The Petrie Multiplier is the simple mathematical model that explains why gender-imbalanced communities are always going to be unpleasant for someone.
Like a lot of guys, I’m sometimes surprised when an environment I’m part of is described as hostile or unpleasant for women. After all, we think, I’m careful not to make inappropriate remarks, I try to be as welcoming and non-sexist as I can, so where are all these reported microaggressions coming from? If I’m not being rude to women or making sexist comments, and most of the guys I know aren’t doing it either, why do the women I know report so much trouble?
Then I learned about the Petrie Multiplier, a specific application of the Base Rate Fallacy that clarifies how any environment that’s too heavily gendered is going to come off as hostile to the minority gender. It lays out in a simple mathematical model that even if we assume that men and women are equally sexist toward the other major gender, and even if we assume that most people of either gender don’t ever act inappropriately, the simple fact of women being outnumbered four to one means that they’ll experience sixteen times more microaggressions than men in this same model.
Let’s see what happens when we have had 70 sexist remarks made.Let’s look at the difference between the experience of men and women. It’s pretty stark.The luckiest man receives zero sexist remarks. But in fact he doesn’t need to be very lucky, because most men receive no remarks. There is an unlucky guy (bottom right) who receives three sexist remarks, as it happens from the same woman. That is not acceptable, and she should stop. But that’s the unluckiest guy out of 40.The luckiest woman receives four sexist remarks. So let’s get this straight: the luckiest woman out of 10 experiences worse sexism than the unluckiest man out of 40.
…Men are no more sexist than women in this thought experiment, but women’s experience is sixteen times worse than the men’s.
Now, normally I’m leery of models that reduce human interaction down to mathematical equations. They tend too often to end up with someone saying “My model predicts that there’s no such thing as racial discrimination, therefore it doesn’t exist!” This one, however, is doing the opposite. It’s not constructing a model and then throwing out data that doesn’t fit, it’s constructing a model that helps explain the way the data keeps coming out in the real world.
There’s a couple of decent statistical criticisms to be made of the simple model, such as that it assumes that people will seek out someone of the opposite sex if there’s not one handy, just to be mean to them. A gent named David Chart ran the numbers correcting for that, reducing the chance that sexist people would aggress in the first place. He also tried reducing the percentage of people who even held sexist attitudes, and ran a variety of different scenarios. Interestingly, it didn’t help much.
What happens if we drop the probability of sexism, so that only 10% of men and 10% of women make sexist remarks, and then only do it 20% of the time?
The results of one 500-encounter run look like this:
Men who encountered 0 sexist remarks: 40 (100%)
Women who encountered 1 sexist remark: 2
Women who encountered 2 sexist remarks: 3
Women who encountered 3 sexist remarks: 2
Women who encountered 4 sexist remarks: 1
Women who encountered 5 sexist remarks: 1
Women who encountered 8 sexist remarks: 1
So, even in a situation in which sexism has been almost completely eliminated, women are still encountering a substantial amount of sexism.
One of Chart’s scenarios even involves making women substantially more sexist than men, and the average woman still encounters more sexism.
The part of the math that there’s no getting around is that as long as some level of sexist microaggressions exist, heavily gender-imbalanced spaces are going to feel hostile to the gender that’s in the minority. (This, incidentally, explains why trans and genderqueer folks tend to get hassled no matter where they go.)
Indeed, the other side of this turns up too. In communities that are predominantly female, one is (in my experience) far more likely to hear tasteless remarks about how men are no good. We’re all liars, we’re all idiots, we’re all pigs or dogs or whatever… you know the kind of nonsense. And I think the math is pretty much the same there. Most women aren’t making those remarks, but when the gender ratio is skewed heavily enough, the overall mass of sexist comments becomes great enough to easily perceive.
So gents, the next time you hear that your company, or your college department, or your comic book store, or whatever is a hostile space for women, don’t get hung up on the point that you’re not doing anything sexist. You don’t have to be; it’s not about you. As long as sexism exists at all, it’s mathematically inevitable that a gender-imbalanced space is going to be unpleasant for the minority gender. The way to fix that is to move beyond your personal virtue, which is a good start, and look at correcting that gender balance.