Gender equity either on paper or by forcing people to change research fields

Suppose that a university employs roughly equal numbers of men and women overall, but the proportions of the genders differ across research fields, or across research and administration, and the university wants gender equality within each subfield. Using the narrowest definition of a research field, each field has either one or zero people, so in the smallest fields, gender equality is impossible. From now on, the focus is on fields or administrative units that have at least two people.
Gender equity can be achieved on paper by redrawing the administrative boundaries or redefining research fields. A simple algorithm (not the only possible algorithm) is to form pairs of one male and one female employee and call each such pair an administrative unit. Larger units can be formed by adding many male-female pairs together. If the numbers of men and women are not exactly equal, then some single-gender pairs will be left over, but most administrative units will have perfect gender equality.
The same idea can be used less radically by reassigning people who do interdisciplinary work and could plausibly belong to multiple research fields. Each person who is „between” fields gets assigned to the field that has a smaller fraction of that person’s gender. This increases gender equality in both the field that the person joins and the field that the person left. The field with a bigger surplus of that person’s gender loses one of that gender, and the field with a smaller surplus gains one.
Other than reassigning people or redrawing administrative boundaries, gender equity requires inducing people to change their research fields. To some of my colleagues, directing researchers to change their area is ideologically unacceptable. However, if equity is the goal and people’s field change is necessary to achieve it, then several methods can be used. The inducements can be softer or harder. A hard inducement is a hiring policy (and job ads) that restrict hiring to only one gender. The same can be done with promotion and retention. If this policy was explicitly stated to everyone, then it would become more effective, and also more acceptable to people than when they are surprised with it upon applying for promotion.
Soft inducements consist of hints that one gender is preferred, which are usually stated in political doublespeak like „we are committed to equity” or „we are an equal opportunity employer”. If many more candidates of one gender apply, then giving all candidates an equal opportunity of getting hired does not result in equal proportions of men and women employed. I am in favour of clear guidelines and transparency, for example of explicitly stating in job ads and promotion policies that the underrepresented gender is preferred, and which gender is currently underrepresented. Clearly telling people that switching fields is good for their career is likely to have a bigger effect than the currently used hints.
It may be easier to shift the research areas of people who are earlier in their careers. Encouraging more young people of a given gender to go to an area where their gender is underrepresented is one way of inducing them to change their field (relative to their preference).
Current equity policies are focussing almost exclusively on the inflow of employees. Gender balance can also be improved by managing the outflow, for example by offering early retirement schemes to one gender, or expanding these to a wider age range for one gender. If there are gender differences in the propensity of accepting certain inducements to leave, then the same inducements can be offered to both genders (seemingly gender-neutrally), with the desired result that one gender exits more.

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