The Petrie Multiplier: Why an Attack on Sexism in Tech is NOT an Attack on Men

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Image links to large nonlooping animation.
Looping version also available.

If you don't think sexism in Tech and Computer Science is a major problem, you really have not been paying attention. The seven links in the last sentence are to seven different incidents displaying appalling sexism - or worse - in Tech, so may upset you. And in case you feel my selection does not include some of the "best", i.e. worst, incidents, that's because I have selected these seven just from the last two months.

So it's everybody's responsibility to attack sexism in Tech. Unfortunately, this can often be viewed as an attack on men.  

So we need a powerful argument that an attack on sexism in Tech is not an attack on men. 

Here it is.  I call it the Petrie Multiplier. 

The wonderful thing about the Petrie Multiplier is that there is nothing in it about men being worse people or more sexist than women. And still we get women experiencing dramatically more sexism than men. It's because of the gender disparity in Tech, and the fact that this multiplies up to the detriment of the minority group. 

The Petrie Multiplier is the amazing effect that the amount of sexism experienced by women compared to men goes as the square of the gender ratio in Tech. And this is assuming that women are equally sexist towards men as men are towards women.  

The Petrie Multiplier is not hard to explain, so I'll do it in this post.  It was invented by Karen Petrie, but named by me since she is not so immodest to call it after herself!  

Let's say that we have 20% women and 80% men in Tech.  And that 20% of people make inappropriate remarks or other sexist moves towards people of the opposite gender.  So 20% of men make sexist remarks to women, and 20% of women make sexist remarks to men.  

Let's start with 50 people.  Here's a picture, where the darker squares are people who make sexist remarks and the lighter circles are people who don't.  Pink is for men, and blue for women.  Given the 20% ratios, we have 40 men and 10 women, and 8 of the 40 men sometimes make sexist remarks towards women, while 2 of the 10 women make sexist remarks to men. I can't emphasise enough that there is no difference in sexism between the genders.  

Women are blue and men are pink, of course, because those are the gender-appropriate colours. As has been said, "The generally accepted rule is pink for the boys, and blue for the girls. The reason is that pink, being a more decided and stronger color, is more suitable for the boy, while blue, which is more delicate and dainty, is prettier for the girl." That was said in 1918, so think about that change over the last 100 years if you think that some other difference (e.g. gender ratio in Tech) cannot be changed.  

But if you really hate dealing with pink=man, there's a pink=woman version at the end of this post.

Now we'll let some sexist remarks start flowing. I'll indicate this by an arrow from one of the dark square boxes to one of the people of the opposite gender.

The first one is a man (near the bottom), being sexist towards a woman (near the top).  The second is a woman on the right being sexist to a man.  The lengths of arrows have no significance, but are just chosen by the graph layout program. 

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. 

Of course it gets worse. The unluckiest woman experiences nine incidents.  On average? The mean number of sexist remarks per man is 0.35, while for women it is 5.6.  There's a gender disparity of 4:1 but the disparity in experience is 16:1.

Men are no more sexist than women in this thought experiment, but women's experience is sixteen times worse than the men's.

The maths that explains this is simple. With 20% women the gender ratio is 1:4.  So there are 4 times as many men to make sexist remarks, so 4 times as many sexist remarks are made to women as to men. But there are 4 times fewer women to receive sexist remarks, so each individual woman is four times as likely to receive a given remark than an individual man is.  These effects multiply, so in this example the mean number of sexist remarks per woman is 16 times the number per man.  This holds in general, so with a gender ratio of 1:r, women will receive r² times as many sexist remarks as men. 

That is the Petrie Multiplier. An argument that an attack on sexism in Tech is NOT an attack on men. 

Image links to larger animated gif without looping.

Update: One of the first comments I got was that the pink/blue swap was confusing.  So here is a version with the colours swapped to the current gender-colour stereotypes instead of the ones from 95 years ago.

Update 20 October 2013.  Here's a video of me talking about the Petrie Multiplier to our students, part of a longer talk. 

Update 20 October 2013: One of the most common remarks on the Petrie Multiplier is that men have a quota of sexist remarks to make, so have to seek out women to make them to.  David Chart has run a model which eliminates that problem, but gets similar results.  Blog Post here

p.s. In case you're wondering about who Karen Petrie is, she's a senior lecturer in Computer Science at Dundee University.  Is she a geek? These photos might help you decide.

Karen Petrie in St Andrews on her wedding day, flanked by her wedding cakes, or more properly wedding pixels. Karen is blonde and wore a light dress, but has never needed rescuing from a castle. Her husband is indeed dark haired but does not wear a moustache and has been known to pay other people to do plumbing.

Images © Ian Gent, 2008.
Reusable under a Creative Commons License

Credits: Thanks to Karen for the effect of course, plus Chris Jefferson for helping with a python script to generate the random graphs.  

Copyright: All images are created by me, but I am putting all images of the Petrie Multiplier into the public domain so they can be used freely, while the photos on this page are licensed CC.

If somebody has come across the Petrie Multiplier under a different name, i.e. if somebody invented it before Karen, please let me know so I can give them credit.