Sunday 13 October 2013

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

This image is explained below.
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
Creative Commons Licence

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.


  1. Pretty clever! But isn't it simplistic (by which I mean, probably wrong) to assume that sexist people make sexist remarks on a regular schedule whenever they feel that sexist urge - say, once a day - and make a great effort to hunt down somebody of the appropriate sex to make it to?

    In other words, shouldn't there be a term here for the number of interactions between people of each gender, because those are the natural opportunities for sexism?

    And then, because there will be fewer interactions between men and women than between men and men in cases where women are outnumbered, aren't you going to end up concluding that in order to explain the obvious situation that women experience much more sexism, then men must be (on average) arseholes after all? :)

    I agree there's a big problem with men in the tech industry getting crazy defensive when it comes to this kind of thing, and it isn't helpful to demonise some of the people who need to make the problem better. So, all in favour of the intention, but this feels like sleight-of-hand to me.

    1. Thanks quen-elf.

      Yes of course it's simplistic. I'm not sure I want to agree it's wrong, because it's more of a thought experiment. That is, the maths is right, but indeed it might well not apply to real life, but I'm not sure that makes it wrong.

      You are right that in this thought experiment men who make sexist remarks have a certain number they have to use in a given time. So they might end up seeking out women to make sexist remarks to. Which does sound a bit unrealistic. On the other hand, if men are not regularly encountering women, that is a major problem in itself. Also, I think in real life it's reasonable to expect that the fewer women there are, the more likely they are to encounter sexist remarks: not because people are seeking them out but the more male-dominated an environment, the more likely sexist comments will be made thoughtlessly.

      So you do identify a genuine issue with the thought-experiment. But I hope it's not (and it certainly wasn't intended as) sleight-of-hand.

      And while you are criticising the argument it never occurred to me you were trying to demonise me or the argument, so thanks very much for the very friendly tone of the criticism!

    2. Well, it's just a law-of-large-numbers situation. There is some mean-number of sexist remarks that are made by men (and women) to men (and women) over some time period. On average, the average sexist person will regress to the mean. One important thing I think you might miss is that some sexist remarks occur, but are hidden (by virtue of, eg, a man making a female-oriented sexist remark to only other men). But even so, that'd only reduce the overall experience of sexism to be bounded by the ratio 1:r on the bottom, and 1:r^2 on the top. With Reality somewhere in between. That's still O(r^2) more sexist remarks made at the minorty -- this formulation also reveals an interesting fact -- The best-case scenario for systems in which there is a non-zero amount of sexism is that there will be Theta(r) more sexist remarks made at the minority, where r is the ratio of one gender to the other. This value, of course, is minimized at an even number of each gender.

      The nice thing about this metric as well is that it generalizes pretty cleanly to many different groups. We might also consider casual Racism, Transphobic, Homophobic, Politiphobic, etc remarks and examine clearly how people of varying classifications feel in the context of our community.

      I'm a mathematician by training, so it is my first instinct to find ways to measure and understand problems before trying to deduce methodologies to solve them. These Petrie Graphs/The Petrie Multiplier offer a really effective way to gain insight to this problem, and -- if we find a decent way to measure the 'rate of sexism' -- or more generally the 'rate of phobia' -- then we can start to evaluate how varying strategies effect change in either the ratio of people subject to that phobia/not subject, and in the rate of phobic-remarks/actions made. This is a very necessary and useful tool, thanks for writing about it.

    3. This is very interesting and easy to understand. Thanks for the post and please thank Petrie for her tool to do the analysis.
      While I was reading it, couldn't stop thinking on the hypothesis that both men and women are both as sexist (I mean, have "the same level" of sexism). It would be great to validate it, i.e. by checking what happens to men in environments where the ratio is reversed (much more women than men).

    4. Bijaro, thanks.

      I don't know what happens in reversed situations, but it's important to remember this is a thought experiment, so there's no claim the hypotheses apply in the real world.

    5. Well of course in reverse situations the reverse would be the case, assuming the same scenario as here. It's just a matter of swapping the two variables' names.
      Assuming this fixed ratio of sexism within the population would yield similar results for men in, say, education or nursing, as it does for women in tech probably (i'm not familiar with the gender ratio in the US but here in Italy education and nursing are both very female dominated fields).

      How close to the reality the assumption of a fixed ratio of sexist people actually gets, is still something that can be debated, but it's surely an interesting thought experiment.

      What buggs me, however is, that it would suggest that the optimal outcome (in terms of sexism minimization) would be a completely single-gender dominated/isolated field. On the other hand the optimal outcome in terms of fairness (equal distribution of sexism) would be a 1/1 ratio, i.e. 50% women and 50% men.

