No doubt many of my readers are aware that there is a stream of feminism, which calls itself “gender critical”, that rejects the idea that transgender women are women and aims to “protect” cis women from having these women in women-only spaces. In the 1970s and 1990s this manifested as an internecine feminist turf war over whether trans women should be allowed into women’s spaces. This battle appeared to die down in the 2000s but a new generation of gender critical feminists are now attempting to defend women’s bathrooms, sports and changing rooms from transgender women. They seem to be particularly active in the UK, where feminists like Professor Kathleen Stock are attempting to fight changes to the Gender Recognition Act that would lead to people being able to use the bathroom of the gender they identify with, rather than the gender they were born as.

A core demand of these feminists is that only women who were born female should be able to use women’s bathrooms. In this post I am going to use Bayes’ Rule to show that the inevitable consequence of this political position, if it were to be enforced, would be the widespread harassment of natal women. I will also present anecdotal evidence that this is exactly what is happening now as their ideas gain traction, and discuss the inevitable hypocrisy and contradiction in the gender critical position in light of their responses to the concerns that some (primarily butch-presenting) lesbians have raised about their cause.

Content warning: This post will use a lot of language associated with the “woke” American left, like the prefix “cis”, and also the language of these gender critical feminists, like “natal woman” and the weird distinction they insist on between “woman” and “female.” I will explain my choice of language at the end. Bear with me!

Applying Bayes’ Theorem to Bathroom Exclusion

So how does bathroom exclusion work? The goal of gender critical feminists is that women who were not born female – that is transgender women – are not allowed to use women’s bathrooms, and that this exclusion should be enforced through codification in the Gender Recognition Act. They don’t specify exactly what follows from this but the obvious implication is that if a natal woman in a bathroom fears that another woman in the bathroom is actually a natal man she should be able to confront that person and demand they leave and go to the men’s bathroom, fully supported by the force of the law, public opprobrium and if necessary state force (represented in the US, let us remember, by an armed and trigger-happy police force that has little regard for people who do not follow strict white middle-class standards of dress and behavior).

In practice what this will mean is that a natal woman will need to judge whether another woman in the bathroom is a “real” woman or not by her face, clothes and manner. She certainly won’t be able to demand a genital check[1], so her entire means of discrimination will be by a visual check. Now, discrimination of this kind is a statistical process on which a large amount of theoretical work has been done since the 18th century, and in particular in public health we use Bayes’ Rule to determine the effectiveness of a discrimination process. Bayes rule provides us with a formula that links the sensitivity and specificity of a test to the probability of correctly discriminating between two groups. It depends on three essential quantities:

  • The sensitivity of the test, which is the probability that the test will correctly identify a person with a condition as having the condition
  • The specificity of the test, which is the probability that the test will correctly identify a person without the condition as not having the condition
  • The prevalence of the condition being tested

Wikipedia offers an example based on drug testing, but the rule is universal: it applies to any attempt to discriminate between two classes of a thing with a test that is imperfect, and it has some alarming and counter-intuitive results in the case that the condition being tested is rare.

In the case of bathroom exclusion, we want to know the following three things:

  • What is the probability a normal person[2] will correctly identify that a transgender woman is a transgender woman?
  • What is the probability a normal person will correctly identify a non-transgender woman as non-transgender?
  • What is the prevalence of transgender women in the population?

How good do you think you are at the first two of these things? I’m not aware of any tests of ordinary bathroom users, but facial recognition software has reached high levels of accuracy above 90%. So, let’s suppose that we were to put a facial recognition device on a bathroom door that had 90% sensitivity and specificity, and assume that 5% of women are transgender. Bayes’ Rule tells us that we would have a positive predictive value of 32%. That is, only 32% of the women refused access to the bathroom would be transgender women: 68% of women rejected (2 in every 3) would be natal women who had been misclassified as transgender.

Now, I think that 5% is way too high an estimate of the prevalence of transgender women. At 3%, with the same specificity and sensitivity, only 22% of rejections are correct – 80% of women refused admission to the bathroom are natal women. Figure 1 shows the relationship between specificity and this proportion at a prevalence of 3% for three different levels of sensitivity.

Figure 1: Proportion of women harassed in a bathroom who are natal women, for three different levels of sensitivity. Prevalence of transgender women is set at 3%. The x-axis shows specificity (percentage chance of correctly identifying a non-transgender woman is not a transgender woman)

As should be quite clear from this figure, even at very high specificity – for example where you are 95% likely to correctly identify natal women as natal women, and 99% likely to identify transgender women as transgender women, more than half of all women rejected from the bathroom will be natal women, not transgender.

