talent

How to detect discrimination, empirically

PNRJ core principles, ethics, inequality, mathematical models, public policy, tribal paradigm , , , , , , , , , ,

Aug 25 JDN 2460548

For concreteness, I’ll use men and women as my example, though the same principles would apply for race, sexual orientation, and so on. Suppose we find that there are more men than women in a given profession; does this mean that women are being discriminated against?

Not necessarily. Maybe women are less interested in that kind of work, or innately less qualified. Is there a way we can determine empirically that it really is discrimination?

It turns out that there is. All we need is a reliable measure of performance in that profession. Then, we compare performance between men and women, and that comparison can tell us whether discrimination is happening or not. The key insight is that workers in a job are not a random sample; they are a selected sample. The results of that selection can tell us whether discrimination is happening.

Here’s a simple model to show how this works.

Suppose there are five different skill levels in the job, from 1 to 5 where 5 is the most skilled. And suppose there are 5 women and 5 men in the population.

1. Baseline

The baseline case to consider is when innate talents are equal and there is no discrimination. In that case, we should expect men and women to be equally represented in the profession.

For the simplest case, let’s say that there is one person at each skill level:

MenWomen
11
22
33
44
55

Now suppose that everyone above a certain skill threshold gets hired. Since we’re assuming no discrimination, the threshold should be the same for men and women. Let’s say it’s 3; then these are the people who get hired:

Hired MenHired Women
33
44
55

The result is that not only are there the same number of men and women in the job, their skill levels are also the same. There are just as many highly-competent men as highly-competent women.

2. Innate Differences

Now, suppose there is some innate difference in talent between men and women for this job. For most jobs this seems suspicious, but consider pro sports: Men really are better at basketball, in general, than women, and this is pretty clearly genetic. So it’s not absurd to suppose that for at least some jobs, there might be some innate differences. What would that look like?


Again suppose a population of 5 men and 5 women, but now the women are a bit less qualified: There are two 1s and no 5s among the women.

MenWomen
11
21
32
43
54

Then, this is the group that will get hired:

Hired MenHired Women
33
44
5

The result will be fewer women who are on average less qualified. The most highly-qualified individuals at that job will be almost entirely men. (In this simple model, entirely men; but you can easily extend it so that there are a few top-qualified women.)

This is in fact what we see for a lot of pro sports; in a head-to-head match, even the best WNBA teams would generally lose against most NBA teams. That’s what it looks like when there are real innate differences.

But it’s hard to find clear examples outside of sports. The genuine, large differences in size and physical strength between the sexes just don’t seem to be associated with similar differences in mental capabilities or even personality. You can find some subtler effects, but nothing very large—and certainly nothing large enough to explain the huge gender gaps in various industries.

3. Discrimination

What does it look like when there is discrimination?

Now assume that men and women are equally qualified, but it’s harder for women to get hired, because of discrimination. The key insight here is that this amounts to women facing a higher threshold. Where men only need to have level 3 competence to get hired, women need level 4.

So if the population looks like this:

MenWomen
11
22
33
44
55

The hired employees will look like this:

Hired MenHired Women
3
44
55

Once again we’ll have fewer women in the profession, but they will be on average more qualified. The top-performing individuals will be as likely to be women as they are to be men, while the lowest-performing individuals will be almost entirely men.

This is the kind of pattern we observe when there is discrimination. Do we see it in real life?

Yes, we see it all the time.

Corporations with women CEOs are more profitable.

Women doctors have better patient outcomes.

Startups led by women are more likely to succeed.

This shows that there is some discrimination happening, somewhere in the process. Does it mean that individual firms are actively discriminating in their hiring process? No, it doesn’t. The discrimination could be happening somewhere else; maybe it happens during education, or once women get hired. Maybe it’s a product of sexism in society as a whole, that isn’t directly under the control of employers. But it must be in there somewhere. If women are both rarer and more competent, there must be some discrimination going on.

What if there is also innate difference? We can detect that too!

4. Both

Suppose now that men are on average more talented, but there is also discrimination against women. Then the population might look like this:

MenWomen
11
21
32
43
54

And the hired employees might look like this:

Hired MenHired Women
3
4
54

In such a scenario, you’ll see a large gender imbalance, but there may not be a clear difference in competence. The tiny fraction of women who get hired will perform about as well as the men, on average.

Of course, this assumes that the two effects are of equal strength. In reality, we might see a whole spectrum of possibilities, from very strong discrimination with no innate differences, all the way to very large innate differences with no discrimination. The outcomes will then be similarly along a spectrum: When discrimination is much larger than innate difference, women will be rare but more competent. When innate difference is much larger than discrimination, women will be rare and less competent. And when there is a mix of both, women will be rare but won’t show as much difference in competence.

