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    Categories: Feminism

Proving and Quantifying Sexism

In many areas of life, especially in cases where a person must apply to enter an organization, field or job, there are large gender gaps. Whenever feminists call for equal representation by women in a particular endeavor, detractors often claim that adding more women means better-qualified men will get bumped down. They claim that in order to get an equal number of women and men, the bar must be lowered on quality. For example, some in the skeptic movement have claimed that adding more women speakers at skeptic and atheist conferences means replacing more qualified men with less qualified women.

As a feminist, I don’t believe this is true. I believe that increasing representation of women will increase the quality of the endeavor. I also believe  the thing keeping women from certain fields in which they are under-represented is institutionalized sexism. As a social scientist though, I don’t just want to believe these things. I want to prove them and I want to measure them. To do that, we have to find something measurable that would be an effect of institutionalized sexism.

First, lets create a game theory model to come up with a hypothesis of how the world should look if there is sexism present. Then, we’ll go out into the real world to see if we can find examples of it in action.

Lets say we’re a conference and we’re putting together a panel of experts. We want 6 people on our panel but we have 10 candidates: five women and five men. The men and women have varying qualifications for the panel, which we’ll rate on a scale of 1-5 (with 5 being the most qualified). Here they all are, with the women represented in purplish-pink and the men in blue (because if we’re already assuming only two genders exist for this problem, we might as well go with the cultural representations of those genders). The numbers represent their qualification rating. Two individuals with the same rating are considered of equal qualification (so the woman rated as 4 is exactly as qualified as the man rated as 4).

 

In a world with no sexism, it’s really simple to choose the 6 individuals for our panel. The most qualified panel would consist of the following individuals:

This panel is ½ men and ½ women. The men on the panel have an average qualification of 4 and so do the women. The average qualification of the entire Board is 4. Even if we assume slight sexism where men are always chosen above women of exactly equal ability, we would still end up with our three men and three women panel.

Now, lets change things up a bit. Lets assume there is some institutionalized sexism and women are perceived to be one qualification level lower than their actual level. Additionally, whenever a man and woman are perceived to be of equal ability, the man is always chosen before the woman. Now, our panel will look a little something like this:

We now have have a panel that consists of 2/3 men and 1/3 women. The average qualification score of the men on the panel is now 3.5 (a 0.5pt decrease) and the women’s is 4.5 (a 0.5pt increase). The average qualification of the entire panel has dropped from 4 in our gender-neutral world to 3.8.

We now have a testable hypothesis!

In any grouping that is supposed to consist of the most qualified people and has a large gender imbalance, if that gender imbalance was caused by institutionalized sexism either in the choice of individuals or the admittance of individuals into the pool of candidates (for example, discouraging women from studying in STEM fields), then the women in the group will be more qualified on average than the men in the group. Additionally, rival groups with more equal representation of women will be more qualified on average than rival groups with fewer women.

Now that we have a hypothesis, lets go out into the world to see if it holds true. Luckily, we don’t need to do this ourselves because other scientists have already looked into this. Here are three studies that show that this hypothesis holds water:

  • The boards of Fortune 500 companies in the US consist of a mere 16% women. But, within those 500 companies, there is a lot of variation.  According to our hypothesis, if the lack of women on boards of large corporations is due to sexism, then boards that contain more women should be, on average, better than Boards that contain fewer women. A recent study shows that this is in fact the case and that the stocks of companies with more women on their Board do better, on average, than their less equal counterparts.
  • Only 18% of hedge funds on Wall Street are run by women. If women are just as capable as men and the imbalance is due to institutionalized sexism, then the woman-run hedge funds should do better on average than the man-run hedge funds. Again, a recent study shows that hedge funds run by women produce an average return of 9% while the industry standard is a mere 3%.
  • The current 113th Congress will contain a record 20 women in the Senate and 78 in the House for a grand total of 18%. According to our theory, if the gender imbalance is caused by voter sexism, these 98 women should be better politicians than their male counterparts. Since the 113th Congress is new, we don’t have stats on them yet, but a study in 2011 found that Congresswomen outperformed Congressmen by bringing more federal money to their districts and sponsoring and co-sponsoring more bills, even after controlling for party affiliation.*

If you know of any other similar studies that show women outperforming men in fields that lack diversity, please leave a note in the comments. I’d really love to learn about more studies of this type.