      What i'd like to mention, is that this is (i think) not meant to suggest behavior or policies of any kind, it's however a good demonstration to prove a point i think.

      btw. chapeau to Joe Ferdette for using landau symbols!

  2. Interesting.

    I think this model misses something, however. If you set the proportion of offensive actors to 100%, you get that minority still receive quadratically more offensive comments than the majority. But if every comment is counted then this doesn't make sense - you'd expect every actor to receive the same number of comments (from all the other actors), so each minority actor should receive a number of comments from majority actors that is proportional to the imbalance ratio, not to its square.

    The effect that I think needs addressing is that the minority simply have fewer interactions as there are fewer of them. I believe that you should pick interactions uniformly at random rather than picking the offensive ones in the way that you are doing. One way of looking at this is that in any comment from one group to another, the chance of it being a majority -> minority comment is 50%. Independently of the direction, it is offensive to its recipient with probability 20%. But there are fewer in the minority so the density of offensive comments is higher, in proportion to the imbalance ratio.

    With symbols, if the proportion of minority (resp. majority) actors is a (resp. b), the total population is p, the total number of comments uttered per actor is n, and the proportion of offensive actors is s (independently of the choice of group) then if comments occur uniformly at random between actors then there are abnps offensive comments from minority to majority and the same number of offensive comments from majority to minority. There are bp actors in the majority so each receives abnps/bp = ans offensive comments, and there are ap actors in the minority so each receives abnps/ap = bns offensive comments. Therefore each actor in the minority receives bns/ans = b/a times as many offensive comments as the actors in the majority.

    This gives the answer '4' with your concrete numbers which is still fairly horrendous in my book.

    1. the point is that the bias is not uniform - sexist women don't attack everyone, they attack the opposite group (same as the guys do). or to put it more simply: this model assumes that there ar etwo groups, and that the two groups are being jerks to each other, not at random.

    2. Thanks Unknown.

      In your first para, no I'm not missing something. The square effect is unaffected by the sexist remark percentage so it does still hold if 100% of actors are offensive as long as they are offensive only to members of the opposite sex.

      The rest of your post is right though. I.e. it's just a different model with a different result, as you say still horrendous. Remembering that these are just thought experiments rather than claims on how reality is.

      I think which model is closer to reality ... depends.

    3. The number of interactions (pairs) is related to the square of the number of individuals - that's where the squared term is coming from.

      Note that this is true of *any* kind of interaction.

    4. White knighting/chivalry/feminism/foo means a lot of men are sexist against men though, especially when women are present. Also, there's a cascade effect when an asshole women ends up with such men as proxies and a strong bias against any targeted man fighting back in any way. Is that just being ignored?

  3. Wonderful analysis, the only thing I don't like is the assumption that the sexist remarks by a man are made to a woman, and vice-versa. I would expect that given a sexist person making a sexist remark, the distribution of WHO they make that remark to should be in proportion to the target audience size (as a whole). In my real-world experience, this is actually a bit naive, given that a sexist person seems more to feel comfortable making sexist remarks to their peers.

    We can make the assumption that the opposite gender might be more distressed by those remarks, it is NOT okay to assume that gender peers would be okay with them, nor is it okay to assume that they are not harmful to the cause of eradicating sexism.

    1. Yes I agree. That's a good point.

      I think the phrase "sexist remark" is maybe not ideal. I was trying to something which was fairly mild and not a trigger.

      But you are certainly right, I certainly dislike sexist remarks made by other men with or without women present.

      Thanks for commenting.

    2. Yes, and there is one more point. How about whether the sexist remark is anti-male or anti-female? I've been on interview panels where there has been a preference for female candidates. That's clearly sexist.

      Also, it's generally seen as acceptable to make a pro-female sexist comment. "Women are better programmers" is more likely to come across as thought-provoking than sexist. Such a climate can also be seen as patronizing to women - "We need to help women" etc.

    3. I agree that apparently pro female comments can be patronising, so I don't exclude those.
      It is true that I'm ignoring comments overheard, i.e. the model assumes that a sexist remark is made by one person and heard by only one person who is of the opposite gender.

    4. Regardless of what you consider 'sexist', once you establish a definition, the above applies. However, the point of the target audience not being of the gender that's being discriminated against is a very good one. If anything, personal experience teaches me that speaking with people of the same gender actually increases the odds of hearing sexist remarks.

      Assuming that these remarks are only made to and offensive to people of the non-target gender is a mistake. However, although the assumption that all genders are equally sexist is fair, at least for the sake of argument - the assumption that everyone is equally offended by sexist remarks, regardless of their own gender, seems a bit far out.

      Adding to the complexity: in some office subcultures sexism even serves as bonding mechanism and results in peer pressure for others to engage in sexist behavior. I've only worked in male majority environment (as I have a job in software development and design), but I assume women in opposite environments would have similar experiences.

