# An Agent-Based Simulation of How Promotion Biases Impact Corporate Gender Diversity
## 5 Results
### 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 [31]. 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 a 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 towards the executive level, that funnel is straight in the absence of biases, it becomes a bit narrower at higher ranks when the promotion bias is low and becomes dramatically narrower when the 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 but not the promotion bias would lead to a narrower but straight funnel. 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 6A, we see that setting the promotion bias to 0.3 and the hiring bias to 0.4 results in just over 30% 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 6B, the promotion bias remains at 0.3, but the hiring bias is lowered to \(-0.1\) so that the recruitment at entry level favors women. As expected, the bias favoring the hiring of women widens the base of the \"funnel,\" leading to approximately 60% women at the 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 6C, the promotion bias is lowered to 0.2. With the absence of a hiring bias, women make up more than half of the entry level, while the somewhat lower promotion bias leaves nearly 25% women in the top ranks. These results closely match the gender data reported by McKinsey for the Banking and Consumer Finance sector. Finally, Figure 6D 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. 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:  
\[RMSD_{i}=\sqrt{\frac{\left(LO_{D}-LO_{S}\right)^{2}+\left(L1_{D}-L1_{S}\right) ^{2}+\left(L2_{D}-L2_{S}\right)^{2}+\left(L3_{D}-L3_{S}\right)^{2}}{4}}\]  
where \(RMSD_{i}\) 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.