Institutionalized Sexism isn’t just some crazy idea feminists came up with to try to get qualified men fired and replaced by unqualified women. Evidence out in the real world shows that in areas which contain large gender imbalances, the women are generally better at their jobs than the men. Since we don’t have any good reason to believe that women are somehow just innately better than men, then it means that sexism present either in the choices of individuals or in the pool of individuals that the choices will come from.

MRA’s often say that feminists think that women are better than men. In actuality, the more sexism that is present, the more women will be better than their male counterparts. When gender diversity increases in a group, we should see the average ability of women in the group decline to be more equal to that of the men and the average quality of the entire group rise.

If we apply this to skeptic and atheist conferences, which often contain far more male speakers than female, increasing the number of women speakers should increase the overall quality of the conference. In the STEM fields, which tend to lack women, increasing the number of women will raise the quality of the scientists graduating with STEM degrees. In large companies that often lack female leadership, companies that strive to have more gender-balance will be more likely to out-compete their competitors. Once you get a hang of the idea that diversity=quality, you start to see potential for gains everywhere.

*Full Disclosure: The study author Christopher Berry was one of my graduate degree professors.

Jamie Bernstein :Jamie Bernstein is a data, stats, policy and economics nerd who sometimes pretends she is a photographer. She is @uajamie on Twitter and Instagram. If you like my work here at Mad Art Lab, consider sending me a little sumthin' in my TipJar: @uajamie

View Comments (62)

    • Oh, that article is so interesting! I remember learning about how historically orchestras were almost entirely male until they instituted blind auditions But, I had no idea there was still gender discrimination in orchestras going on today. Orchestras would be smart to institute a blind audition process because it would result in a better orchestra than they would get with a non-blind audition process.

  • Jamie, Women in Secularism is a pretty good example. The entire conference's quality went up as they had more women speakers.

  • Wow, loved this thought experiment. (I am a woman in a STEM field, worn down from the constant sexism.)
    One request: Please, please! Get the difference between "less" and "fewer" straight. In a snip of your comment (below), I can't tell if you think that they have fewer qualified candidates, or if they have poorer quality candidates. The next bit literally reads that you think they have partial women. ;-)

    "So, lets say you have a firm out in a rural area. In this case, they might have less qualified candidates to choose from and less women to choose from."

  • The model makes a lot of sense. I think there's a slight deficiency in the first two examples inasmuch as they all report better *collective* performance -- which is a prediction of the model, but the model says that the mechanism for better collective performance in less sexist groups is specifically due to higher qualification levels among the women, not overall. So what I'm suggesting is that the first two examples are consistent with less sexist groups having higher qualification levels among men as well as women, without much difference between men and women. It seems like examples like the Congress data provide better support for your model than the CEO and hedge fund data. Maybe the orchestra dissertation has something like that as well?

    • Oops sorry, my cat walked on my laptop as I was typing and pressed enter. (<-- True story!)

      There are two different predictions to the model: Gender diverse groups will have little quality difference between men and women and they will have a higher overall quality rating than the sexist groups.

      In other words, the model takes collective performance into account. The overall qualification level of the gender diverse group in the example was 4 while the sexist group had an avg quality of 3.8. This was the result of less qualified men taking the place of higher qualified women. If these groups were competing, we would expect the diverse group to win most of the time.

      So, when a gender diverse and a sexist group are competing, on average the gender diverse group should do better. This is what we see in example 1. Additionally, in sexist groups, the quality difference between the men and women should be high, with the women rated higher than the men. This is what we see in examples 2 and 3. It's two different results from the same model.

  • I once took a look at the figures from the APA on women in philosophy departments in the US (philosophy is one of the fields in which women are most poorly represented at all levels: it's the worst humanity subject for it). They showed that those departments which were ranked higher tended to have a higher percentage of full-time, permanent women faculty than for philosophy departments as a whole (22% of faculty in top-51 institutions, as opposed to 16.6% of faculty nationally).

    I got interested in this after reading about these guys: http://www.nationalpost.com/m/wp/news/blog.html?b=news.nationalpost.com%2F2012%2F08%2F10%2Fphilosophy-gender-war-sparked-by-call-for-larger-role-for-women

  • Do you know of any studies that quantify how effective different measures are at reducing sexism in organisations?