      The basic math of the Petrie Multiplier is sound, but I doubt the model tells us a lot about the actual statistics and experience of sexism - even under a number of generous assumptions.

  4. Lonny Eachus here. I did not realize this account did not have my name on it.

    The "Petrie Multiplier" is nothing more than a specific application of the math behind the "Base Rate Fallacy" in statistics. But I give kudos to Petrie for noticing (or deducing) it independently.

    Without resorting to Wikipedia's statistical symbology, I will describe it here:

    Main Requirement: You have a large population, in which there is a relatively small probability of some occurrence. One example is drug abuse (the Base Rate fallacy is why random drug screening is an abusive practice). But let's use discrimination because it is relevant. These numbers are not intended to be accurate; they have just been pulled from the air for purposes of illustration:

    Say you have a population of 1 million. 900,000 male, 100,000 female.

    Say also, a small BUT EQUAL percentage of each will discriminate against the opposite sex. Let's say 5%.

    So there are 45,000 male discriminators, 855000 male non-discriminators.

    There are 5000 female discriminators, 95000 female non-discriminators.

    Therefore, the probability of a male being discriminated against at any given time is

    males experiencing discrimination = 5000 / 900,000 = about 0.55%

    The probability that a female will be discriminated against in the same time period is

    females experiencing discrimination = 45,000 / 100,000 = about 45%.

    So we see, using a perfectly plausible scenario, that even without either group being "worse" than the other, the smaller group still experiences about 80 times more discrimination than the larger group.

    Pretty big difference, there. But again my point is that this is nothing more than a straightforward application of the math behind the Base Rate Fallacy. Using the same basic mathematical principle, it is easy to show why random drug screening results in many times more innocent people being rejected for hire than "guilty" people.

    1. To be clear: I used 9 to 1 in order to at least somewhat resemble the tech industry ratio of sexes.

    2. Another clarification: in the case of drug screening, it isn't "discriminators vs. non-discriminators" but "false positives vs. false negatives".

    3. Many thanks for your comments, Lonny.

      Certainly your example maths is the same, and indeed I see how the base rate fallacy causes the drug testing example: assuming that there are more false positives than real drug users. I think of this as the "prosecutor's fallacy" which I think is a single example of the base rate fallacy.

      I'm still having a problem understanding why the Petrie Multiplier itself is a direct example of this. That is, I don't see what the prior probability is and then what the extra information is that changes it. Sorry if I'm being dim!

      thanks again

    4. Lonny here again.

      See Example 3 on the wikipedia page. In that example, non-terrorists are analogous to the male population above, terrorists to the famale population. The failures of the system (equal probability of false positives and false negatives) are analogous to male-female and female-male discrimination (also assumed to be equal probability).

      Where the term "base rate fallacy" comes in, is that many people will assume that if the "base rate" of discrimination is 5% on both sides, then both sides will actually EXPERIENCE the base rate of 5%. This shows that to be a fallacy: one side will experience much more, the other much less.

      The "Petrie Multiplier" is simply Example 3, applied to different circumstances.

    5. Thanks Lonny. I think I get it now.

      The specific maths in the Petrie multiplier is different (i.e. the squaring of the ratio), but yes, people thinking that because sexism is equal in the model, women would experience it equally, is an example of the base rate fallacy.

      thanks for that.

  5. @gilbazoid contacted me via twitter because of problems commenting on the blog (sorry about that.)

    What you call the Petrie multiplier is sometimes called the principle of mass action. e.g. In chemical reactions, epidemiological SIR models and in Newton's formula for gravity.

  6. your argument seems sound, yet there is a reductive aspect; i could not find the 'pink=woman version' at the end. was this deliberate?

  7. Not intentionally ... it's not the same size but it's the image just above the word "Update". Click on it for larger animated version (though still not that large).

  8. The above is your opinion and you are entitled to it. However, I don't think that there is a big problem with sexism in the tech community. I've worked in IT for more than 20 years and the only sexism I've seen was by a woman directed towards men.

    IT, science and engineering are male dominated industries and they attract very large numbers of men with behavioural issues such as Asperger's, ADHD, etc. Such men have varying degrees of social issues, i.e. problems with social interactions with people in general, not just women.

    I have followed a lot of the so-called misogynistic events which have resulted in twitch hunts on Twitter and the blogosphere in general. IMHO they have been grossly overblown and have resulted in men losing their jobs to cheers from various quarters. What is missing from this hysteria is the simple fact that the same people are apt to behave inappropriately towards members of their own sex as women.

    I think that women, who may well have behavioural problems themselves, of course, need to be aware that they have chosen to work in an unusual environment with a large proportion of men who suffer from what are rightly considered to be disabilities. The personality clashes they experience are simply different manifestations of problems men have working in the same industry with such people.

