## A Bayesian norm-relevancy account of gender

The core idea of Katharine Jenkins’ (2018) norm-relevancy account of gender is that someone’s gender is defined in terms of the gender norms they experience as relevant – whether or not they comply with those norms. I’m not sure if this is enough to define gender; however, I think it’s a very interesting theory of how people – especially trans and nonbinary people – might decode their gender. Jenkins uses a crisp classical binary logic approach. This blog post is an attempt to explore what happens if we add probabilities.

I’m using Bayesian networks because they are well-supported by software that does the sums (the analyses below were produced using GeNIe Modeler). The direction of the arrows below is not meant to imply causation. Rather, the idea is from the assumption that someone is a particular gender, it is straightforward to guess the probability that a particular gender norm would be relevant. The Bayes trick then is to go in reverse from experiencing the relevance of particular norms to decoding one’s gender.

Let’s get started with some pictures.

The network below shows the setup in the absence of evidence.

The goal is to infer  gender and at present the probabilities are 49-49% for man/woman and 1% for nonbinary. That’s probably too high for the latter. Also I’m assuming there are only three discrete gender identities, which is false.

Each node with an arrow leading into it represents a conditional probability. The table below shows a conditional probability probability distribution defined for one of the norm-relevancy nodes.

Norm Man Woman Nonbinary
Relevant 20% 80% 50%
Irrelevant 80% 20% 50%

So, in this case if someone is a man then this norm is 80% likely to be irrelevant; if someone is a woman then it is 80% likely to be relevant; and if someone is nonbinary there is a 50-50 split. I’ve set up all the nodes in this pattern, just flipping the 80% to 20% and vice versa depending on whether a norm is for men or for women.

The idea then is to the use the Bayesian network to calculate how likely it is that someone is a man, woman, or nonbinary based on the relevance or irrelevance of the norms.

I have not yet mentioned the Spaces node top left. This is a convenient way to change the prior probabilities of each gender; so in LGBT spaces the prior probability for nonbinary raises from 1% to 20% since there are likely to be more nonbinary people around. This also captures the intuition that it’s easier to work out whether a particular identity applies to you if you meet more people who hold that identity. See the picture below. Note how LGBT is now bold and underlined over top left. That means we are conditioning on that, i.e., assuming that it is true.

But let’s go back to cisgendered spaces.

Suppose most (but not necessarily all) of the male norms are experienced as irrelevant and most (but not necessarily all) of the female norms are perceived as relevant. As you can see below, the probability that someone is a woman increases to over 90%

Similarly, for the converse where most male norms are relevant and most female norms are irrelevant now the probability that someone is a man rises to over 90%:

Now what if all the norms are relevant? Let’s also reset the evidence on whether someone is in a cis or LGBT space.

The probability of being nonbinary has gone up a little to 4%, but in this state there is most likely confusion about whether the gender is male or female since they both have the highest probability and that probability is the same.

Similarly, if all the norms are irrelevant, then the probability of nonbinary is 4%. Again, it is unlikely that you would infer that you are nonbinary.

But increasing the prior probability of nonbinary gender, for instance through meeting more nonbinary people in LGBTQ+ spaces, now makes nonbinary the most likely gender.

To emphasise again, there are many more varieties of gender identity here and an obvious thought might be that someone could be gender nonconforming but still a cis man or woman – especially if someone views gender as coupled to chromosomes/genitals. I think it’s also interesting how the underdetermination of scientific theories can apply to people’s ruminations about identity given how they feel and what other evidence they have.

The situation can also be fuzzier, e.g., where the difference between one of the binary genders and nonbinary is closer:

We undoubtedly don’t have conscious access to mental probabilities to two decimal places(!), so scenarios like these may feel equiprobable.

So far we have explored the simple situation where people are only aware of three male norms and three female norms. What happens if we had more, but kept the probability distributions on each the same…? Now we’re tip-toeing towards a more realistic scenario:

Everything works as before for men and women; however, something different now happens for nonbinary people. Suppose all the norms are experienced as irrelevant (it works the same for relevant):

Now the most probable gender is nonbinary (though man and woman are still far from zero: 24%).

This is true even in cis spaces:

Finally, there’s another way to bump up the probability of nonbinary. Let’s go back to two gender norms, one male and one female. However, set the probabilities so that if you’re a woman, it’s 99.99% probable that the female norm will apply (and similar for men and male norms). Set it to 50-50 for nonbinary. Now we get a strong inference towards nonbinary if neither or both norms are relevant, even in cis spaces.

In summary:

1. It is possible to view norm-relevancy through probabilities and as a sort of Bayesian self-identity decoding process.
2. When there is a small number of norms and (say) 80% chance of a norm being relevant for a particular binary gender, the prior probability of nonbinary has a big impact on whether someone decodes their gender that way.
3. As the number of norms increases, it is easier to infer nonbinary as a possibility.
4. Additionally, if there are only a few norms, but the probability that they apply for men and women is very high, then seeing them as all relevant or irrelevant is strong evidence for nonbinary.

### References

Jenkins, K. (2018). Toward an account of gender identity. Ergo, 5(27), 713-744.

## Labels are for jars…? (Not quite)

‘What are labels for? They’re not glitter, darling, and if you say “identity politics” then you can tootle off right now to your intellectual dark web videos and Spiked columns. What they do is they help me to understand myself, help other people to understand me and help me to find other people who are like me. Categories are not harmful unless you’re put in one unwillingly. Unless you actually think my sexuality, my gender and my disabilities are something to be ashamed of?’

## The first mention of genderqueer in print

‘The fight against gender oppression has been joined for centuries, perhaps millennia. What’s new today, is that it’s moving into the arena of open political activism. And nope, this is not just one more civil rights struggle for one more narrowly defined minority. It’s about all of us who are genderqueer: diesel dykes and stone butches, leatherqueens and radical fairies, nelly fags, crossdressers, intersexed, transexuals, transvestites, transgendered, transgressively gendered, intersexed, and those of us whose gender expressions are so complex they haven’t even been named yet. More than that, it’s about the gender oppression which affects everyone: the college sweetheart who develops life-threatening anorexia nervosa trying to look “feminine,” the Joe Sixpack dead at 45 from cirrhosis of the liver because “real men” are hard drinkers. But maybe we genderqueers feel it most keenly, because it hits us each time we walk out the front door openly and proudly. And that’s why these pages are only going to grow. We’re not invisible anymore. We’re not well behaved. And we’re not going away. Political activism is here to stay.

‘So get out. Get active. Picket someone’s transphobic ass. Get in someone’s genderphobic face. And while you’re at it, pass the word: the gendeRevolution has begun, and we’re going to win.’

Riki Anne Wilchins, In Your Face No. 1 (Spring 1995)