Moreover, if you look closer at the distribution of performance, you can still detect the two effects independently. If the lowest-performing workers are almost all men, that’s evidence of discrimination against women; while if the highest-performing workers are almost all men, that’s evidence of innate difference. And if you look at the table above, that’s exactly what we see: Both the 3 and the 5 are men, indicating the presence of both effects.

What does affirmative action do?

Effectively, affirmative action lowers the threshold for hiring women (or minorities) in order to equalize representation in the workplace. In the presence of discrimination raising that threshold, this is exactly what we need! It can take us from case 3 (discrimination) to case 1 (equality), or from case 4 (both discrimination and innate difference) to case 2 (innate difference only).

Of course, it’s possible for us to overshoot, using more affirmative action than we should have. If we achieve better representation of women, but the lowest performers at the job are women, then we have overshot, effectively now discriminating against men. Fortunately, there is very little evidence of this in practice. In general, even with affirmative action programs in place, we tend to find that the lowest performers are still men—so there is still discrimination against women that we’ve failed to compensate for.

What if we can’t measure competence?

Of course, it’s possible that we don’t have good measures of competence in a given industry. (One must wonder how firms decide who to hire, but frankly I’m prepared to believe they’re just really bad at it.) Then we can’t observe discrimination statistically in this way. What do we do then?

Well, there is at least one avenue left for us to detect discrimination: We can do direct experiments comparing resumes with male names versus female names. These sorts of experiments typically don’t find very much, though—at least for women. For different races, they absolutely do find strong results. They also find evidence of discrimination against people with disabilities, older people, and people who are physically unattractive. There’s also evidence of intersectional effects, where women of particular ethnic groups get discriminated against even when women in general don’t.

But this will only pick up discrimination if it occurs during the hiring process. The advantage of having a competence measure is that it can detect discrimination that occurs anywhere—even outside employer control. Of course, if we don’t know where the discrimination is happening, that makes it very hard to fix; so the two approaches are complementary.

And there is room for new methods too; right now we don’t have a good way to detect discrimination in promotion decisions, for example. Many of us suspect that it occurs, but unless you have a good measure of competence, you can’t really distinguish promotion discrimination from innate differences in talent. We don’t have a good method for testing that in a direct experiment, either, because unlike hiring, we can’t just use fake resumes with masculine or feminine names on them.

The injustice of talent

PNRJ core principles, ethics, inequality, mathematical models, personal , , , , , , , , , , , , , , , ,

Sep 4 JDN 2459827

Consider the following two principles of distributive justice.

A: People deserve to be rewarded in proportion to what they accomplish.

B: People deserve to be rewarded in proportion to the effort they put in.

Both principles sound pretty reasonable, don’t they? They both seem like sensible notions of fairness, and I think most people would broadly agree with both them.

This is a problem, because they are mutually contradictory. We cannot possibly follow them both.

For, as much as our society would like to pretend otherwise—and I think this contradiction is precisely why our society would like to pretend otherwise—what you accomplish is not simply a function of the effort you put in.

Don’t get me wrong; it is partly a function of the effort you put in. Hard work does contribute to success. But it is neither sufficient, nor strictly necessary.

Rather, success is a function of three factors: Effort, Environment, and Talent.

Effort is the work you yourself put in, and basically everyone agrees you deserve to be rewarded for that.

Environment includes all the outside factors that affect you—including both natural and social environment. Inheritance, illness, and just plain luck are all in here, and there is general, if not universal, agreement that society should make at least some efforts to minimize inequality created by such causes.

And then, there is talent. Talent includes whatever capacities you innately have. It could be strictly genetic, or it could be acquired in childhood or even in the womb. But by the time you are an adult and responsible for your own life, these factors are largely fixed and immutable. This includes things like intelligence, disability, even height. The trillion-dollar question is: How much should we reward talent?

For talent clearly does matter. I will never swim like Michael Phelps, run like Usain Bolt, or shoot hoops like Steph Curry. It doesn’t matter how much effort I put in, how many hours I spend training—I will never reach their level of capability. Never. It’s impossible. I could certainly improve from my current condition; perhaps it would even be good for me to do so. But there are certain hard fundamental constraints imposed by biology that give them more potential in these skills than I will ever have.

