### Invisible privileges

1.

Let’s review the evidence.

African-Americans are twice as likely to be stopped by the police. Police officers speak less respectfully to them. They are more likely to use violence against them. Overall, African-American men get killed by the police 2.5 times as often as White men. Then, African-Americans face discrimination at every stage of the justice system. For an identical case and history, African-American defendants have 10% higher odds of being incarcerated. When they are, they receive 10% longer sentences for the same crime.

African-Americans also face discrimination when they are the victims. Criminals receive lighter sentences when their victim is black1 However, it is not clear whether this is really due to discrimination or to other factors. In fatal traffic accidents, drivers receive a 53% shorter sentence if the person they killed happens to be black. When a black person goes missing, there is 3.1 times less media coverage than if the victim is white2This is called the Missing White Woman Syndrome. This study was conducted in 2016, before the Black Lives Matter movement gained popularity. It would be interesting to see how things have changed as a result..

Institutional discrimination also appears in the education system. Teachers systematically give better grades to students from the white majority than to ethnic minorities, for identical works3There are two kinds of methodologies to address this question. The most common is to compare the grades obtained by a student when the teacher knows her identity, with grades obtained by the same student on blind examinations. The second one is to fabricate a fake essay and ask teachers to grade it, while changing only the name of the student, and see if they are graded differently.. At school, African-American children receive harsher punishments for the same behavior as well as closer surveillance from teachers. And overall, in the US, African-Americans are 12% less likely to access higher education than white people.

Then, there is housing discrimination. When ethnic minorities apply to rent an apartment, their odds of receiving a positive response are 47% lower, everything else equal. With no surprise, African-Americans are 4.5 times as likely to be homeless, and then 45% less likely to be sheltered.

In addition, ethnic minorities generally have poorer health than white people. Black people work more dangerous jobs, making them 33% more likely than white people to be injured at work. They are 16 % more likely to die on their workplace. On average, the life of black people is 4.3 years shorter than white people’s.

Most of those results are from large studies, they are solid and have been replicated many times. Yet some people decide to completely ignore all the evidence, and still deny the existence of racist discrimination. How is it even possible? What is going on in the head of racism-deniers?

2.

Men are 2.5 times more likely than women to be stopped by the police. Police officers are more likely to arrest men and more lenient toward women. Overall, men get killed by the police 20 times more often than women. Then, men face discrimination at every stage of the justice system. Men are more likely to be considered guilty and receive harsher sentences than women for an identical case and history4These studies are called “mock juror trials”. They use a panel of jurors who are presented with a fictional case, where only the gender or ethnicity of the defendant is changed, and asked what the sentence should be. This way, everything is exactly identical except the gender of the defendant, so any difference can be attributed to discrimination. Some studies even staged fake audiences with comedians for extra realism.. Men have 1.64 to 2.15 times higher odds of being incarcerated, depending on the study. When they are, men also receive 30% to 63% longer sentences for the same crime compared to women5These are observational studies, meaning they look at the outcomes of a large number of real-life cases, taking into account offense severity, previous offenses, whether the defendant has to take care of children, and other confounders.. The sexist bias favoring women is much larger than the racial bias – that is, black women are treated better than white men. As you might expect, justice’s double-standard against men is especially marked for sexual offenses.

Men also face discrimination when they are the victims. Criminals receive lighter sentences when their victim is a man6With the same caveat as for racial discrimination.. In fatal traffic accidents, drivers receive a 36% shorter sentence if the person they killed happens to be a man. When a man goes missing, there is 2.9 times less media coverage than if the victim is a woman.

Institutional discrimination also appears in the education system. Teachers systematically give better grades to girls than to boys, for identical works. This happens already in elementary school, continues in middle school, and again in high school, and again in college7Interestingly, these studies found that female teachers were on average more biased in favor of girls than male teachers.. This favoritism for girls has measurable effects on boys’ progress and future career orientation. Parents also invest more time teaching girls than boys and spend 25% more money on girls’ education. At school, boys receive harsher punishments for the same behavior as well as closer surveillance from teachers. And overall, in the US, men are 16% less likely to access higher education than women. Here again, the gender gap is larger than the racial gap8Moreover, unlike for ethnic minorities, there is no affirmative action attempting to correct this disparity – even when women are more likely to access higher education, affirmative action is still in favor of women..

