## A Bayesian norm-relevancy account of gender

This is sketchy thinking in progress…

The core idea of Jenkins’ 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 (there’s a lot more to the account than this – forgive me and please read the original). I’m not sure if this is enough to define gender; however, I think it’s an interesting idea for how 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 do the sums for me. 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 inferĀ  gender and at present the probabilities are 49-49% for man/woman and 1% for non-binary. 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 Non-binary
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 non-binary 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 non-binary 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 non-binary raises from 1% to 20% since there are likely to be more non-binary 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 non-binary 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 non-binary is 4%. Again, it is unlikely that you would infer that you are non-binary.

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

To emphasise again, there are many more varieties of gender identity here and an obvious thought might be that gender nonconforming but still cis man or woman could apply – especially if someone views gender as closely 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 non-binary is closer:

We 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 non-binary people. Suppose all the norms are experienced as irrelevant (it works the same for relevant):

Now the most probable gender is non-binary (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 non-binary. 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 non-binary. Now we get a strong inference towards non-binary 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 non-binary has a big impact on whether someone decodes their gender that way.
3. As the number of norms increases, it is easier to infer non-binary 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 non-binary.

More experiments needed.