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We introduce a model based on Ordinary Differential Equations to describe howtwo mutually exclusive groups progress through a career hierarchy, whether in asingle organization, or in an entire economic sector. The intended applicationis to gender imbalance at the top of the academic hierarchy in EuropeanUniversities, however, the model is entirely generic and may be applied inother contexts also. Previous research on gender imbalance in Europeanuniversities has focused on large-scale statistical studies. Our modelrepresents a point of departure, as it is deterministic (i.e. based on OrdinaryDifferential Equations). The model requires a precise definition of theprogression rates for the different groups through the hierarchy; these are keyparameters governing the dynamics of career progression. The progression ratefor each group can be decomposed into a product: the proportion of groupmembers at a low level in the hierarchy who compete for promotion to the nextlevel a given year, multiplied by the in-competition success rate for the groupin question. Either of these two parameters can differ across the groups underconsideration; this introduces a group asymmetry into the organization'scomposition. We introduce a glass-ceiling index to summarize this asymmetrysuccinctly. Using case studies from the literature, we demonstrate how themathematical framework can pinpoint the proximate cause of the glass ceiling inEuropean academia.

A differential-equation model shows the proximate cause of the glass ceiling in European academia