Then, there is housing discrimination. When women apply to rent an apartment, their odds of receiving a positive response are 28% higher than men, everything else equal. With no surprise, men are 1.5 times as likely to be homeless, and then 40% less likely to be sheltered. A study in France found that 90% of the people who die in the streets are men9It should be noted that the gender gap in homelessness is more marked in France than in the USA..

In addition, men generally have poorer health than women. Men work more dangerous jobs, making them 40% more likely than women to be injured at work. They are 8 times more likely to die on their workplace. On average, the life of men is 5 years shorter than women’s10The gap in life expectancy is commonly attributed to biological factors, as a legitimizing myth. However, this study on monks and nuns (who do pretty much the exact same things throughout their lives) found that at most one year of the gap could be attributed to biological differences.. In spite of this, there is much more scientific research and US national offices dedicated to women’s health. Medical research on women’s health receives considerably more funding than men’s health, even for conditions that affect men more often11See the tables from page 56. For lung cancer, in 2016 the NIH spent $180,000,000 for women-specific research,$318,000 (!) for men-specific research, and $136,000,000 for lung cancer in general. They also spent$1,916,000 for women’s suicides, and only $156,000 for men’s suicides, despite men dying from suicide about four times as often.. Like for racism, most of those results are from large studies, they are solid and have been replicated many times. Yet some people decide to completely ignore all the evidence, and still deny the existence of discrimination privileging women. Just like racism, discrimination against men has been systematically made invisible. 3. I am aware that many readers will hear about discrimination against men for the first time. Perhaps you’ve heard about discrimination from the police beforehand, but did you know about the grading discrimination? Did you know about the housing discrimination? If not, why didn’t anybody tell you about it? One thing to consider is that people can’t really tell how much discrimination they face based on their subjective experience. In their classic 1997 book Social Dominance, social psychologists Jim Sidanius and Felicia Pratto report that (in 1997) many African-Americans had no clue about how much racism they faced12See page 106 of the book.. In the 1990s, 58% of African-Americans believed they had the same housing opportunities as white people. 46% thought they had the same chances at employment, and 63% thought they had the same chances in education – despite clear evidence of the contrary13Sidanius and Pratto dedicate the third part of their book to evidence of discrimination against black people. However, they completely disregard discrimination against men – to be fair, most of the evidence that I discussed here was published after the book Social Dominance came out, so you can’t blame the authors.. This is one of the universal patterns described in Social Dominance: unfair treatment against subordinate groups is overlooked, legitimized, and actively erased by the dominant status quo, until even the discriminated population believes it is not real. It is perfectly possible to face discrimination on a daily basis and be completely unaware of it. In addition, there is growing evidence that people (academics, the media, people in general) care very little about the issues that affect men. Most people know about manspreading, but have never heard about the teacher grading gap. People think gender balance at work is important, but only in professions where women are underrepresented. Scientific studies that find a bias against women are cited far more often than studies that find a bias against men, even when the later use larger samples. Remember the kidnapping study I mentioned above, which found that there is less media coverage when a man goes missing? This is the same process. Presumably, this attention disparity is the result of traditional gender roles, which (among many other things) say that men are not expected to complain, and will be shamed if they do so – but this is a complicated topic that deserves a future blog post on its own. As a takeaway, there is a striking similarity between discrimination against ethnic minorities and discrimination against men. My point is not to say that minorities or men “have it harder”, nor is it that racism is exactly identical to sexism – the historical and social mechanisms are obviously entirely different. My point is that, currently, men and ethnic minorities experience a similar pattern of stereotyping and discrimination in their daily life. The strange polarization of the culture wars makes it even harder to notice: the political tribes who care about racism are sharply separated from the tribes who care about men’s issues. This is unfortunate, because both tribes share the common goal of eliminating discrimination14Of course, there are also traditionalists who just use men’s issues as an excuse to attack feminism, hoping to restore traditional gender roles. I personally believe, on the contrary, that traditional gender roles are the cause for discrimination, and that we need to step away from them. – maybe their filter bubbles only show them one side of the problem? It took decades for the majority of the population to realize that racist discrimination is real. For sexism