    Given that many men in these industries suffer from disabilities, when subjected to attack they are likely to much more severely affected by them than those without such disabilities. Given that those demanding an end to sexism in tech are so hot on their anti-discrimination credentials, I am sure that they will appreciate the need not to persecute people for their (hidden) disabilities. They are in danger of persecuting people, making them lose their jobs and making life extremely unpleasant for people who really do not deserve to be persecuted for health problems they can't help.

    1. There seem to be two entirely separate points here.

      The first is that sexism in tech is not a major or widespread problem. Apparently it is not a problem to you, but I absolutely guarantee you that it is a major problem to many many women. The incidents you read about are the tips of the tip of the iceberg. They are the tip because they are the ones women have the courage to speak out about to an unsympathetic world. And they are the tips because they are not the everyday sexism that women are so used to. Such as the suggestion that women should put up with sexism because they chose to work in tech: absolutely not!

      The second point you have is that people with disabilities should not be subject to attack. That is absolutely 100% right. You seem to imply that people against sexism are somehow anti disabled. There may be such people but I'm not one of them. If somebody has a disability they need to be helped in every appropriate way. An analogy might help: if a kleptomaniac has a genuine illness that makes them steal, they need help and to be supported. But we do not need to tell shopkeepers that they must put up with their stuff being stolen.

    2. By the way, apparently you missed the point that this post was about NOT attacking men in the first place.

      And yes of course I condemn a woman being sexist to a man, and indeed condemned the fictional woman in the thought experiment who was sexist to the fictional man.

    3. I see where your sympathies lie Mr Gent. I believe that you and others exaggerate the trials and tribulations of womanhood considerably. I don't condone overt sexism but I think it needs to be put into context: women do subject men to sexism too and I can imagine working in female dominated occupations has its problems for men.

      I did not suggest that women put up with sexism. Not at all. They should speak up about it. However, I don't think that this should extend to witch hunts culminating in men being sacked for being inconsiderate, whether they have disabilities or not.

      I am not suggesting that people who are against sexism are anti-disabled. I do think that many of the feminists campaigners are ideologues for who this is issue is far more important than anything else on earth and they don't mind who they trample over to prove exactly how important. Something of an industry has grown up around publicising such incidents in extremely strident and unpleasant ways which would not garner much in the way of sympathy from reasonable people. When faced with someone fulminating about perceived misogyny where what we are dealing with is no more than personality clashes and personal misunderstandings, it doesn't elicit much in the way of sympathy either particularly when the intention is turn a molehill into a mountain. All IMHO.

    4. P.S. I'm not sure that I can square your claims that men are not being attacked with men actually being sacked from their jobs. I think for many involved it is very much about attacking men in no uncertain terms.

    5. We agree that women should not put up with sexism, so that's good.

    6. And also, we agree that men should not put up with sexism too.

    7. I, too, work in the IT community, in 3D gaming. I've had colleagues with Aspergers and the whole spectrum of social disorders and you know what? They have never been the problem. Socially uncomfortable does not equal sexist. Some of kindest, most thoughtful (and intelligent) men I've known "suffer" from what you are calling disabilities. In my experience, it's the socially popular guy who is a sexist, and it's usually to get a laugh.

      Even though I've been the only girl in the studio, I've never been personally harmed by sexism. Part of that is because I usually had co-workers who knew where to draw the line between funny and sexist all by themselves. And when they saw some sexist jack-asses demeaning or verbally abusing a woman to make themselves look clever or tough, they put an end to it immediately. Not every tech workplace has a high enough percentage of decent folk (or the right key people) to make that work. A workplace that has the popular sexist jerk in charge can be a nightmare for his targets.

      Your post is unfair to the women who've gone through this while you were oblivious and to the men who are neither 'disabled" nor unable to recognize sexism just because they aren't "jocks".

    8. Annick, thanks for that. It's great to hear you haven't been personally harmed by sexism.

    9. Thank *you* for the Petrie Multiplier and post. Such an excellent visualization.
      I've been very fortunate to work with some terrific teams but I know plenty of people (male and female) who weren't so lucky.

    10. You're very kind, Annick! I only take credit for *naming* the Petrie Multiplier after Karen. But yes, I did do the visualisation (apart from Karen's husband Chris writing a python script). My workflow for doing it was horribly kludgy but I'm delighted you liked the result!

    11. Annick, you speak of your own individual experience with a few colleagues with Asperger's. You should appreciate that there is quite a wide spectrum of behavioural disorders encompassing autism, Asperger's and ADHD. The people you complain of may well be suffering, undiagnosed, from ADHD. You are guilty of judging people every bit as much as they may have judged you. If you appreciate this then you will, hopefully, realise that the problem is two-way and that you are part of it too.

