Monday, April 17, 2017

Proving discrimination from personal experience

Here’s an interaction you might’ve participated in:

Member of minority group: I just had [negative interaction] with John. I don’t think he would’ve done that if I hadn’t been a minority.
Listener: That sucks. do you know it was because you were a minority? Maybe he was just having a bad day or he was really busy or …

The negative interaction might be, say, that John talked down to them or didn’t include them on a project.  The listener’s reaction is totally reasonable and well-intentioned (at least, I hope it is, because I’ve had it myself). Sometimes it isn’t even said out loud; the listener just thinks it. Here I argue that this reaction is not the most useful one. I explain why, both in English and in math, and then I suggest four more useful reactions.

The problem with this reaction is not that it’s false. It’s that it’s obvious. If a minority tells you about something bad that happened to them, you can almost always attribute it to factors other than their minority status. (Throughout this essay, I’ll refer to negative behavior that’s due to someone’s minority status as “discrimination”.) Worse, this uncertainty will persist even if the discrimination occurs repeatedly and is quite significant. The core reason for this is that human behavior is complicated, there are lots of things that could explain a given interaction, and in our lives we observe only a small number of interactions. Because it is so hard to rule out other factors, individual discrimination suits have notoriously low success rates.

Let’s be clear: I’m not saying you can never prove discrimination from someone’s individual experience.  Obviously, there some experiences which are so blatant that discrimination is the only explanation: if someone drops a racial slur or grabs their female coworker by the whatever, we know they’re a president bigot. But, in today’s workplaces, problematic discrimination is rarely so overt -- hence the term “second generation” discrimination. Here’s a picture:
Here’s a simple mathematical model that formalizes this idea. If you don’t like math, feel free to skip to the “What should we do instead” section. Let’s say the result of an interaction, Y, depends on a number of observable factors, X, one of which is whether someone’s a minority. Specifically, let:

Screen Shot 2017-04-05 at 11.48.48 AM.png
where beta is a set of coefficients describing how much each factor matters, and noise is due to random things we don’t observe. So, for example, Y might be your grade on a computer science assignment, X might include factors like “does your code produce the correct output” and “are you a minority” and noise might be due to stuff like how quickly the TA is grading [1].

If we want to know whether there’s discrimination, we need to figure out the value of betaminority: this will tell us whether minorities get worse outcomes just for being minorities. We can infer this value using linear regression, and importantly, we can also infer the uncertainty on the value.

Here’s the problem. When you do linear regression on a small number of datapoints (which is all a person has, given that they don’t observe that many interactions) you’re going to have huge uncertainty in the inferred values. To illustrate this, I ran a simulation using the model above with two groups, call them A and B, each half the population. I set the parameters so there was a strong discrimination effect against B. Specifically, even though A and B are equal along other dimensions, the average person in A will be ranked higher than about two thirds of people in B, due solely to discrimination; if you look at people in the top 5%, less than a third will be B. So this is enough discrimination to produce substantial underrepresentation. But when we try to infer the value of the discrimination coefficient, we can’t be sure there’s discrimination. In the plot below, the horizontal axis is how many interactions we observe; the blue area shows the 95% confidence interval for the discrimination coefficient (with negative values showing discrimination against B); the black line shows a world with no discrimination.

The important point being that the blue shaded area overlaps 0 -- meaning no discrimination is possible -- even if you have literally dozens of interactions, which is way more than you often have. (For fewer than about 5 interactions, the errorbars just blow up and you can’t even graph it.) You can alter simulation parameters or simulate things slightly differently, but I don’t think you’ll change the basic point: you can’t infer effect sizes on sample sizes this small with any confidence.

This model also illustrates some features which make concluding discrimination harder. For example, our errorbars will be larger if other features in X are correlated with being a minority. (“No no, I didn’t promote him because he’s a man. I promoted him because we work well together because we always go out to dinner together / play basketball together / he sounds so much more confident. Well, yes, my wife says I can’t go out to dinner with women…”) Also, your errorbars will be larger if you’re observing repeated interactions from the same person. (If you’re trying to compare your treatment to that of a single coworker, it’s even harder to be sure if it’s because you’re a minority or because of one of the innumerable other ways in which you’ll inevitably differ.) Last, you’re going to be in even more trouble if your minority is a very small fraction of the population whose interactions you observe (say, computer scientists) -- I don’t know if most computer scientists are prejudiced against African-American students because I’ve literally never seen them interact with one.