against men, such a shift in collective consciousness has yet to happen. If you spot any mistake or inaccuracy in this text or the supporting evidence, please let me know in the comments, so I can correct it. ### Annex: what about hiring discrimination? Hiring discrimination can be measured by sending fictional resumes to employers, only changing the ethnicity or gender of the applicant, and counting how many replies you get. As you expect, equally-qualified ethnic minorities are far less likely to be hired. Regarding gender discrimination, the evidence is much more mixed. This makes it very easy to cherry-pick studies that show discrimination against women (if you read feminist sources) or against men (if you read MRA sources). This meta-analysis found moderate discrimination against men, but only in female-dominated jobs. This systematic review lists 11 studies looking at pure gender discrimination (man vs woman). Two of them found discrimination against women, four of them found discrimination against men, and the rest found no discrimination. A recent study which tracked recruiters’ behavior on online hiring markets found that women face a 6.7% penalty in men-dominated occupations, and that men face a 12.6% penalty in women-dominated occupations. Overall, gender discrimination in hiring is much less systematic than racial discrimination. This discrepancy is probably a remnant of the traditional gender division of labor, since men were traditionally assigned to salaried jobs. In any case, the common claim that it is harder for women to find employment appears to be wrong. Changelog: 30-11-2020 – According Leeth et al., 2005, the racial gaps in fatal and non-fatal workplace injuries are respectively 16% and 33%, not 20% as previously reported. 01-02-2021 – A few studies on the effect of victim gender/origins on sentencing found no evidence for discrimination after controlling for case details. Thanks Greg for pointing that out. I also moved hiring discrimination to an annex, and added the recent study by Hangartner et al. ### 90% true: Agriculture from the Future This post is only 90% true. Among these ten items, one was deliberately made-up. Each items includes links to sources, so you can easily check if they are true. Can you find the fake item? (More information about the series here.) 1. Insect-resistant, genetically-modified maize have been cultivated in Spain and Portugal for more than twenty years. A 2019 study analyzed the environmental effects: aside from the obvious decrease in pesticide pollution and water savings, there was a measurable drop in greenhouse-gas emissions. This is because diesel-powered tractors were no longer needed to spray the insecticides. The downside of insect-resistant GMOs is that new pests will eventually emerge after a few decades, just like they do with chemical pesticides. Biotechnology could also have an impact on climate change in a more direct manner – for example, engineering the gut microbiota of cows to minimize the production of methane by cattle, or genetically modifying poplars for wood production so they no longer release isoprene, a pollutant that increases the air concentration of ozone and methane. 2. You might think that millions of years of evolution would have fully optimized photosynthesis, but it is not quite the case. Many crops are much less efficient than what would be possible in theory. Multiple genetic strategies are possible to increase the yield of crops, for example to increase their carbohydrate production. In soybeans, rice and wheat, the process of photorespiration diverts part of the energy obtained from photosynthesis. Using tobacco plants as a model, researchers were able to increase biomass by more than 20% in field trials, just by optimizing the expression levels of various photosynthetic components. 3. Improving the nutritional qualities of crops through genetic modification is also promising, especially in third-world countries were malnutrition is rampant. The “golden rice”, a variant of rice with a high level of vitamin A was developed more than fifteen years ago. So far, it has not been widely adopted (in part due to efforts from Greenpeace to undermine it). More recently, by enhancing cassava with an iron transporter and the iron-storage protein ferritin, it was possible to increase the plant’s iron and zinc content by about ten-fold. 4. Even without genetic modification, the fruits and vegetables we eat are very different from what is found in nature, owing to centuries of breeding. This is visible in still-life paintings from the Renaissance where fruits are on display. If you are wondering what vegetables looked like in their natural, not-genetically-modified forms, here are pictures of wild-type bananas, wild-type corn, and wild-type carrots1This last links points to a website called World Carrot Museum, with the tagline “discover the power of carrots”. That might not be an academic source, but I am sure we can trust them for all our carrot questions.. 5. Since humans started agriculture thousands of years ago, the selection of plants by breeding has completely changed our food habits. This, in turn, put an evolutionary selection pressure on humans themselves. The textbook example is lactase persistence, when the domestication of cows gave a great advantage to humans who could digest cow milk. Now, according to some research, modern humans have evolved some kind of dependency to selected plants. That is, if all the domesticated plants were to suddenly go back to their wild state, most humans would have trouble finding food they can digest. 