Conversely, there are likely things I can do that they will never be able to do, though this is less obvious. Could Michael Phelps never be as good a programmer or as skilled a mathematician as I am? He certainly isn’t now. Maybe, with enough time, enough training, he could be; I honestly don’t know. But I can tell you this: I’m sure it would be harder for him than it was for me. He couldn’t breeze through college-level courses in differential equations and quantum mechanics the way I did. There is something I have that he doesn’t, and I’m pretty sure I was born with it. Call it spatial working memory, or mathematical intuition, or just plain IQ. Whatever it is, math comes easy to me in not so different a way from how swimming comes easy to Michael Phelps. I have talent for math; he has talent for swimming.

Moreover, these are not small differences. It’s not like we all come with basically the same capabilities with a little bit of variation that can be easily washed out by effort. We’d like to believe that—we have all sorts of cultural tropes that try to inculcate that belief in us—but it’s obviously not true. The vast majority of quantum physicists are people born with high IQ. The vast majority of pro athletes are people born with physical prowess. The vast majority of movie stars are people born with pretty faces. For many types of jobs, the determining factor seems to be talent.

This isn’t too surprising, actually—even if effort matters a lot, we would still expect talent to show up as the determining factor much of the time.

Let’s go back to that contest function model I used to analyze the job market awhile back (the one that suggests we spend way too much time and money in the hiring process). This time let’s focus on the perspective of the employees themselves.

Each employee has a level of talent, h. Employee X has talent hx and exerts effort x, producing output of a quality that is the product of these: hx x. Similarly, employee Z has talent hz and exerts effort z, producing output hz z.

Then, there’s a certain amount of luck that factors in. The most successful output isn’t necessarily the best, or maybe what should have been the best wasn’t because some random circumstance prevailed. But we’ll say that the probability an individual succeeds is proportional to the quality of their output.

So the probability that employee X succeeds is: hx x / ( hx x + hz z)

I’ll skip the algebra this time (if you’re interested you can look back at that previous post), but to make a long story short, in Nash equilibrium the two employees will exert exactly the same amount of effort.

Then, which one succeeds will be entirely determined by talent; because x = z, the probability that X succeeds is hx / ( hx + hz).

It’s not that effort doesn’t matter—it absolutely does matter, and in fact in this model, with zero effort you get zero output (which isn’t necessarily the case in real life). It’s that in equilibrium, everyone is exerting the same amount of effort; so what determines who wins is innate talent. And I gotta say, that sounds an awful lot like how professional sports works. It’s less clear whether it applies to quantum physicists.

But maybe we don’t really exert the same amount of effort! This is true. Indeed, it seems like actually effort is easier for people with higher talent—that the same hour spent running on a track is easier for Usain Bolt than for me, and the same hour studying calculus is easier for me than it would be for Usain Bolt. So in the end our equilibrium effort isn’t the same—but rather than compensating, this effect only serves to exaggerate the difference in innate talent between us.

It’s simple enough to generalize the model to allow for such a thing. For instance, I could say that the cost of producing a unit of effort is inversely proportional to your talent; then instead of hx / ( hx + hz ), in equilibrium the probability of X succeeding would become hx2 / ( hx2 + hz2). The equilibrium effort would also be different, with x > z if hx > hz.

Once we acknowledge that talent is genuinely important, we face an ethical problem. Do we want to reward people for their accomplishment (A), or for their effort (B)? There are good cases to be made for each.

Rewarding for accomplishment, which we might call meritocracy,will tend to, well, maximize accomplishment. We’ll get the best basketball players playing basketball, the best surgeons doing surgery. Moreover, accomplishment is often quite easy to measure, even when effort isn’t.

Rewarding for effort, which we might call egalitarianism, will give people the most control over their lives, and might well feel the most fair. Those who succeed will be precisely those who work hard, even if they do things they are objectively bad at. Even people who are born with very little talent will still be able to make a living by working hard. And it will ensure that people do work hard, which meritocracy can actually fail at: If you are extremely talented, you don’t really need to work hard because you just automatically succeed.

Capitalism, as an economic system, is very good at rewarding accomplishment. I think part of what makes socialism appealing to so many people is that it tries to reward effort instead. (Is it very good at that? Not so clear.)

The more extreme differences are actually in terms of disability. There’s a certain baseline level of activities that most people are capable of, which we think of as “normal”: most people can talk; most people can run, if not necessarily very fast; most people can throw a ball, if not pitch a proper curveball. But some people can’t throw. Some people can’t run. Some people can’t even talk. It’s not that they are bad at it; it’s that they are literally not capable of it. No amount of effort could have made Stephen Hawking into a baseball player—not even a bad one.