It’s worth noting that there are a lot of other subtleties in detecting discrimination which have nothing to do with small sample size and which this model doesn’t capture (see the intro to this paper for a brief, clear introduction) but I think small sample size is probably the biggest challenge in the individual-human-experience-setting, so it’s what I focused on here.

What should we do instead?  

So it isn’t useful to tell someone that they can’t be sure their experience is due to discrimination, because even in cases when a large amount of discrimination is occurring, people often won’t observe the data to conclusively rule out other factors. What should we do instead?

Here’s one thing I don’t think we should do: assume that discrimination is occurring every time a minority says they think it might be. (I do think we should assume they’re telling the truth about what occurred). The solution to uncertainty and bad data is not to always rule in favor of one party, since it creates perverse incentives and people’s lives get wrecked both by discrimination and by allegations of discrimination. Instead:

  1. Recognize the severity of the problem that minorities deal with. It’s not that they hallucinate discrimination everywhere or are incapable of logical thinking or rigorous standards of proof. It’s that proving discrimination from anecdotal experience is frequently an extremely difficult statistical task. Also, it’s exhausting to continually deal with the unprovable possibility of discrimination: to wonder, every time something doesn’t work out, if some subtle injustice was at play.
  2. Use common sense. Statisticians call this “a prior”: ie, you let your prior knowledge about how the world inform how you interpret the data. So, for example, if you hear someone refer to a black student as “articulate” or a female professor as “aggressive”, you don’t need to hear one hundred more examples to suspect prejudice may be at play. Your prior knowledge about how those adjectives are used helps you conclude discrimination more quickly. (I suspect that one reason female judges are more inclined to rule in favor of discrimination suits is because they have different prior beliefs about how common discrimination is.)
  3. Aggregate data. If one person’s experience doesn’t give you enough data to rule out other factors, aggregate experiences. Class-action lawsuits are an essential means of going after discriminatory employers for this reason. Climate surveys within departments are another example, as is publishing systematic salary gap data (as Britain now does). The sexual assault reporting system Callisto, which aggregates accusations of assault against the same accuser, is based on a related idea, as I’ve discussed.
  4. Conduct workplace audit studies. This idea is kind of crazy and might get you fired, but here it is: if it’s hard to prove discrimination because there are too many other factors at play, keep the other factors constant. Here are some examples:
    1. When a female employee says something in a meeting and people ignore it and then a male employee says the exact same thing and gets a more positive response, we’re more convinced that’s discrimination. (There are a hilarious number of Google results for that phenomenon, by the way.)
    2. A few years ago, I spent a few weeks emailing the NYT’s technical team and getting no response; finally I asked my boyfriend to send them the exact same question, and they immediately responded.
    3. Or take this recent case, where a male and female employee switched their email accounts and were treated dramatically differently.

All these examples feel like compelling evidence of discrimination because it’s hard to pin the different outcome on extraneous factors; everything except minority status remains the same.

So, could you do this in your workplace? More and more interactions occur online, making it easier to switch identities: for example, you could imagine switching Slack accounts for a week. Obviously there are 14 million ways this could go wrong, but drop me a line if you try it.


[1]  This is easily extended to binary outcomes: Y ~ Bernoulli(sigmoid(X * beta + noise))


  1. Saw your article in Wired, nice job, and found your blog. This is a good example of what you were talking about, how to ethically ascribe meaning to results. We all recognize linear least squares is generally a bad approach, as you address at the end, but even with better results the issue remains that there's always uncertainty in the answer. In physics, where I work, "Oh well, maybe the density coefficient isn't quite 1g/cm^3 but the application tolerances can adjust," but in humanities people may not appreciate the tolerances. Worse, for your field is that in physics we know the approximations and inaccuracies of our model (your other coefficients), but you have less to build on.

    What probability distribution and amplitude did you give the noise in this example, Gaussian?