    Also, Really good post.

  • Hi.
    I'm curious about whether your proposed model takes into account, or whether you've tried to use it for, other possible factors of bias such as racism or class-based discrimination.

    For example, sports seems like a rich area for research:

    http://www.arthurhu.com/index/asports.htm - I frankly don't know what to make of this page in total - like whether it is somehow arguing for equal representation of Asians in sports - but it was one of the few pages I could find in a quick Google search that attempts to list statistics about representation in sports.

    http://partners.nytimes.com/library/national/race/070200sports-transcript.html - this is a kind of roundtable discussion on the topic.

    Do you think your model explains race or class imbalances in sports? Or why even great athletes who are nonwhite or female seem to have trouble breaking into the management of sports teams? Or how to break down cause and effect in cases where class might figure in (racket sports or equestrian sports)?

    Sincerely,
    intercoastalone

    • If race/class imbalances are caused by racism then it should follow the same model. In order to determine that the lack of Asians in the NBA was caused by racism, you'd have to show that Asian NBA players are on average better players than their non-Asian counterparts. You could do the same with white NBA members or with Black team owners if you think racism might be present there as well. You just need an objective measure of ability to use to compare. In a world with no racism, on average all ethnic groups within the league should play at about the same ability. If a group is better than average, it would indicate that racism may play a factor.

      As you mentioned, ethnic groups are more likely to come from vastly different backgrounds than are men and women. In more posh sports like racket sports or equestrian, as you mentioned, its possible we're seeing more white people just because they're more likely to grow up in a community that plays these sports. However the model should still hold. The important part of the model is that the presence of an underrepresented minority does not imply sexism/racism. It is only if the average ability of the minority group is higher than that of the majority group that we can say it was likely caused by sexism/racism. If we measure the abilities of all the players at Wimbledon (because that's the only tennis thing I know) and we find that the white and non-white players are on average of equal ability, we can say that racism was probably not involved and that the lack of non-white players was caused by other factors (perhaps class, cultural interest, etc). However, if we find that the non-white players are better on average than the white players, it makes it likely that racism is involved.

      That's why this model is so great. It can separate out whether racism or sexism was involved from non-direct racist/sexist factors that might decrease minority involvement.

  • Hi Jamie,
    You may want to read "A Case Study of Gender Bias at the Postdoctoral Level in Physics,
    and its Resulting Impact on the Academic Career Advancement of Females" by Sherry Towers. It looks at this effect in physics.

    • Oh, I found a link to the study: http://arxiv.org/pdf/0804.2026v3.pdf

      I don't have time to read the whole thing right this second, but from the abstract it definitely seems like this would be another example, The line that stands out to me is "The study ?nds that the female researchers were on average signi?cantly more productive
      compared to their male peers." That alone shows that there was likely bias involved in getting their research positions.

  • You make a lot of assumptions to prove your case. First of all, you assume that sexism is the reason for disparities in male dominated fields. Where is your conclusive evidence? Second, you assume that there is such a thing as "perceived equal ability", as in every resume given to every company always has an equal but gender opposite resume to pick from. How can you even remotely come to that conclusion confidently? Your entire first paragraph is based on the assumption that adding more women makes everything better because they are women. On a scale of one to five, if you have all level five men and a level 4 woman and you only want the top 5 speaking at your conference, it makes no sense to include the level 4 woman by removing a level 5 man. We are talking about merit here. But, lets get to your idea that women are more qualified, on average, than men when there is a large disparity in small group. Since you know how averages work already, I'm going to create a demonstration of how your argument is flawed. There is a disparity in nurses at a hospital. Fifteen of them are women and 5 are men. On average, men are more qualified than women because there are fewer of them. This is probably true no matter what group you use and here's why; average is the collective amount "qualification" divided by the total. All it takes is a few crappy female nurses to bring the average way down. All it takes for the small number of men to appear better at their job is to be good at it. Less men= Lower failure rate. Antivaxxers use this same way of thinking to show that vaccines are harmful. They say that more unvaccinated kids, on average, are healthier than vaccinated kids, which is true before you discover the fact that way more kids get vaccinated. Obviously you are going to see this result.

    • Ok, I'll play!

      1. First of all, you assume that sexism is the reason for disparities in male dominated fields. Where is your conclusive evidence?