    12. Anonymous

      If somebody has undiagnosed ADHD they need to get it diagnosed. But neither diagnosed nor undiagnosed ADHD excuses unacceptable behaviour. The victim of the ADHD absolutely deserves sympathy and help but not the right to behave badly. If it is absolutely impossible for them to stop themselves, the work or study environment must put mechanisms in place to stop them adversely affecting others.

    13. Anonymous

      Please do not say in one comment that you think women should speak out about sexism, and then say that one who does is part of the problem.

  9. This comment has been removed by the author.

  10. Oh dear, oh dear. What I am saying, Mr Gent, is that both you and Annick are part of the problem. I am not discriminating against Annick.

    Perhaps you don't fully understand what a diagnosis of ADHD means? Essentially, someone with a diagnosis of ADHD has a problem with what is known as executive function(some people with Asperger's are also diagnosed with ADHD - there is a distinct connection because the conditions are adjacent on the autistic spectrum). In other words, the parts of the brain responsible for decision making are malformed, damaged or otherwise exhibit problems. Consequently, people with ADHD are apt to say and do things which some people consider inappropriate and for which they are not responsible. Implying that ADHD people can, somehow, help their behaviour is akin to approaching a disabled person in a wheelchair and advising them that they really could walk if they tried hard enough.

    People with ADHD need understanding of their condition not persecution. Clearly, sexism should not have priority over disablism. All forms of discrimination are equally wrong. ADHD may well be an invisible disability but it can't be assumed that because someone is a "socially popular guy", he does not have ADHD or Asperger's/ADHD.

    I realise that having to take into account the possibility that people who behave objectionably may well themselves be suffering from a disability and therefore not responsible for their actions rather puts a dampener on the indignation of those who want make a big issue of sexism in IT but I'm afraid they must. Any man with ADHD who suffers discrimination on the grounds of his alleged sexist behaviour has a pretty good defence. If he goes on to lose his job over it then he will have grounds to sue for disability discrimination. I would therefore suggest that the "campaign against sexism in tech" adopts a slightly more softly, softly approach to the matter than they have done until now.

    1. Thanks for your comments Anonymous. I consider this piece of correspondence closed. I will delete future comments from you.

      Before you complain about free speech please note that I am giving you the last word and I'm not responding to your last points.

      However I will correct you on one point. You claimed you were attacking me and Annick equally, but the post I was commenting on was clearly addressed to Annick.

    2. To be clear, I do not regard Anon's comments as offensive or I would have deleted them. But I do not think that this part of the conversation is useful. I've given Anon the last word on the substantive points because obviously there's nothing anyone can say to him or her that will stop him or her responding.

    3. Not to my great surprise I've had to delete a new comment from Anonymous declaring that my action in closing this conversation was fascist.

      Anonymous, if there is somewhere else you wish to take this conversation please post a link (e.g. to your own blog) and I'll leave it in here as long as it's not to an offensive site.

    4. {I understand you may choose not to allow this - given the blog is not about this. But if you choose to leave the comments made by this person about ADHD - then I'd appreciate you adding this.}
      As a DIFFERENT anonymous, I have to say that relating ADHD and sexism is absurd and stupid. ADHD is challenging, without question. It is completely misunderstood by most people, even many with ADHD.

      The line of thinking above, were anyone to believe it, seems to mean that it would be understandable (or okay) to be a racist if you have ADHD. That is absurd.

      ADHD may cause you to say what is on YOUR mind and throw ideas out that might cause people to see you as critical (among other things). The KEY point here, is that you would be saying things that are on your mind. So if you ARE a sexist or racist and state that you are by speaking - don't hide behind a legitimate challenge that people have (ADHD).

    5. Thanks very much, different Anonymous. Really nothing for me to say, excellent comments.

    6. I'd like to reply to this last comment as I believe not allowing a right of reply to this would be extremely unreasonable. It seriously misinterprets my views.

      My point is that people with ADHD often say and do things which DO NOT represent their true feelings on various matters. They often speak without thinking because a key aspect of ADHD is that those with ADHD are frequently unable to look ahead and consider the consequences of their speech or actions. They may say things which the hypersensitive would wish to interpret as sexist, racist, homophobic, etc., etc., but they were not meant to be.

      Either anonymous above does not understand ADHD either or chooses not to understand and misinterpret what I'm saying to further their own agenda.

      People with ADHD symptoms and I think there are very many more than is generally accepted, deserve to be given the benefit of the doubt and should not be discriminated against and persecuted as with other minorities. The climate of political correctness is a complete nightmare for anyone with ADHD and in my opinion needs to scaled back in recognition that many people who fall foul of the thought police have this, or other similar conditions.