  2. I think there are a lot of publications in this area - both formal an informal studies that are very powerful, but also some that are weak. Sometimes judgement is hard when studies go against personal experience though. I am a White Man and have rarely seen evidence of discrimination (although some of the few cases I have knowingly seen have been pretty horrific) and never have I knowingly seen it in the workplace. A lot of these anecdotes didn't do a lot to convince me (and generally I will still believe the best of people until there is stronger evidence). The studies that convinced me workplace discrimination is a problem is the studies where identical C.Vs get sent out and the response rates for names strongly associated with different ethnicities are compared. Being able to do pairwise comparisons whilst holding everything else constant makes for powerful comparisons. Quite possibly because I am not well read enough I have never seen positive results for this approach to identify sex discrimination though. Somewhat playing the devil's advocate, even the examples you give of women receiving a different response to the same statement/suggestion to the response a man receives can be difficult as there is a question as to is it due to two people suggesting it or is it because a man does so.

    At the aggregate level thinks might be more straightforward but it is still not easy and there are a couple of difficulties (well difficuties for me - I am still new to the topic and finding my way around) that you skip over (short article so nothing wrong with focusing on the most important points).

    The first issue is correlation. How do you tell the difference between discrimination (say based on ethnicity or gender) and discrimination based on something correlated with ethnicity or gender? With large enough data sets well split between men and women you can see if height, for example, can better play a role in predicting salary and whether it can explain differences within male and female groups. The problem is that there is no shortage of variable like this when you search for them and the more thorough we are in accounting for other explanations the greater the uncertainty is on any measure associated with the simple minority grouping. I used height as an example as it would still (by common moral standards) still be considered discriminatory but just that the grouping would be misidentified.

    The other big issue I am trying to get my head round is how granular an analysis should be. A big organisation may have a thousand different teams within it and some of them will certainly look discriminatory, just through chance. I am having trouble working out how much to infer about an organisation from those teams that are significant.

    The more I think through the (limited) data I have the more trouble I have (is this normal?). If I compare salaries, is this identifying discrimination or past discrimination? If someone was held back in another company for 10 years before joining their current employer it would show up in their current salary (even if the current employer treated them the same way as anyone else with their level of senior experience). My approach was to look at times between promotions and rate of pay increase instead - even then it gets very complex by different patterns of different groups moving between companies. On the other hand the paper that you linked to seems like it might be useful for some of my problems (if a group performs better in appraisal following a promotion than another group, does it mean the bar was set higher for them?).

    I certainly appreciate blogs like this though - I feel that having an open discussion about what aspects of the problem can be addressed objectively and with some high confidence bounds is a big step forwards. I am not sure I feel I know the subject better but maybe I am a slightly more informed type of perplexed.

  3. If you need your ex-girlfriend or ex-boyfriend to come crawling back to you on their knees (even if they're dating somebody else now) you must watch this video
    right away...

    (VIDEO) Have your ex CRAWLING back to you...?

  4. {Download} $12,234 within 2 months Casino Software?

    Let me tell it straight.

    I don't care about sports. Shame on me but I don't even know the basketball rules.

    I tried everything from forex & stocks to internet marketing and affiliate networks.. I even made some money but then blew it all when the stock market went south.

    I think I finally found it. Grab It TODAY!

  5. There's shocking news in the sports betting industry.

    It has been said that any bettor needs to see this,

    Watch this now or stop placing bets on sports...

    Sports Cash System - Robotic Sports Betting Software


    Get professional trading signals sent to your cell phone daily.

    Start following our signals right now & earn up to 270% daily.

  7. سميت بحشرات الفراش لانها غالبا ما تتواجد شركة مكافحة حشرات بمكة فيه وتعيش وتتغذى على الدم سواء دم الإنسان أو الحيوان شركة تنظيف شقق بمكة تعد الحيوانات شركة تنظيف خزانات بمكة الأليفة ذات الشعر شركة مكافحة حشرات بالطائف الكثيف أيضاً أحد المصادر الناقلة لهذه العدوى تقوم حشرة البق بوضع البيض شركة نقل عفش بمكة الخاص بها على المراتب والآسرة شركة تنظيف خزانات بالطائف والذي يتميز بلون ابيض شفاف وملمس لز