6. Starting in the 1950s, exposing crops to radiation became a popular way to generate new mutant varieties. The typical “gamma garden” design involves a circular field with a Cobalt-60 gamma ray source in the middle. This way, seeds are exposed to a gradient of radioactivity – the plants near the center usually die, the peripheral plants are unaltered, and interesting things can happen in the intermediate range. Needless to say, gamma rays produce mutations all over the genome, and large chromosomal rearrangements are frequently observed. Despite being much messier than genetic modification techniques like CRISPR, plants obtained through “atomic gardening” are not legally considered GMOs. They may even be accepted in organic food. 7. There are no Terminator seeds. The legend goes that some greedy GMO company sold seeds that would turn sterile after the first generation, so that farmers could not sow them and would have to buy it again from the company every year. The underlying technology does exist, but it was never used in any commercialized product. That being said, farmers buying new seeds every year is nothing new (and not restricted to GMOs): for decades they have relied on hybrids from inbred plants, which have desirable properties but can be sowed only once since their offspring would be too heterogeneous. 8. Local production has become an important criterion for consumers. Somehow, people are starting to realize there might be something wrong about shipping fruits and vegetables from the other side of the planet. In general, the more local, the greener. But there is a loophole: not all places are equally fertile. According to a study from 2020, only one third of the world population could sustainably feed on food produced in a radius of 100 km. In some cases, outsourcing food production to more fertile grounds could allow to spare land (i.e. growing forests), which is a good way to sequester GHG. In fact, a recent paper advocated for combining high-yield farming in some spots with land-sparing in other spots, as the optimal strategy for environment-friendly agriculture. 9. According to large surveys of representative samples in the USA, France and Germany, extreme opponents of genetically modified foods know the least but think they know the most (this is one of the best titles for a scientific article). 10. Like cellphones, micro-wave ovens and every other new technology, GMOs have been accused of causing cancer2For some reason, it’s always cancer. I have never met anybody who feared GMOs would cause pica or Capgras syndrome, although that would be pretty funny.. And technically speaking, yes, they do – but just as much as regular food. Carcinogenic substances can be found in small amounts in all kinds of food, e.g. in red meat, cereals, apple juice3In most cases, the amount is negligibly small. The only association that I would take seriously is red meat.… In fact, it is even possible to engineer plants so that they protect against cancer, like this broccoli. Could you find the false item? If you have doubts, feel free to discuss about it in the comment section. ### 90% true: Introduction Around 2015 was the Golden Age of numbered lists on the Internet. Articles whose title started with “10 things that…” quickly filled the web. Today, I want to bring back this forgotten format from the dead. The problem with numbered lists was that, out of 10 items, about half turned out to be complete bullshit. As a result, people started to associate it with clickbait and stigmatize the format. But my clickbait will not be like other clickbaits. In mine, you know that exactly 90% of the list is real, and 10% is made up. This series will be known as 90% true and will contain 9 true items and 1 fabricated item about various politically-sensitive topics. This way, you are somehow required to do a little bit of fact-checking, or at the very least exert some suspicion. I think this is one of the most effective methods against confirmation bias. In regular blog posts, if one piece of information flatters your own opinions, you are more likely to believe it without checking. But not in 90% true – imagine how shameful you would feel if the item you believed the most was revealed to be false? I hope the threat of feeling dumb will ensure you remain critical at all time. It goes a bit deeper than that: since one item is false, you have to be critical and do some fact-checking. But since I know you will be doing some fact-checking, I have to be as honest and rigorous as possible, because you would spot any attempt from me to be dishonest. In some paradoxical way, the deliberately fake element is a proof of my honesty to you. I’ll make sure that the false item is not too obfuscated, so you do not need to spend a lot of time researching obscure literature to find it. Just following the links to the sources should be enough, and you can always discuss in the comment section. One last thing: I sometimes make mistakes, so there is no guarantee that the number of bullshit items will always be exactly one. But you were going to fact-check anyway, weren’t you? ### Articles in the 90% true series ### Celebrities, numerosity and the Weber-Fechner law This article uses the net worth of celebrities as a practical example. Net worth values were shamelessly taken from celebritynetworth.com as of August 2020. They may fluctuate and become obsolete within days, but it does not change anything to the point of the article. Also, I will assume that you, the reader, have a net worth of$0 (trust me, it’s not going to matter).