      I don't make the assumption that sexism is the reason for disparities in male dominated fields. I lay out a game theory based model for how to test whether sexism plays a role in male dominated fields.

      2. you assume that there is such a thing as “perceived equal ability”, as in every resume given to every company always has an equal but gender opposite resume to pick from.

      I don't believe I ever mentioned resumes anywhere. I laid out a game theory model that is mathematically based. It doesn't matter if you can't always measure things perfectly in the real world because it's just a model of the real world.

      3. Your entire first paragraph is based on the assumption that adding more women makes everything better because they are women.

      My entire first paragraph was actually about how some people believe that women are less capable than men and that adding more women makes things worse. It's pretty clear. Maybe you read it wrong? Try reading it again.

      4. On a scale of one to five, if you have all level five men and a level 4 woman and you only want the top 5 speaking at your conference, it makes no sense to include the level 4 woman by removing a level 5 man.

      In this situation, the final panel would be made up of all men and you would not be able to use the test I laid out to determine whether sexism played a role because there is no average ability of the women on the panel because there are no women on the panel. The model cannot be used for this situation because you can't divide by 0.

      If you change it slightly to make it a 6 person panel, you would end up with five men on the panel with an average ability of 5 and one woman on the panel with an average ability of 4. Since the average ability of the women is less than the men, the model says that sexism was not a factor in the gender disparity of the panel.

      Out in the world, if we see situations where there is a large gender disparity and the object measurement of ability of the women is lower than that of the men, then likely sexism of the sort where the bar to entry is higher for women is not a factor.

      5. lets get to your idea that women are more qualified, on average, than men when there is a large disparity in small group

      I do not believe that women are more qualified on average than men whenever there is a gender disparity. As I already mentioned, all I did was lay out a model for how to test whether a certain type of sexism was involved in the gender disparity. When there is a gender disparity and the women are on average more qualified than the men, it means that sexism involving a higher bar for entry for women played a part. When women are equal or lower on average than the men, the model says that the type of sexism I laid out was probably not a factor.

      6. There is a disparity in nurses at a hospital. Fifteen of them are women and 5 are men. On average, men are more qualified than women because there are fewer of them. This is probably true no matter what group you use and here’s why; average is the collective amount “qualification” divided by the total.

      What I laid out was a mathematical model that has perfect information, hence the small n used in the examples I provided. If you were going to apply the model out in the real world, you would never, ever apply it to an n of 20. None of the studies I mentioned that included real world data had small n's.

      If you did try to apply it to an n of 15 you are sort of right and sort of wrong. The smaller the n, the more variation you would see which could result in much higher or much lower averages. In this case, both 15 and 5 are so small that you would have huge variation in both. But, let's say there were 100 nurses and 95 were women and 5 were men. We could probably get a pretty good average for the 95 women because the n is high. We would have trouble getting a good average for the men because there are only 5 of them and as you mentioned, one outlier could have a big effect on the average. However, it would absolutely not mean that we would always find that the average for the men is always higher than that of the women because there are less of them. It just means it's more variable. We would be just as likely to see a very low average for the men as a very high average because one outlier could pull the average up or down by a lot.

      However, none of this is a problem for the model I laid out because it's a model based in game theory and not an actual statistical study of real world events.

      7. Antivaxxers use this same way of thinking to show that vaccines are harmful. They say that more unvaccinated kids, on average, are healthier than vaccinated kids, which is true before you discover the fact that way more kids get vaccinated.

      Yes anti-vaxxers do say that unvaccinated kids are healthier than vaccinated kids, but the reason this can sometimes be the case is not because there are less unvaccinated kids. As I mentioned in my previous point, having a lower n could result in much higher OR much lower averages. The more likely explanation is that families that do not vaccinate are on average more well-off financially and are more likely to do things like eat healthy and promote exercise. Also, families with sick children are far more likely to vaccinate because their children are in more danger if they get diseases. In other words, the problem with a vaccinated versus unvaccinated study is that correlation does not equal causation, not that the number of unvaccinated children is too small.

      In all, you seem a little bit confused about what game theory is and how it works. Although I've never read it myself, I've heard that this book is a great primer on game theory that is great for people without a deep mathematical background, so if you're considering learning more you might want to read it. https://www.amazon.com/gp/product/0393310353/