    7. Ok I'm not going to delete this comment even though I said I would ... maybe I'm just feeling nice today.

      There is a really important point here. The direction of Anonymous (1)'s argument is that some people who make sexist remarks MIGHT have ADHD, and therefore we must accept that some people will make sexist remarks. This is utterly unacceptable. What we do NOT do is accept sexist remarks because the person MIGHT have a medical condition which MIGHT lead them to make the wrong kind of statement.

      If somebody has a diagnosed condition, then understanding must be shown to that person and their condition, absolutely 100%. The only proper way to deal with that is with proper medical advice and training from workplace professionals. And 100% that person should not be discriminated against because of their condition. So the company or other environment takes advice, and trains co-workers to deal with this person effectively and fairly. Also we avoid any negative stereotyping, for example the stereotype that people with ADHD make sexist remarks.

      And if we could try to remember the point of the original post... even if Anonymous 1 is right, if the prevalance of ADHD is gender-neutral, the effect STILL falls more on women and dramatically so.

      This part of the conversation is now closed, for real this time. Anonymous 1 does not and never did have a right to reply. However, the offer to post a link to somewhere else to continue this part of the discussion remains.

  11. Very interesting post! I had never thought about the numbers in this way.

    There seems to be some discussion here in the comments about the words "sexist remarks" and how they wouldn't necessarily go from one gender to the other. The argument was that men wouldn't seek out the few women to express them, but might as well express them to peers. For the moment ignoring same-sex situations, I think perhaps an even better example would be "uncomfortable sexual approaches".

    Putting the numbers at 90%/10% (which is accurate for the type of game development I do), and also considering that men are culturally expected to take initiatives (at least here), it is not hard to see how the average woman could end up getting uncomfortably hit on a hundred times or more for each time the average man is approached in the same manner. I'm sure that specific situation can get rather tedious in a big workplace where you might want to focus on your career!

    1. Thanks... yes I'm certainly aware that your example is also realistic, but I was trying to keep this at a fairly mild level, i.e. not necessarily taking people into more uncomfortable area. Also that even the milder version of sexist remarks is subject to the amplification effect which can make them worse.

  12. The first thing that comes to mind is that this format would be unacceptable if used to "prove" that Islam has a terrorism problem.

    The next thing that comes to mind is how you're using examples of how in many cases adolescents or adult idiots treat people within tech as indicators of problems in tech: that's not fair because it's painting the engineers and scientists as core part of the problem when in reality, the people making threats against game developers can and probably would do that to movie stars, authors, even cashiers.

    Why is this a big deal to me? Because it doesn't give me any useful way to help with the problem. In the office, there are very few women, this is true. I can't fix that because there are very few female applicants. So the problem is further upstream than I can influence out side of encouraging my daughter to pursue her interests.

    But when the news is constantly telling us about the ter'rists who are out to get you, it can start to adversely affect your perception. I fear this can be the same. Can I disagree with a project manager without being called sexist? It can become an impossible debate where accusations fly such as you wouldn't disagree with this if I were a man. I can say I still would until I'm blue in the face.. Impossible argument.

    The last thing I'll say is I don't agree that sexual harassment is a valid measurement of sexism because those behaviors are part of a more general set of inappropriate conduct that doesn't have to cross sex boundaries.

  13. I certainly agree that sexual harrassment is only one measure of sexism and there are many others.

    But I have to disagree with your second paragraph. There are very many examples of men who are in no way idiots treating women in tech very badly. It might make you feel better to call these people idiots, but it's totally unhelpful because nobody could have identified them as such until their behavious was found out. So yes, I do think that some engineers and scientists are part of the problem.

    1. Okay, just to be clear I wasn't trying to suggest that sexism is made up, just that if you want to talk about sexism in tech you could provide more concrete examples other than twitter threats coming from outside. I'm saying that the insistence that tech is rife with sexism won't get us very far because it's not demonstrably true outside of the kind of awful high profile cases you bring up. I can't believe I'm about to type this, but: not all politicians are awful crooks.

      Also my point was that sexual harassment isn't really sexism. Sex exists, it's a real thing unlike race, so if someone is sexual harassing someone at work its not helpful to focus on whether or not it is based on sex difference - asking a colleague for a sexual favor is inappropriate for everyone, and harassing someone about it is the same as doing it over religion, or child/less status, or diet. It's a completely different set of behavior that has its own set of HR policies, etc.

      Now where I can see sexism coming in to play is if the employer feels like such conduct is normal for, as an example, men to do to women. But in tech? Where are the stats to show that is the case even slightly?

    2. Also, men treating women badly isn't sexist until they are doing it because it is a woman. I'm thinking of Linus here. To be clear, I am not suggesting that it doesn't happen. Just that it's easy to misconstrue a person who is basically a jerk for someone who hates women. I know plenty of people who have very little tact but for our intents and purposes are blind towards sex or gender.

