More on statistical discrimination

A few of you have raised objections to my recent statistical discrimination hypothesis on the grounds that, if it were true, minority group members who “made it to the top” should be the super-achievers, since they had to pass through so many screens and implicit taxes.  I wrote back the following (edited) in an email:

Maybe, but I think you are assuming fixed quality of talent within each sector.

Let’s say there are two sectors. In the first, the CEO sector, women face statistical discrimination and there are multiple levels. In the second there is no statistical discrimination, let us call it women’s tennis but of course there are other examples too.

It could be that most of the talented women, those who can judge where they really will succeed best and most easily, flock to the latter sectors.  In which case the winners in the CEO sector need not be so special, including in the presence of discrimination.

That also means that employers and intermediaries have no special incentives to hunt for that talent: it has run away to other, less discriminatory sectors (and lowered wages in those sectors, I might add).

By the way, here was one good comment by Willitts on that post:

…if the signal of skill is “years of experience,” then the person filtered at the lower level will always look objectively worse at the higher level filters.

You’re assuming that the higher level decision makers have the opportunity (and desire) to consider walk-on candidates. You’re also assuming that those walk-ons will have adequate means to signal their superiority to those who passed through the filters.

I might be able to be the best CEO who ever lived, but my lack of management experience would never get me in the door for an interview. If (mild) discrimination at several rungs of the ladder kept me from rising to the penultimate rung, I’d have ZERO chance of attaining the top rung, not merely a small chance

And David:

Most elite performers are impressive throughout their lives. But they can stay constantly motivated, by rising through the ranks quickly. A stat-discriminated person might not have that advantage either.

And Jwilli7122:

Well, with the first gatekeeper there’s really no motivation to gamble on the marginalized, because a) there’s not yet a big gap and b) doing so would give up the profit of stereotyping (see the Bayesian analysis referenced in #3 of Dan’s post).

And as you get to the subsequent gatekeepers, a larger actual ability gap starts to form because the discrimination of prior gatekeepers prevented the marginalized group from gaining valuable experience.

I will continue to ponder this problem.


I was somewhat skeptical of the original post (and still am), but these are some very good points.

There are only two groups in the U.S. that are consistently and officially discriminated against; white men and Christians.

Corporate jobs, academia, and political landscape in America certainly does not support your claim.

Academia does support his claim.

A quarter of the country is Evangelical. A further 20% are mainline Protestant and historically black Protestant. Only 17% of Harvard freshmen identify as any form of Protestant. Catholics are also under represented at Harvard.

All non-Christian groups (atheist, agnostic, Hindu, etc.) are over represented at Harvard.

We could take such demographics with a grain of salt, except for the fact that we have admissions officers on record discussing if they should admit students who attended religious undergraduate programs. We have paired resume data suggesting that "President of the Evangelical student association" is much worse than "President of the Hindu student association".

Among the professors, again the non-religious and non-Christians are massively over represented. It gets worse we we drill down to things like Evangelicism (e.g. <6% of professors affirm the Evangelical understanding of the Bible, a view also shared by traditionalist Catholics and other religious groups).

We can take all such evidence of disparity as not indicating discrimination ... but the I wonder what evidence is left for Cowen's thesis at all? The most common methods of asserting discrimination certainly make a decent a priori case that academia discriminates against Evangelicals.

What about pentecostals?

Only 17%. Only 17% of the country is evangelical today. And only about 16% of 18-29 year olds are Protestant in any form - so it seems that they are over represented at Harvard, not under represented.

Thanks, not bad article. Some time ago I've intersted this issue and found a lot of info , but this article made me to review my opinion.

You actually make a good point here. However, I do not think that this is at all inconsistent with Cowen's thesis.

It's inconsistent with majorecon's post, which is what he was responding to

Please, do not comment unless you have read the thread

And never a mention of Liberty University when talking about 'academia.' Sad.