I.

I recently had a discussion with my brother about Cristiano Ronaldo becoming the first billionaire footballer ever. We were both surprised, but for opposite reasons. He was surprised that no footballer ever before became a billionaire, while I was surprised that it was ever possible to reach one billion through football, even with associated income like advertisement and clothing. I think this disagreement gives some insight about the way we process large numbers. There are essentially two ways for humans to mentally handle quantities: one  is called numeracy and resorts to a set of symbols with rules that tell you how to work with them. The other one is called numerosity and is some kind of analogue scale we use to compare things without resorting to symbols. To demonstrate that numerosity is more sophisticated than it looks, let’s do a thought experiment.

Imagine you are in a large room with Jeff Bezos, the richest person in the world. There is a line painted on the floor, with numbers written on each end. One side is marked with a big 0, the other side is marked with « $190 billions ». Mmm, it looks like we are in a thought experiment where we have to stand on a line depending on our net worth, you think. As Jeff Bezos stands on the$190 billion mark, you reluctantly walk to the zero mark right next to the wall, where you belong.

You see Bezos smirking at you from the other side. Suddenly, the door opens, and a bunch of world-class football players enter the room. Intuitively, where do you think they will stand on the line?

This may come as a surprise, but compared to Jeff Bezos, the net worth of all these legendary footballers is not so different from yours (remember, you’re worth $0). Football players might be millionaires, but they are very unlikely to become billionaires, Cristiano Ronaldo being the exception. Thus, on a line from$0 to \$190B, they are basically piled up right next to you. What about superstar singers?

Some singers become much richer than footballers, but they are still much closer to you than to Jeff Bezos. Let’s add a few famous billionaires. Like, people who are actually famous because they are billionaires.

Surprisingly, they are still very close to you in absolute value. Their wealth is still several orders of magnitude below Bezos. What happens if we look at big tech CEOs, like Elon Musk or Larry Page? Surely they belong to the same world as Bezos?

Now, this is indeed getting closer to Bezos. However, in absolute distance, they are still closer to you. Here is the punchline – the absolute wealth difference between Elon Musk and you is smaller than between Elon Musk and Jeff Bezos. This becomes obvious once you realize Bezos’s wealth is more than twice as much as Musk’s wealth.

II.

Why is this so counter-intuitive? This is because, unless we look carefully into the numbers, we are comparing all these large quantities using the numerosity scale, which is logarithmic. Musk has hundreds of thousands times more money than you, and only 3 times less money than Bezos. Since 3 is smaller than hundreds of thousands, you intuitively estimate that Musk is closer to Bezos than to you.

It makes sense: in the graphs above (which use linear scales), the dots for everybody under one billion are almost impossible to distinguish. If you wanted to display these people’s net worth in a readable way, you would need to use a log-scale. In the case of wealth, a log scale is especially appropriate since wealth accumulation is a multiplicative process: the more dollars you already have, the easier it is to acquire one extra dollar. In consequence, wealth can be well-approximated with a log-normal distribution, which is strongly skewed towards low values. Most values are lower than the average, but then you’ve got a few very high values that drive the mean up. A typical feature of this kind of distributions is that high values fall very far from each other. That’s why the richest human in the world (Bezos) beats the second richest (currently Bill Gates, not shown on the graphs) by a margin of several billions.