It’s these cases when I think egalitarianism becomes most appealing: It just seems deeply unfair that people with severe disabilities should have to suffer in poverty. Even if they really can’t do much productive work on their own, it just seems wrong not to help them, at least enough that they can get by. But capitalism by itself absolutely would not do that—if you aren’t making a profit for the company, they’re not going to keep you employed. So we need some kind of social safety net to help such people. And it turns out that such people are quite numerous, and our current system is really not adequate to help them.

But meritocracy has its pull as well. Especially when the job is really important—like surgery, not so much basketball—we really want the highest quality work. It’s not so important whether the neurosurgeon who removes your tumor worked really hard at it or found it a breeze; what we care about is getting that tumor out.

Where does this leave us?

I think we have no choice but to compromise, on both principles. We will reward both effort and accomplishment, to greater or lesser degree—perhaps varying based on circumstances. We will never be able to entirely reward accomplishment or entirely reward effort.

This is more or less what we already do in practice, so why worry about it? Well, because we don’t like to admit that it’s what we do in practice, and a lot of problems seem to stem from that.

We have people acting like billionaires are such brilliant, hard-working people just because they’re rich—because our society rewards effort, right? So they couldn’t be so successful if they didn’t work so hard, right? Right?

Conversely, we have people who denigrate the poor as lazy and stupid just because they are poor. Because it couldn’t possibly be that their circumstances were worse than yours? Or hey, even if they are genuinely less talented than you—do less talented people deserve to be homeless and starving?

We tell kids from a young age, “You can be whatever you want to be”, and “Work hard and you’ll succeed”; and these things simply aren’t true. There are limitations on what you can achieve through effort—limitations imposed by your environment, and limitations imposed by your innate talents.

I’m not saying we should crush children’s dreams; I’m saying we should help them to build more realistic dreams, dreams that can actually be achieved in the real world. And then, when they grow up, they either will actually succeed, or when they don’t, at least they won’t hate themselves for failing to live up to what you told them they’d be able to do.

If you were wondering why Millennials are so depressed, that’s clearly a big part of it: We were told we could be and do whatever we wanted if we worked hard enough, and then that didn’t happen; and we had so internalized what we were told that we thought it had to be our fault that we failed. We didn’t try hard enough. We weren’t good enough. I have spent years feeling this way—on some level I do still feel this way—and it was not because adults tried to crush my dreams when I was a child, but on the contrary because they didn’t do anything to temper them. They never told me that life is hard, and people fail, and that I would probably fail at my most ambitious goals—and it wouldn’t be my fault, and it would still turn out okay.

That’s really it, I think: They never told me that it’s okay not to be wildly successful. They never told me that I’d still be good enough even if I never had any great world-class accomplishments. Instead, they kept feeding me the lie that I would have great world-class accomplishments; and then, when I didn’t, I felt like a failure and I hated myself. I think my own experience may be particularly extreme in this regard, but I know a lot of other people in my generation who had similar experiences, especially those who were also considered “gifted” as children. And we are all now suffering from depression, anxiety, and Impostor Syndrome.

All because nobody wanted to admit that talent, effort, and success are not the same thing.

Against “doing your best”

PNRJ heuristics and biases, personal , , , , ,

Oct 3 JDN 2459491

It’s an appealing sentiment: Since we all have different skill levels, rather than be held to some constant standard which may be easy for some but hard for others, we should each do our best. This will ensure that we achieve the best possible outcome.

Yet it turns out that this advice is not so easy to follow: What is “your best”?

Is your best the theoretical ideal of what your performance could be if all obstacles were removed and you worked at your greatest possible potential? Then no one in history has ever done their best, and when people get close, they usually end up winning Nobel Prizes.

Is your best the performance you could attain if you pushed yourself to your limit, ignored all pain and fatigue, and forced yourself to work at maximum effort until you literally can’t anymore? Then doing your best doesn’t sound like such a great thing anymore—and you’re certainly not going to be able to do it all the time.

Is your best the performance you would attain by continuing to work at your usual level of effort? Then how is that “your best”? Is it the best you could attain if you work at a level of effort that is considered standard or normative? Is it the best you could do under some constraint limiting the amount of pain or fatigue you are willing to bear? If so, what constraint?

How does “your best” change under different circumstances? Does it become less demanding when you are sick, or when you have a migraine? What if you’re depressed? What if you’re simply not feeling motivated? What if you can’t tell whether this demotivation is a special circumstance, a depression system, a random fluctuation, or a failure to motivate yourself?

There’s another problem: Sometimes you really aren’t good at something.

