more uniform for this simulation. However, more runs will need to be executed to confirm this finding.

Implications and Future Directions

Most of the results from the simulations were expected. However, it is interesting that even for the default biases set which are relatively 'favorable' (0.8 manager bias and 0.6 executive bias) the disparity between white and black worker agents in the top leadership position can be significantly high (70% white in executive level).

Although increasing the proportion of black to white workers decreases the disparity, this simulation does not represent a realistic context. In the real world, it is not ideal that issues of inclusion can be addressed by merely increasing the number of black workers to surpass the number of white workers. Furthermore, this model ignores the presence of hiring biases. In the setup for this model, there is a 50/50 proportion of white and black workers that are placed in the entry level. In reality, however, the representation of black workers is likely disproportionate even in lower levels of companies. Regardless, it would be more beneficial for promotion biases to be addressed directly.

This model adds to existing literature and models on work discrimination contexts by modeling level-specific promotion biases. Instead of using one type of promotion bias across all levels, this model employs two types of promotion biases. This allowed for separate simulations to investigate each bias individually. In particular, it was interesting to see how changing manager bias but holding executive bias at 1 still resulted in a disparity between white and black workers at the executive level, likely reflecting a bottleneck effect wherein black workers are restricted from entering the manager level and therefore never have the opportunity to be promoted to the executive level.

There are numerous future directions for this model. Due to its simplicity, there are many potential avenues to study more complex issues related to promotion and workplace discrimination. For instance, it is possible to include more individual-level attributes such as individual performance level to help determine whether promotions occur. Another simple addition to the model could include more types of worker agents with other promotion biases to model the differing biases that affect certain populations. For instance, although women in general are promoted less than men, black women are less likely to be promoted than white women. Another potential future direction already alluded to in this report is the addition of a hiring bias. It would be interesting to more accurately model the representation of black and white workers at the hiring stage and in entry levels to execute a more accurate experiment of how these biases affect the representation of black workers at tope leadership levels. Finally, this simple model uses three generic levels to represent the hierarchies of a company. In reality, companies operate with many different departments and divisions that interplay and are directed by a fewer number of workers in the top leadership roles. It would be interesting to model a more realistic structure of company dynamics to model how promotion biases in different departments affect equitable representation in top leadership positions.

References

ZHANG, CHIBIN; Gaudiano, Paolo (2020): An Agent-Based Simulation of How Promotion Biases Impact Corporate Gender Diversity. Advance. Preprint. https://doi.org/10.31124/advance.12400691.v1

Henry Smart. NetLogo Model: Local policing and Colorism (2016)

McKinsey&Company, Women in the Workplace Report (2018)