  8. تعمل على توفير كل خدمات عمليات التنظيف شركة تنظيف بالبخار بجدة بالإضافة إلى الخدمات الاخري شركة تنظيف كنب بالبخار بجدة التي تحتاجها ربات البيوت وأصحاب الشركات شركة تنظيف سجاد بالبخار بجدة والعقارات ومن خلال شركتنا المتمزية فى خدمات تنظيف المفروشات شركة تنظيف مجالس بالبخار بجدة بالبخار بافضل الاسعار تعرف على كافة شركة تنظيف بالبخار بمكة الخدمات المتميزة التى نقدمها شركة نقل عفش بمكة اليكن والى كل عملائنا الكرام

  9. شركة نظافة خزانات بمكة تقدم خدمات لا يوجد شركة تنظيف بمكة منشأة لا تحتاج لها حيث أن الخزانات تعد من أهم المحتويات التي تحتاج لها المنشآت المختلفة خاصة شركة مكافحة حشرات بمكة في المملكة العربية السعودية التي تعتمد على المياه الجوفية ومياه الآبار شركة تنظيف خزانات بمكة والعيون وتخزينها في خزانات شركة تنظيف بالبخار بمكة بعد تصفيتها وتنقيتها لذا ظهرت الحاجة الشديدة للاستعانة بشركة متخصصة شركة نقل عفش بمكة يستعين بها مختلف الأشخاص في تنظيف وتعقيم الخزانات لديهم من أجل الحفاظ على المياه نظيفة وغير ملوثة

  10. العمالة الفلبينية معروفة بأنها تتعلم شركة نقل عفش بجدة بسرعة كبيرة وجميع الأعمال التي تسند اليها تخرج جودتها بمستوى عالية فى حين ان مستوى الاجور لها منخفض وعليه فإن الشركة شركة تنظيف بالبخار بجدة تعمل على توفير تلك النوعية شركة تنظيف دكت المكيفات بمكة من العمالة ومن خلال افضل شركة نقل عفش بجده شركة تنظيف دكت المكيفات بجدة عمالة فلبينية سوف يتم الحصول على عمال متفوقين وقادرين شركة تنظيف دكت المكيفات بالطائف على نقل الاثاث بعناية كبيرة من اي مكان حتى الادوار العالية وتتم عملية النقل تبعا للأسلوب الحديث وهي كالتالي :-

  11. توفر شركة تنظيف دبي أفضل خدمات نظافة شركة تنظيف بدبي من خلال خبراء في عالم النظافة شركة تنظيف كنب بدبي لديهم احتراف ومهارة عالية وعلى درجة كبيرة من الأمانة والالتزام لديهم حلول شركة تنظيف عجمان عملية وسريعة لجميع شركة تنظيف بالشارقة مشاكل التنظيف ملتزمون بتلبية شركة تنظيف ابو ظبي رغبات العملاء وتنفيذها وعدم إهدار الوقت

  12. تنظيف المساحات الشاسعة ليس بالأمر الهين شركة تنظيف دبي ولا يقدر عليه فرد واحد أو الخدم الذين قد يتواجدون شركة تنظيف ابو ظبي بالمنشأة حيث أنه يلزم توافر معدات خاصة شركة تنظيف كنب بدبي من أجل التنظيف تساعد شركة تنظيف بالشارقة على تقديم أفضل الخدمات وتعمل على تيسيرها بأسعار لا تعد عبء على من يبحث عن شركة تنظيف عجمان هذه الخدمات لذا تقدم الشركة كافة الخدمات التي تلزم في تنظيف الفلل شركة تنظيف العين بما تحتويه من محتويات وأغراض

  13. يمكنكم اللجوء لتنظيف منازل عجمان إذا شركة تنظيف دبي أصبحتم في حاجة إلى تنظيف المنزل شركة تنظيف عجمان في أي وقت تحددوه أنتم , فقط اتصلوا بتنظيف منازل عجمان شركة تنظيف بالشارقة وسوف يرد عليكم فريق متخصص من خدمة العملاء والذي يحدد معكم المطلوب شركة تنظيف ابو ظبي والوقت المحدد لإتمام تلك المهمة الضرورية وفي أسرع وقت ممكن سوف تجدونها انتهت شركة تنظيف كنب بدبي , فقط انسوا هم الأسعار التي تقلق الجميع في حالة الرغبة في التعامل مع أي شركة نظافة

  14. German Translation Legal Translation services German Translation The German German Translation dubai language has a great influence on the world because Germany plays a vital role in the European Union chinese Translation dubai . Also, the economy of Germany russian translation in dubai encourages the growth Translation services in Dubai of the English Translation dubai German translation industry.