'a view also shared by traditionalist Catholics'

Wrong. Including the fact that Catholics and evangelicals cannot even agree on which version of the Bible is correct.

Actually, no, the understanding of both traditionalist Catholics and Protestants is that the Bible is the "inspired" word of God. In contrast, academics are much more inclined to hold that the Bible is a collection of fables. For the actual survey instrument used, traditionalists from both actually gave the same response.

As far as differing "Bibles", actually no. Both Protestants and Catholics today affirm the primacy of the surviving original language texts (e.g. the Masoretic Text) and have done so since Pius XII. This has given rise to the Nova Vulgata precisely because Catholics stopped holding the Vulgate of Jerome as their primary source.

Catholics and Protestants differ in their translation of the Bible, but we also do this for Beowulf yet still it the same work. They also differ about the status of the deuterocanonical books ins some cases, but a number of Protestants also hold to them.

So yes Protestants have the same understanding of the Bible as measured by Pew. College professors have a different understanding.

"It could be that most of the talented women, those who can judge where they really will succeed best and most easily, flock to the latter sectors."

I dont think this is correct. You get way fewer women or say black CEOs but unless there is a weird counterpossing selection coincidence you still get way above average among those who do make it.

Think of the problem this way conditional on passing X levels of discrimination whay is the probability that you are less than Y talented where ehy is in the top of elite distribution.

Your prior on talent would have to be way hella low not to get a small prob of being less than Y. But if thats true then the statistical discrimination at each level is actually way lower than the actual bias in the applicant pool.

I'm willing to buy that either model could work. We need parameters that can be estimated and domains for the parameter estimates... explicit model.

Right. Willitts, David, and Jwilli7122 all miss the point. It's not that the previously filtered out individuals will somehow "walk on" later. Rather, the average qualifications of the individuals in the discriminated-against group that *pass through* the lower level filters will be higher as a result of the discrimination. These individuals will not suffer from lack of opportunities to gain experience because they will have passed the filter. The low level filters *change* the population statistics. The logical flaw in Tyler's original post was assuming that high-level filters would be based on population statistics facing the low-level filters rather than the *conditional* statistics facing the high-level filters, conditional on having passed the low-level filters. It's not much more complicated than noting that the average qualifications of, say, the top 30% of women are higher than the average qualifications of the top 40%. If only 30% of women pass a filter instead of 40% due to discrimination, then the average qualifications of women passing the filter will be higher at the next level.

This does not mean that the lower-level filters won't result in fewer women reaching the top level. It's just that there won't be a cascading effect due to the multiple levels compared to a single level, which I thought was the claim in Tyler's original post.

The fact that women passing through low-level filters aren't denied opportunities to gain experience, in contrast to women not passing through the filters, is a key point and highlights one shortcoming of thinking of individuals exclusively as members of an identity group. *Individuals* may suffer discrimination from belonging to a group but not all individuals in that group suffer the consequences of that discrimination (such as losing opportunities to gain experience). Only the marginal individuals do. All group members do not suffer an average amount of discrimination. Rather, the marginal individuals suffer all the discrimination, raising the average discrimination across the group.

I wasn't modeling people as only members of their group, I just assumed, that discrimination hits every group member equally hard, instead of acting more as a tie break. Your model sounds actually more plausible, I'll admit. Is there research showing that, that's how discrimination works?
Assuming this is true,
there still could be cascading effects, if a gatekeeper has trouble differentiating between the quality of candidates at all (though that would be an uncharacteristically bad gatekeeper or a very weird gate, I suppose).

This line of thinking assumes that any woman that all candidates that pass through a filter receive equal treatment and equal investment in human capital. This does not happen in reality. Some projects are always better than others. Managers tend to invest time in those that they think will succeed. Even a small differential in skill development will increase over many years and positions.

'In the second there is no statistical discrimination, let us call it women’s tennis but of course there are other examples too.'