Do you think that most women using bathrooms have greater than 95% accuracy at accurately determining other women’s birth gender based solely on their appearance? Do you think they have better than 98%? If not, then you are basically setting up a system of harassment of natal women. I have prepared figure 1 in terms of specificity because it is specificity that determines how many natal women you harass in your project to exclude trans women from bathrooms. By way of comparison, the specificity of commonly-used HIV tests is better than 99.998%: less than 1 mistake in 50,000. Can you be that good?

How will discrimination work in practice?

Bayes’ rule is an absolute law of discrimination tests, not some weird philosophical notion. If you set out to discriminate between two groups of people your results are determined by Bayes’ Law, without exception. It applies equally to HIV tests, gender selection, screening terrorists at airports, or picking penis size from nose length. Those three numbers – prevalence, specificity and sensitivity – determine how well you discriminate, without any exception in any cases. When you stride across the bathroom to grab that girl and tell her she’s not a “real” woman and should go to the urinal, you make yourself subject to Bayes’ Law.

Of course in practice your sensitivity and specificity depends on something: you don’t discriminate randomly, but on the basis of certain visual cues. What are those cues? Of course they will be markers of femininity: breasts, long hair, feminine facial features, make up, feminine style clothes. This will be especially the case if the Gender Recognition Act is not changed and a narrative of exclusionary behavior is established that encourages ordinary cis women with no experience of trans issues to begin singling out women for exclusion. These women will have no idea what trans women look like, how much they can “pass” as natal, or what kind of styles and manners butch-presenting lesbians use. The result of this will be what we always see when we establish discriminatory systems: non-conforming people, poor people, non-white people and people with disabilities will be singled out for discrimination. The gender critical feminists will achieve a strange paradox in which in order to be protected from trans women in the bathroom, natal women will have to act extra feminine and hew more clearly to gender stereotypes. We see this being reported now as the bathroom exclusion principle begins to apply. Consider this tweet from a queer Scottish woman:

This woman has had to begin wearing a badge that specifies her birth gender, because feminists keep mistaking her for a transgender woman. This problem will also affect any other women who do not look sufficiently womanly: women with a little bit of facial hair (which is more prevalent in women with certain sorts of illness), sportswomen who don’t dress femme, non-white women who confuse the white majority’s facial recognition, butch-presenting lesbians, and (particularly ironically) feminist women who reject standard stereotypes of feminine dress and behavior. That 80% of women excluded from bathrooms who are actually natal women and not transgender are more likely to be non-white, disabled, or non-gender conforming. They’re also more likely to be lesbians.

This is what gender critical feminism’s completely uncritical approach to bathroom exclusion will do. Here is another example of this, tweeted by a butch-presenting lesbian:

How have gender critical feminists responded?

The first thing to note about gender critical feminists is they seem to be very ignorant of the history of this debate. Holly Lawford-Smith seems to think the whole thing became a feminist issue in the 2010s, and appears to be completely ignorant of the history of transgender wars in women’s spaces in the 1970s and 1990s. Kathleen Stock, one of the major proponents of bathroom exclusion in the UK, responded to the above tweet with this:

“Worse things happen at sea.” Clearly, Stock is willing to throw her lesbian comrades under the bus in order to attack transgender women, and has given no thought to the relative balance of probabilities. She and her colleagues in the gender critical world know nothing about how this discrimination will actually work, haven’t bothered to consider who will be the real victims of their exclusionary practice, and don’t think it will affect many natal women. As I have shown, quite the opposite is the case: the majority of people affected by this exclusionary approach will be natal women.

But the gender critical feminists have become increasingly radical as they have been challenged more on this. Not only do they not take the risk of exclusion seriously, they have also begun to make their definitions stricter and more exclusionary. We see this particularly in response to the controversy around Caster Semenya, where a lot of gender critical feminists appear to have decided that she is “male” on the basis of having difference in sexual development. See, for example, this reddit thread in which they debate whether she is a man or not. So in response to criticism of their original exclusionary position they have extended their definition from “born with female genitals” to “born with female genitals AND normal testosterone.” I don’t think it’s a coincidence that these white feminists from a rich European country have decided to define a black woman who beat feminine-presenting white women as actually a man: this is another example of how their discriminatory practices will play out in practice, as a series of overlapping forms of prejudice work to punish the poor, the dark-skinned and the disabled far more effectively than the wealthy, white, feminine-presenting heterosexual women who make up the majority of the female population. Their concern with “protecting” women is really only about middle class cis white women.