  14. I certainly agree that sexual harrassment is wrong in whatever context and I assume that almost all employers will have policies in place to deal with it. So it's not that it's officially accepted.

    On the other hand, it's important to remember that the seven examples I gave are the tip of the iceberg in two ways. One way is that the women concerned have to have the guts to talk about them in public: and often in a way that could harm their career. And second, they are the ones that float up to gain significant public attention.

    Also another point which is important is that even if a woman is not subject to sexual harrassment, there is still a lot of sexism around. This could be as slight a point as people consistently referring to computer scientists as "he". I've talked more about this on a previous blog post (well really a slidedeck)

    1. Can you give some examples? The he part is a little weak don't you think? I'll read the blog post when I get home but you surely aren't basing your sexism indictment on colloquialisms? Most developers are men. It seems like it's mostly just a slip of the tongue.


  15. If you want good scientific evidence that sexism matters NOW, this is a good example. Men were judged as being better than women by *scientists* based *only* on having male names.

    1. THAT is really sad. The only thing I can do is say I can at least guarantee I've not been an unwitting perpetrator of such unfairness as I've never even had a single female resume to review. What a sad state of affairs.

  16. From a more practical perspective, how do you actually make use of this information to make changes since in any unbalanced environment the majority group is going to have to be 1-2 orders of magnitude better behaved in order to achieve an 'equally sexist' environment. This doesn't seem like a realistically feasible task and unfortunately we can't address many of the issues of women not picking up computer science at University level since we tend to lose them from our pipelines in primary and secondary schools.

    Secondly (and I know it doesn't affect the maths) how much of the perception of sexism in the environment is due to linguistic and bonding ritual differences between men and women? As an asexual sitting in pretty much any group I have to accept that people are going to bring up standards that utterly erase me however at the same time I acknowledge that for the majority of the population sex and sexuality are topics that do come up.

  17. "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."

    It's even more wonderful than that, in that it applies to any minority, and to any attitude – positive or negative – that you might care to consider.

    For example, you can use precisely the same argument to show that the amount of supportive behaviour experienced by women compared to men increases as the square of the gender ratio; or that in any workforce with a minority of women, the women experience disproportionately more racist behaviour than the men, even if the entire workforce is white; or that in an all-male environment with a minority of Catholics, the Catholics experience quadratically more sexism than the non-Catholics; and so on ...

    No doubt I'm missing the point spectacularly, but I'm not really sure where that leaves us, except that it shows that intersectionality really is a major issue.

    1. I'm not sure about missing THE point, but you are missing A key point.

      A critical assumption is that the (desirable or undesirable) behaviour is related to the minority group. So it is completely true that (e.g.) if Catholics are in a minority then they will experience quadratically more anti-Catholic comments than non-Catholics will experience anti-non-Catholic comments. Because the comments are only directed between the groups.

      But it is not true that Catholics will experience more sexist comments than non-Catholics.

      So yes the effect works for any minority and for either positive or negative comments. BUT it only works for comments which are directed only between the minority/majority groups, rather than within a group.

  18. Good post. The only thing I'd take issue with is the implication that women can be sexist against men. By definition, it's impossible for a group without power to use power against a group with more power; sexism refers to beliefs about the inferiority of a particular gender that have the power of social, political, religious, and/or violent policing to back them up. In a patriarchy, there is no such thing as sexism against men -- certainly individual women might hold negative beliefs about men, but without the power to systematically oppress men, these beliefs don't pose a threat to men as a whole.

    (Not to say that women have no power at all -- for example, white women as a group have power over Black men as a group -- but that reflects racism, not sexism.)

    Implying that the systematic oppression of women in a kyriarchy or patriarchy is equivalent to a few women thinking unkind thoughts about men trivializes women's oppression.

    1. Thanks Tim for dropping by, I'm honoured!

      It does seem to me, though, that there are two definitions of sexism that you are conflating. Certainly in my idiolect, if a women says "all men are brainless idiots who can't count", that is a sexist remark. Obviously it's that meaning of sexist that the post is about.

      So your last paragraph is clearly correct, but I didn't think I was implying that.

    2. It took me a little while to double check, but I did remember correctly that this was you. Brilliant!

      I desperately tried to avoid this mistake in trying to sell the importance of gender imbalance in computing, but I'd be interested in any comments in case I failed. Talking especially about slide 26-28 of the talk linked here.

  19. Unfortunately, there is a fallacy in the argument, which is that the rate at which sexist remarks are made is independent of the sex ratio itself. Now, it might go up with, or it might go down with, or is more likely to be some complicated function of, the sex ratio - but it is highly unlikely to be constant.

    Pseudoscience like this does not help to win any arguments.