  15. كما يقوم فريق العمل بتنظيف الموكيت حيث أن الموكيت شركة تنظيف بدبي يعتبر من أهم الأشياء التي توجد في المنزل ويتميز بوجود الزخارف المختلفة شركة تنظيف بالعين به، لهذا فإنه يحتاج إلى التنظيف بكل دقة وحرص ويتم هذا من خلال استخدام شركة تنظيف عجمان الماء الفاتر والمنظفات المخصصة للموكيت، أو يتم تنظيفه عن طريق البخار شركة تنظيف كنب بدبي حتى يعطي أفضل النتائج وفي أسرع وقت
    تعتبر طريقة التنظيف بالبخار من أفضل شركة تنظيف بدبي وأحدث الطرق التي تستخدم في عمليات التنظيف شركة تنظيف كنب بدبي للوصول إلى أفضل النتائج، وتقوم شركة تنظيف بالبخار في دبي شركة تنظيف بالشارقة في استخدامه في العديد من عمليات التنظيف؛ لهذا فإن جميع الأعمال شركة تنظيف ابو ظبي التي تقوم بها الشركة شركة تنظيف بعجمان تكون على درجة شركة تنظيف بدبي عالية من الكفاءة شركة تنظيف بالشارقة

  16. Everyone has had some thought, good or bad, nag at them from time to time. But to be obsessive means that you can’t get the distressing thoughts out of your mind no matter how hard you try. These obsessions are usually negative in nature. They can be violent thoughts or even thoughts about germs and sanitation. These thoughts often cause you to be unproductive and withdrawn from society.

  17. Hello everyone, my name is ALFREED SIANG i am here to say a big thank you to my doctor DR OLU who helped me enlarge my penis.i have never had a happy relationship in my life because of my inability to perform well due to my small penis, due to frustration,i went online in search of solution to ending my predicament and than i came across testimony on how DR OLU has helped them, so i contacted him and he promised to help me with penis enlargement,i doubted at first but i gave him a trial and he sent me the product which i used according to his prescription and in less than a week,i saw changes in my penis and it grow to the size i wanted and since then,i am now a happy man and no lady complains again about my penis.if you also need the services of my doctor,you can also contact him on his or his whataspp is +2348140654426

  18. Guaranteed #1 Search Engine Ranking Supreme Free Viral Traffic Join Now Get Millions Of Hits Free To Your Site/Blog!

    PornKings Adult Shopping Backlinks-Shopping Mega Store Legendary Stars As Stormy Daniels,Shawna Edwards,Jenna Jamison-New Adult Stars Movies,Adult Toys,Enhancers,Merchandise-More !

    Hits Express Rotator System Do You Need Visitors to Your Website or Affiliate Program? If your looking to gain more visitors to your website Hits Express is your answer. With our program your site is being shown to people all over the world 24/7 365 days a year!

    Payserve Euro Live MYSEX GIRLS KITTEN/CamsGlobal Networks Portals!

    FreeLinkExchanges Be Seen In 12 Nations 312 Sites Over 30 Millions Viewers Monthly Buy Featured Link Now With 150 Search Engines Crawling The Network!

    New-Legendary Pornstars Famed Digital Gamma #1 4K HD Networks!

    How do I get guaranteed traffic? When someone signs up from your site, they must first click on your classified ad which will open a new window leading to your main website. They will have to wait a few seconds for the code to appear on a separate frame at the top of the screen reach millions free now!

    Blast Your Ad to Over 23,000 Opt-in Prospects at ShowMyLinks Submit Your Solo Email Ad to All Showmylinks Members GET YOUR TEXT LINK ADs LISTED 100% FREE FOR LIFE PLUS EARN MONEY TO YOUR PAYPAL!!

    Adult Store Empires Backlinks Resources Search Engine XXX!

    GET YOUR OWN MONEY-MAKING AD BOARD -- Integrating Text ad, Banner Ad and Email Ad into one Portal Make Money Fast With Your Paypal Reach Million Dollars In A Year Fast !