Still sticking to the realistic examples, as if most people can easily decide between being a CEO or a professional athlete, even with the caveat of 'other examples.' (Though considering the role of golf in corporate America, maybe pro golfer would have been at least a mildly amusing twist.)

Possibly though, maybe something more familiar could have been used as an example, as discussed here by Prof. Tabarrok-

(And when looking for that link, this popped up in the searches involving EJMR and Tyler Cowen, as faulty memory suggested that the MR post about economics as a profession with a proven track record was related to that web site and him -

"It could be that most of the talented women, those who can judge where they really will succeed best and most easily, flock to [women's tennis]. In which case the winners in the CEO sector need not be so special, including in the presence of discrimination. That also means that employers and intermediaries have no special incentives to hunt for that talent: it has run away to other, less discriminatory sectors ...."

If the most talented women flock to women's tennis (and are successful at it?), then employers and their intermediaries will recruit women who have flocked to women's tennis.

To clarify, if talented women signal their talent by "flocking" to women's tennis and/or by their success at women's tennis, then employers won't need to rely on crude proxies like stereotypes about women, i.e., they won't engage in statistical discrimination. That is necessary only when there is no direct information about individual women's talents.

I can think of a few examples of where the representatives of the discriminated group that got through the sieve tended to be very skilled.

In the early years of integrated baseball, say, 1947-1960 or so, when teams typically had unwritten rules limiting the number of black ballplayers to the Star and his roommate, black big leaguers tended to be notably better on average than white big leaguers.

If you go back to 1973, there weren't all that many female movie reviewers, but Pauline Kael was the most influential and Judith Crist was perhaps on TV the most. Now there are a lot of female film critics, but none of them are as good as Kael was.

Pauline Kael - I don't know ANYONE who read her reviews.

This comment is either a clever reference to Kael's comment: "I don't know how Nixon won, nobody I know voted for him",

or, it's just stupid.

A current example that looks like Tyler's theory of statistical discrimination involves NFL quarterbacks, and I've been writing about it for many years now. Blacks really are better on average at playing cornerback in the NFL than whites or even Samoans. But is the actual difference so large as to account for the bizarre statistic that no non-black has started at cornerback on any of the 32 teams in the NFL since Jason Sehorn retired 14 seasons ago. That's 996 out of 996 position/team/seasons in which the starting cornerback was black at the beginning of the NFL season.

To get to 0/996 for non-blacks, you probably have to have some prejudice driven statistical discrimination going on of the kind Tyler describes: e.g., a spectacularly gifted white kid could have played cornerback in high school or college, but his coach or his dad figured he'd be more likely to make it to the NFL as a safety or linebacker (or receiver or quarterback).

Sorry about the confusion: I didn't mean to type "quarterback," I'm only referring to cornerbacks.

From PBS ConcussionWatch







Smart people will not field the CornerBack position.

Where's running back in terms of concussions?







From reverse engineered draft selection rules, the ramming bull-dozer (Momentum=Weight*Yard40, 0.889 confidence level):

Rule 34:

Height > 74.63

Weight 2447.55

-> class TE [0.889]

The line eater strikes again.

From reverse engineered draft selection rules, the ramming locomotive (Momentum=Weight*Yard40, 0.889 confidence level):

Rule 34:

Height > 74.63

Weight <= 258

Momentum > 2447.55

-> class TE [0.889]

We live in a culture that is feverish at searching out every possible example of prejudice against blacks, but doesn't care much about prejudice against whites, so it's easier to test the hypothesis in this post involving examples of bias against whites.

For example, it's at least arguable that at his peak around 15 years ago, Eminem was the best rapper of them all. So this would support the idea that the existence of statistical discrimination would lead to small number of discriminated against individuals who make it through the filters being of supreme talent.