    1. You are perfectly correct that the sexist remarks rate is constant in this model. But somebody else has a model which takes account of this, and in his model the effect is actually worse, not better.

      I'm not sure why you use the word "pseudoscience". Inasmuch as this is science (it's a blog post), it's a simple mathematical model which has an unexpected effect. The point is to say that in a world where the model applies, this is what happens. That's not pseudoscience, it's just a fact. I've never claimed this bears on reality.

      An interesting observation is that many people (I assume to be men but I don't know) make a point like this, as if somehow the total absence of woman to make sexist remarks is an indication that we don't have a problem: it's obviously indicative of a bigger problem.

      While on the other hand the other critical remark that I most often get (from women or feminist supporting men) is that the basic assumption that women are equally sexist is so far away from reality as to make the whole argument offensive.

    2. Actually just found a mail I sent which might have brought you here which says in part: "to see just one reason why sexism differentially
      affects women in computing, read my blog post about "The Petrie
      Multiplier". So that could be read as saying it bears on reality. Apologies, should have said something like "sexism can differentially" or "might differentially".

  20. Well, if not pseudoscience, it is surely making assumptions coupled with faulty logic:

    "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."

    As well as the assumptions, there could be many other reasons your assertion might be true.

    For example, have you considered that women experience might experience more sexism because, biologically, men are more predisposed to be sexist (i.e. to draw attention to [supposed or real] gender differences than women are)?

    The word "because" is certainly a non-sequitor.

    Again, if you are trying to reduce sexism, it does not help to put up badly formulated arguments about its cause.

    1. Ah, that segment you have quoted is *intended* to refer to the world of the model. In the model this is a statement of fact. I have no problem accepting it's worded badly to fail to make that clear.

      I am trying to reduce sexism, though not actually trying to put up arguments about its cause, well or badly formulated. The point of the blog post is to give one possible explanation how people's *experience* of sexism can be variant between sexes even if both genders are equally sexist.

      Anyway I'm sorry I've disappointed you.

  21. Sorry for being late to the party. Can't argue with the math, though interesting to question the match with the real world. Main thought would be whether sexist people seek out the opposite group to be nasty too (as Marc also mentions up the page).

    My suspicion (based on family, friends and taxi drivers with racist attitudes) is that sexists would not store up their remarks for the opposite group and would direct them to who ever was around, expecting positive reinforcement of their views. In addition, I wouldn't necessarily expect a constant stream of comments so that a person confronted with a member of their target group might make more rather than less attacks.

    On the positive side, this is a nice model to show the importance of being a minority friend, thereby increasing the effective size of minority group, and reducing the power of the square law.

    1. I'm even later to the party, I came here via Vi Hart's interactive infographic on squares and triangles, which is making the rounds. I'd just like to make a point that no one has made yet: this model also tells us something about what will not work.

      "Sensitivity training"-type exercises, even if they should succeed in, say, halving sexism, would only make a small dent in the experienced sexism of a minority. So while this model makes a good case for quotas (or other means of valuing diversity), it also makes a good case against

      1. individual effort to become less sexist (if you're even considering it, you're probably OK anyway)

      2. Inferring from experiences of sexism from men in tech, that they as a group are sexist. They might be far less sexist than the average man (hell, they might be less sexist than the woman in question), and that would still be compatible with her negative experiences.

      You can't really compare taxi driver-style racism, as you do. The sexism of men in the workplace often takes the form of unwanted advances. It's quite reasonable to think people prone to make unwanted advances DO seek out people they want to make them to, in a way a racist does not seek out a racial minority to insult (although that can happen, too - remember, in the model it doesn't have to happen often, or be the most common form of racism, it'll still have a big impact in this model).

      I do not think your assumption that being a "minority friend" effectively grows the minority under the model's assumption. If the people making unwanted advances started hitting on you instead, then it would. But I don't think it works that way ;)

  22. Very good. It applies to any minority discriminated group and to the detection of any rare occurrence creating many false positives. I thinks it's classic Bayesian math.

  23. No. The model is stupid. All subjects receive a limited exposure to the population. Every woman in tech does not encounter every man in tech.

    Would the only woman in a group of 1,000,000 receive 1,000 times the abuse of the only woman in a group of 1,000?

    1. Uh, just modify it to the population at hand. I am one of three female technicians in an area that has four IT teams comprising 50 people in total. I assure you that I have met all those 50 people despite being one of the minority 6%. I'm just fortunate that in that population, the incidence of sexist remarks is extremely low across the board.

      Also, for those objecting to how sexist people don't store up their remarks, how about changing the *interval*? A sexist moron will generally manage to average at least one offensive remark a month.

  24. This post really needed to be written, particularly in light of Gamergate and women in coding!

  25. The analysis at takes points 1 and 2 into account, and that actually seems to make the situation worse, not better.