But our perception of numbers as a log-scale is not restricted to the wealth of celebrities. In fact, it appears to be an universal pattern is numerical cognition, called the Weber-Fechner law. Originally, this law is about sensory input, for example light intensity or sound loudness. But it also applies to counting objects:

In this picture (reprinted from Wikipedia), it is much easier to see the difference between 10 and 20 dots, than between 110 and 120 dots. We seem to have a logarithmic scale hard-wired into our brains.

III.

What really puzzles me about the Weber-Fechner law is that we are performing a logarithmic transformation intuitively, without thinking about it. There is evidence that it is rather innate: pre-school children have been shown to use a logarithmic number line before they learn about digital symbols. After a few years of schooling, children tend to switch away from the logarithmic line to a more linear number cognition system, which can be difficult. Eventually, in high school, they have to learn logarithms again, in an abstract formal way. Logarithms are notoriously difficult to teach (I know plenty of well-educated people who still struggle with them). This is a shame, because all these high-schoolers have been using log scales since they were young, without even realizing it.

The train is about to depart. Your ticket in your hand, you check your seat number, walk in the central alley, find your seat and sit down next to another traveler. You look around to see what the other people in the wagon look like.

How many people were there in the wagon you just imagined? If you are like me, it was probably rather crowded, with few empty seats. However, according to these European data, the average occupancy rate of trains is only about 45%, so there should be more empty seats than occupied ones. What is going on?

The issue here is a simple statistical phenomenon: the sample of “all the trains you took in your life” is not quite representative of “all the trains”. The occupancy rate of trains varies all the time. Some trains will be much more crowded than average, some others will be almost empty. And – guess what – the more people there are in a train, the more likely for you to be one of them. A train packed with hundreds of customers will be observed by, well, hundreds of passengers while the empty trains will not be observed at all. Thus, in your empirical sample, trains with n passengers will be over-represented n times compared to trains with only one passenger.

Here is a riddle: you want to estimate the average number of occupants in the trains that arrive to a station. To that end, you survey people leaving the station and ask how many people they saw in the same train. If you were to take the mean of your sample, the average occupancy would be over-estimated, for the reason stated above. How do you calculate the unbiased occupancy rate? Assume every train had at least one occupant (this is necessary since empty trains are never observed, so the number could be virtually anything).

We have an observed distribution P_o(n) and we want to get back to the true distribution P_t(n). As we saw before:

P_o(n) = \frac{nP_t(n)}{\sum_{k}{kP_t(k)}}

Since \sum_{k}{P_t(k)} = 1, the true distribution is

P_t(n) = \frac{P_o(n)/n}{\sum_{k}{P_o(k)/k}}

And the mean occupancy of the trains is

\langle n \rangle = \frac{1}{\sum_{k}{\frac{P_o(k)}{k}}}

which turns out to be the harmonic mean of the observed sample.

Harmonic mean is typically used to average rates. The textbook example is about calculating the average speed of something: if you write down the speed of a car once per kilometer, the average speed is the harmonic mean of your sample, not the arithmetic mean. This is because the car spends less time on the kilometers that it traveled through very fast, so you need to account for that by giving less weight to those kilometers. This is in fact closely related to the train occupancy riddle: in that case, the harmonic mean gives more weight to the trains with fewer people in them, to compensate for the sampling bias.

I don’t know if this statistical bias has a name (if you know, tell me in the comments). It occurs in a lot of situations. A prominent one is the fact that your average Facebook friend has more Facebook friends than average.

Consider how your Facebook friends are sampled: obviously, only people with at least one friend will appear in your sample. So all those idle accounts with no friends at all are already excluded. People with 100 friends are 10 times more likely to appear in your list than people with 10 friends. This leads to a big inflation of the average number of friends your friends have. To put it in a different way, if you have an average number of friends, it’s *perfectly normal* that you have fewer friends than your friends. So there is no need to worry about it.