ABSTRACT We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through a career hierarchy, whether in a single organization, or in an entire economic sector. The intended application is to gender imbalance at the top of the academic hierarchy in European Universities; however, the model is entirely generic and may be applied in other contexts also. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e., based on Ordinary Differential Equations). The model requires a precise definition of the progression rates for the different groups through the hierarchy; these are key parameters governing the dynamics of career progression. The progression rate for each group can be decomposed into a product: the proportion of group members at a low level in the hierarchy who compete for promotion to the next level a given year, multiplied by the in-competition success rate for the group in question. Either of these two parameters can differ across the groups under consideration; this introduces a group asymmetry into the organization’s composition. We introduce a glass-ceiling index to summarize this asymmetry succinctly. Using case studies from the literature, we demonstrate how the mathematical framework can pinpoint the proximate cause of the glass ceiling in European academia.

中文翻译：

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基于微分方程的职业发展玻璃天花板模型

摘要 我们引入了一个基于常微分方程的模型来描述两个相互排斥的群体如何在职业层次中进步，无论是在单个组织中，还是在整个经济部门。预期应用是解决欧洲大学学术等级顶端的性别失衡问题；但是，该模型是完全通用的，也可以应用于其他上下文。先前关于欧洲大学性别失衡的研究主要集中在大规模统计研究上。我们的模型代表了一个出发点，因为它是确定性的（即基于常微分方程）。该模型需要通过层次结构对不同组的进展率进行精确定义；这些是控制职业发展动态的关键参数。每个组的晋级率可以分解为一个乘积：在给定年份竞争晋升到下一个级别的层次结构中低级别的组成员的比例，乘以相关组的竞争成功率. 这两个参数中的任何一个在所考虑的组中都可能不同；这在组织的组成中引入了群体不对称。我们引入了一个玻璃天花板指数来简洁地总结这种不对称性。使用文献中的案例研究，我们展示了数学框架如何确定欧洲学术界玻璃天花板的近因。乘以该组的比赛中成功率。这两个参数中的任何一个在所考虑的组中都可能不同；这在组织的组成中引入了群体不对称。我们引入了一个玻璃天花板指数来简洁地总结这种不对称性。使用文献中的案例研究，我们展示了数学框架如何确定欧洲学术界玻璃天花板的近因。乘以该组的比赛中成功率。这两个参数中的任何一个在所考虑的组中都可能不同；这在组织的组成中引入了群体不对称。我们引入了一个玻璃天花板指数来简洁地总结这种不对称性。使用文献中的案例研究，我们展示了数学框架如何确定欧洲学术界玻璃天花板的近因。