On the other hand, if blacks really are better at something on average, then the whites who get into the field might just be stubborn or not have any alternatives. For example, contrary to this hypothesis, there are no Eminem-like white superstars in the men's 100m dash, in which the last 72 finalists in the Olympics going back through 1984 have all been at least half-black.

What it looks like is the fastest whites go find something else to do besides run the 100 meters. For example, the French white man Christian LeMaitre ran a 9.92 100m in 2011. But then he gave up the 100m to concentrate on the 200m, an event in which the racial gap has been smaller, and was rewarded by winning a bronze medal at the 2016 Olympics.

Another fast Christian, Christian McCaffrey is the grandson of the white man who won the silver medal in the 1960 Olympics 100m. But he focused on football and was a runner up for the Heisman.

Similarly, although there was definitely discrimination against black quarterbacks in the NFL as late as Warren Moon in the late 1970s (Moon, a college star, had to go to Canada to crush everybody before being allowed to play QB in the NFL, where he then had a long, fine career), there has never been a superstar black NFL QB of the Brady-Manning-Favre-Marino-Montana-Elway level.

West African blacks tend to have powerful, thickly muscled bodies. Hence most sprinters and cornerbacks tend to be black. In comparison, many East African blacks tend to be tall and slender and dominate distance running. I don't think there is much racial discrimination in professional sports - too much money is at stake to allow racial prejudice to influence selection.

A quarterback must have a combination of skills - leadership, sufficient physical strength, a strong throwing arm, and excellent decision making under time pressure and stress. The ability to quickly read the field and predict future (1-2 seconds) scenarios is critical. The position requires intelligence. Given that, one wonders why there aren't Asian or Ashkenazi quarterbacks in the NFL. Maybe they have too many other lucrative and less dangerous opportunities, like the diamond business or science and engineering.

There are only 32 NFL teams, only 32 main quarterbacks. Is demand for Asians and Ashkenazis in the STEM and diamond business so strong that even a single one could not be lured away with the millions successful NFL quarterbacks make?

I think the issues are:

1. Small sample size.

2. Forgetting that the pipeline is more important than the raw ingredients. NFL quarterbacks come at the end of a long process of encouraging lots of kids and parents to get into football, selectively encouraging promising players, and investing enough to make keep motivation strong.

See the movie Million Dollar Arm. Even if you screen thousands for the right 'inherent trait', it's not as clear your search method is as good as focusing on training and shaping.

Thank you for a post that shows that un-biased does not mean biased in the other direction.

Yes on 1 and 2. There should be plenty of blacks in the quarterback pipeline. Why aren't there more blacks qbs? Maybe IQ has something to do with it. Or perhaps perception of I, or bigotry.

Blacks are about as represented at NFL quarterback as they are in the population from which NFL quarterbacks are drawn. It's similar to how black actors win about as many Oscars as is proportional to their share of the population, but it's widely considered a crisis that they don't win more than their share.

But there haven't been any all time great black NFL QBs the way the statistical discrimination filtering theory might predict.

On the other other hand, there has only been one Top 100 African-American golfer over the last two decades, but he was the best of the best of the best.

Really? Tiger's the only one? Plus he's half-Asian.

I had to look that up. Seems to be true.

One of the black golf achievements is from... an NBA player who joined a golf board.

But the "statistical discrimination" explanation probably makes sense of this fact as well. As the level of competitiveness increases, types with with more high-value traits capture larger and larger shares, till the top level is thoroughly dominated by whatever type has even a small overall advantage.

It doesn't seem like the whole 'black qb' thing is a crisis anymore. A couple decades ago it was a big deal: first black qb, first one to win a SB, first one to win MVP, etc. Today it's hardly mentioned, except by people obsessed with race. Does anyone make a big deal about Russell Wilson or DeShawn Watson being black?