A certain fraction of performance in most tasks is attributable to something we might call “innate talent”; be it truly genetic or fixed by your early environment, it nevertheless is something that as an adult you are basically powerless to change. Yes, you could always train and practice more, and your performance would thereby improve. But it can only improve so much; you are constrained by your innate talent or lack thereof. No amount of training effort will ever allow me to reach the basketball performance of Michael Jordan, the painting skill of Leonardo Da Vinci, or the mathematical insight of Leonhard Euler. (Of the three, only the third is even visible from my current horizon. As someone with considerable talent and training in mathematics, I can at least imagine what it would be like to be as good as Euler—though I surely never will be. I can do most of the mathematical methods that Euler was famous for; but could I have invented them?)

In fact it’s worse than this; there are levels of performance that would be theoretically possible for someone of your level of talent, yet would be so costly to obtain as to be clearly not worth it. Maybe, after all, there is some way I could become as good a mathematician as Euler—but if it would require me to work 16-hour days doing nothing but studying mathematics for the rest of my life, I am quite unwilling to do so.

With this in mind, what would it mean for me to “do my best” in mathematics? To commit those 16-hour days for the next 30 years and win my Fields Medal—if it doesn’t kill me first? If that’s not what we mean by “my best”, then what do we mean, after all?

Perhaps we should simply abandon the concept, and ask instead what successful people actually do.

This will of course depend on what they were successful at; the behavior of basketball superstars is considerably different from the behavior of Nobel Laureate physicists, which is in turn considerably different from the behavior of billionaire CEOs. But in theory we could each decide for ourselves which kind of success we actually would desire to emulate.

Another pitfall to avoid is looking only at superstars and not comparing them with a suitable control group. Every Nobel Laureate physicist eats food and breathes oxygen, but eating food and breathing oxygen will not automatically give you good odds of winning a Nobel (though I guess your odds are in fact a lot better relative to not doing them!). It is likely that many of the things we observe successful people doing—even less trivial things, like working hard and taking big risks—are in fact the sort of thing that a great many people do with far less success.

Upon making such a comparison, one of the first things that we would notice is that the vast majority of highly-successful people were born with a great deal of privilege. Most of them were born rich or at least upper-middle-class; nearly all of them were born healthy without major disabilities. Yes, there are exceptions to any particular form of privilege, and even particularly exceptional individuals who attained superstar status with more headwinds than tailwinds; but the overwhelming pattern is that people who get home runs in life tend to be people who started the game on third base.

But setting that aside, or recalibrating one’s expectations to try to attain a level of success often achieved by people with roughly the same level of privilege as oneself, we must ask: How often? Should you aspire to the median? The top 20%? The top 10%? The top 1%? And what is your proper comparison group? Should I be comparing against Americans, White male Americans, economists, queer economists, people with depression and chronic migraines, or White/Native American male queer economists with depression and chronic migraines who are American expatriates in Scotland? Make the criteria too narrow, and there won’t be many left in your sample. Make them instead too broad, and you’ll include people with very different circumstances who may not be a fair comparison. Perhaps some sort of weighted average of different groups could work—but with what weighting?

Or maybe it’s right to compare against a very broad group, since this is what ultimately decides our life prospects. What it would take to write the best novel you (or someone “like you” in whatever sense that means) can write may not be the relevant question: What you really needed to know was how likely it is that you could make a living as a novelist.


The depressing truth in such a broad comparison is that you may in fact find yourself faced with so many obstacles that there is no realistic path toward the level of success you were hoping for. If you are reading this, I doubt matters are so dire for you that you’re at serious risk of being homeless and starving—but there definitely are people in this world, millions of people, for whom that is not simply a risk but very likely the best they can hope for.

The question I think we are really trying to ask is this: What is the right standard to hold ourselves against?

Unfortunately, I don’t have a clear answer to this question. I have always been an extremely ambitious individual, and I have inclined toward comparisons with the whole world, or with the superstars of my own fields. It is perhaps not surprising, then, that I have consistently failed to live up to my own expectations for my own achievement—even as I surpass what many others expected for me, and have long-since left behind what most people expect for themselves and each other.

I would thus not exactly recommend my own standards. Yet I also can’t quite bear to abandon them, out of a deep-seated fear that it is only by holding myself to the patently unreasonable standard of trying to be the next Einstein or Schrodinger or Keynes or Nash that I have even managed what meager achievements I have made thus far.

Of course this could be entirely wrong: Perhaps I’d have achieved just as much if I held myself to a lower standard—or I could even have achieved more, by avoiding the pain and stress of continually failing to achieve such unattainable heights. But I also can’t rule out the possibility that it is true. I have no control group.

In general, what I think I want to say is this: Don’t try to do your best. You have no idea what your best is. Instead, try to find the highest standard you can consistently meet.