As part of an analysis of some things, we happened upon an interesting sort of paradox involving the benefits of classroom and small group diversity. Let me explain the assumptions (most of which I think are reasonable for a college physics class, for example, although simplistic):

- We’re looking at gender diversity, and assuming a binary, for this model. Our students are boys and girls. At the classroom level, there is a certain level of diversity which we can parameterize by, for example, the fraction of students who are girls.
- Students work in groups of 4.
- Because of stereotypes associated with the class, some of the girls (but not the boys) prefer to work only with other girls and will form all-girl groups. Let’s call this self-segregation, and we can parameterize it by the fraction of girls who choose to work only with other girls.
- Aside from the girls who self-segregate, all other students join groups randomly, without regard to gender or other factors (I use binary probability distributions).
- Compared with single-gender groups, groups that have 1 girl and 3 boys are less effective in terms of learning outcomes and experiences (I’ll call them “toxic”), perhaps because of in-group/out-group effects within the culture of a masculinized discipline or classroom. Groups with 2 or 3 girls are about as effective as single-gender groups.
- Because of an intervention, we hope to change (ie: decrease) the fraction of girls who choose to self-segregate.
- We are interested in increasing the fraction of girls in a classroom in which they are traditionally a minority.

Then, for some values of the segregation fraction and the fraction of girls in the class, decreasing segregation and/or increasing the fraction of girls in the class will *increase* the fraction of toxic groups, which could have a net detrimental impact on outcomes/experiences. Or, in other words, sometimes, even though women benefit from working together, increasing the fraction of girls in the classroom will result in girls being isolated, and thus performing worse and having worse experiences. Likewise, an intervention that makes students feel more comfortable in the classroom may, in some cases, be net harmful.

Here’s a graph. Imagine self-segregation is 0.5 and your class is 0.25 women (blue line). If you increase the fraction of women in the class to 0.35 (orange line), the fraction of groups with 1 woman & 3 men *increases*. If you introduce an intervention that reduces the self-segregation fraction to 0.4, the fraction of groups with 1 woman & 3 men *increases*.

This isn’t a novel idea. Girls in a boy-dominated class have their self-defense mechanisms in place. They know that being the only girl in a group of all boys is hazardous. They prefer to work with other girls as a way to avoid that experience. Well-intended changes that disrupt that equilibrium without addressing the core inequity may have negative consequences.

Anyway, I thought that little calculation was sort of interesting. Thanks for reading!