Similarly, there are no female superstar tech founders, even though there is a clear hunger for one. The most famous female Silicon Valley founder was Elizabeth Holmes. As John Carreyou wrote in "Bad Blood:"

"As much as she courted the attention, Elizabeth’s sudden fame wasn’t entirely her doing. Her emergence tapped into the public’s hunger to see a female entrepreneur break through in a technology world dominated by men…. In Elizabeth Holmes, the Valley had its first female billionaire tech founder."

I think related to this is the concept of disproportionate gains if you were the employer who worked out this was going on.

In short, using the example of women, if you were to work out that women were being discriminated against unfairly, then as an employer who didn't discriminate you could attract talent that you'd pay less for than your peers (because you hire talented women who have fewer alternative opportunities). I tend to consider the fact that this doesn't happen as evidence that there in fact isn't discrimination of that nature - the market being what it is (and recognising that some of those employers are also women) I'm more inclined to think there's some other underlying process going on other than discrimination.

This shouldn't be a mystery to anyone who has small children. All you have to do is watch the patterns and choices of preschoolers during their free time to realize what is going on in high tech.

Postmodernism has impeded the ability of many to observe and think.

This assumes that the only impact from discrimination is the hiring or promoting of women. However, if discrimination also results in reduced training, reduced access to mentors, reduced access to high profile projects, over time a true skill gap develops. Discrimination is not a static one-time event.

The public desire for stories about a successful female tech founder has no bearing on the desire of venture capital funders to invest in female tech founders and there are charges that they discriminate and sexually harass them.

Although a few legit Silicon Valley superstars like Larry Ellison invested in Elizabeth Holmes' boondoggle, her board largely consisted of the Deep State incarnate: Schultz, Kissinger, Nunn, Mattis, Perry, etc etc.

It's hard to reconcile the conventional wisdom about how Old White Men discriminate against young women with the Holmes story.

'the Deep State incarnate'

Oddly, you seem to think there is a difference between Ellison and the 'Deep State.'

Charmingly amusing for someone apparently able to pinpoint the fine differences between groups, as seen in individuals that belong to those groups.

the Deep State incarnate:

Neither George Schulz, Henry Kissinger, or Sam Nunn qualify as 'deep state'. Nunn was an elected official who never held an executive position. Kissinger and Schulz were political appointees who reported to the President. They're the sort of people undone by the Deep State. The whole point of Kissinger's operation at the National Security Council was to provide policy options supplementary to what Kissinger called 'the bureaucratic consensus'.

Yes, these people would be better categorized as "the thoroughly oldline establishment."

I wrote a cover story for National Review in 1996, "How Jackie Robinson Desegregated America," documenting how the baseball teams that desegregated first and most fully benefited hugely.

For example, in 1946 the World Series was between Ted Williams' Boston Red Sox and Stan Musial's St. Louis Cardinals. Both superstars remained awesome, with both batting over .350 twelve years later in 1958, but neither ever got back to the World Series because their teams were the last in their leagues to hire black players.

In contrast, the Brooklyn Dodgers went to 6 of the next 10 World Series, in large part because their black players won 5 MVP awards and 4 rookie of the year honors.

What do superstars look like in a segregated environment? I imagine a great pitcher would look even greater since he wouldn't ever have to pitch to the greatest hitters on the other side.

On the other hand it does seem to lower the search incentive. Today if I'm filling out a baseball team, I really want to have the world's greatest pitcher on it. Finding the 10th greatest pitcher may easily cost me a lot. In a segregated environment, the 10th greatest pitcher may be fine if the other 9 greater pitchers are in the other league.

"What do superstars look like in a segregated environment? "

We have a pretty well documented example involving Satchel Paige, the legendary Negro League pitcher. His career in segregated baseball tended toward barnstorming and Harlem Globetrotter-style showmanship. But Bill Veeck, owner of the Cleveland Indians, signed him to a major league contract on his 42nd birthday in 1948. He went 6-1 with a 2.48 ERA in his MLB rookie season as the Indians interrupted the mighty Yankees' pennant string and set a new record for attendance, with some huge crowds (e.g., >70,000) when Paige pitched.