The inevitable hypocrisy of trans exclusion

The underlying principle of gender critical feminism appears to be that sex and gender are different, and that gender differences need to be eliminated. Somehow this has been twisted to mean that trans women who choose to present as feminine – wearing dresses, make up and long hair – are simply “acting” female and aren’t really women at all. Before she was banned from twitter Holly Lawford-Smith liked to criticize transgender women who expressed happiness at successfully passing as women, deriding them for thinking that their appearance and their gender had any connection. Yet when it comes to pushing trans women out of women’s spaces these feminists will necessarily have to judge on the basis of how women present, not who they are. Sure, if they successfully get transgender women excluded from women’s prisons and women’s sport they may be able to do it on the basis of checking genitals (though see my footnote 1 below), but when it comes to bathrooms, women’s spaces on campus or at work, prayer rooms, women’s swimming pools and women’s beaches, they’ll have to do it entirely on the basis of how these women present. And like all human beings everywhere, they will be most likely to believe a woman is a woman if she looks femme. The more strongly they push this transgender exclusionary principle the more they will be forced to judge by feminine presentation.

Worse still, once they release their prejudices into the wild with the backing of the state, ordinary non-feminist women with no experience of trans issues will be the ones doing the judging and excluding. And you can bet that when those women decide to exclude a girl from the bathroom they won’t do it by themselves: they’ll call their masculine-presenting cis white boyfriends, or the police, to help them do it. This will lead to women with facial hair, manly physiques, and non-femme aesthetics being harassed, beaten up and potentially imprisoned (in male-focused custodial settings!) for the simple crime of not looking girly enough. Once it is released in the wild, gender critical feminism will become a feminism of harassing women who do not conform with patriarchal expectations of their physique, clothing and manners.

And that is not feminism.

Conclusion

Gender critical feminists need to drop this bathroom exclusion stuff and their opposition to the changes to the Gender Recognition Act. It is leading to the harassment of lesbian and transgender women now, and if their campaign is successful it will lead to much more harassment of non-conforming women. Rather than protecting natal women from men, it will lead to natal women being harassed by cis women, their natal male boyfriends, and the violent agents of the state. They also need to recognize that there is a fundamental hypocrisy at the heart of their exclusionary policies, and the only way that they can be put into practice is by accepting and reinforcing the worst patriarchal norms of gendered behavior and appearance. Their feminism is very bad for transgender women but it is also bad for all women who do not conform to gender stereotypes. It is toxic, dangerous, hypocritical and confused, and they need to rethink their whole approach to gender.

A note on language

I want to target this post at people who support gender critical feminists’ approach to exclusion of transgender women from women’s spaces, and so in the title and much of the text I have used their terms for things: I have used their name for themselves, and their language of “natal women” and “born women”. I also haven’t touched on the issue of trans men, an issue that gender critical feminists are extremely uncomfortable talking about because it completely ruins their ideological certainty. However, I think that the language they use is wrong and also highly unpleasant. They aren’t “gender critical”: it has been made clear by their feminist critics that they haven’t read the literature on this, and don’t understand the history of or long-standing theoretical debates about transgender issues within feminism. They also haven’t bothered to be very critical of the potential consequences of their beliefs. I think they are far better described by the acronym their opponents give them: TERF. They want to exclude trans women from women’s spaces, which makes them trans exclusionary, and their feminism is certainly radical, though not in the sense they want to believe. So they should be called TERFs, and we should not subscribe to their false dichotomies of “natal” versus trans women. We also should not adopt the horrible American practice of calling women “females” as if they were animals. So although I have used their language in this post, I don’t like it at all and I think it’s another part of their philosophy that needs to be kicked to the curb.

fn1: It’s worth bearing in mind that even a genital check is possibly not sufficient if the trans woman in question has had gender confirming surgery, since most cishet women have very little experience of or exposure to other women’s genitals in any detail, and might not be able to identify the difference between “real” genitals[2] and surgically designed genitals. We’ll come back to this issue later in the piece.

fn2: Here I use the word “normal” to indicate that the person is a member of the population with a standard education, upbringing and level of political awareness, not to suggest that natal women are “normal” and transgender women are not normal