Jackie Robinson didn't use his bat to bash in the door of the Dodgers' clubhouse and then write his name into the lineup card for that day's game. His baseball career was made possible by the man that actually integrated baseball, Branch Rickey. Robinson's number 47 has been retired by all major league teams but there is no league-wide day of celebration of Rickey inking him to a contract.

Let me try to sum up my thinking on this question over the last 15 years, using the stunning example of blacks being the last 996 out of 996 starting cornerbacks in the NFL.

- Assume there really is a very large racial difference in cornerback talent due to human biodiversity.

- Assume, however, that it's not quite 996 out of 996, but without statistical differentiation it would be more like 950/996.

- Assume a white kid comes along who impresses his freshman high school coach as a potential NFL cornerback.

- Assume the freshman team coach is a good human being and has the kid's best interest at heart.

Does the high school freshmen team coach tell the white kid to drop everything else in his life and focus on becoming an NFL cornerback? Or does the coach think to himself: "This kid looks to me like he could be the first white cornerback in the NFL since Jason Sehorn. But how do I know I'm right? What are the odds? From a Bayesian perspective, how big is the chance I am potentially ruining this kid's life by telling him to focus solely on cornerback? He's my best football player, so why not have him play safety or bulk up and play middle linebacker? Doesn't he have a much better chance of going a long way in football at a whiter position than an cornerback? Nobody got fired for buying IBM, but a lot of NFL coaches can imagine getting fired for playing a white guy at cornerback -- So can I morally justify exposing my player to that kind of racial discrimination?"

So, a lot of coaches will steer their white stars away from cornerback.

Eventually, there will likely be white cornerback starting in the NFL again. I can imagine two scenarios

- A white superstar talented cornerback who is so good that all the statistical discrimination in the world couldn't stop him -- the Eminem of cornerbacks.

- Or, a white journeyman who is, say, a second string safety and gets patched in at cornerback due to some injuries and does a satisfactory job for awhile.

The first scenario is more likely the smaller the human biodiversity gap between the races and the more that statistical discrimination is the cause of that insane 996/996 statistic.

The second scenario is more likely in cases where there really is a big racial gap in talent due to HBD and statistical discrimination is highly rational.

Why do you care so much about HBD (to what extent it exists and where)?
[just curious, not meant in an accusatory tone or anything]

He may not realize it but it hints at perhaps why all the PC critics of The Bell Curve had a point after all.

Genetic advantage is not genetic domination. For example, I've been told there actually isn't a rule against female players in the NFL but the reality is no female has come anywhere close to being able to compete in NFL play (although my football following Godson told me a few got kind of close as kickers).

In that environment, a coach may view a girl trying out football as a distraction that will never go anywhere. However what happens when the advantage is there but not absolute? Mr Spock would treat 95% as close but not the same as 100%, but are humans so precise? If humans 'round off' 95% as 100% then you introduce a slight bias into the system.

A 5% bias in selecting HS football players is probably no big deal. But Tyler's initial point was what happens when some jobs require passing through many gates and gatekeepers who share that bias? In that case the discrimination grows and starts shaping society.

Where I think he goes wrong is the extent of the 'true' advantage. I think this is likely to be a problem in the reverse case. If, say, white players have a 5% disadvantage that's likely to get blown up to some much larger 'rule of thumb' by gatekeepers (like 20%).

What do I mean by advantage? Well say you set all other variables equal (size, speed, results of tests, performance in practice, etc). In theory 50 white cornerbacks and 50 black cornerbacks should see no statistically significant difference therefore flipping a coin is as good a method as any in deciding which guy gets the position if one is open. If it turns out it is more like 55-45, the coach should flip a coin that lands on black 5% more often when deciding between two potential cornerbacks who seem equal in all other respects. If we were all perfectly rational and 5% is the 'true' advantage carried by 'genes' or whatever then that would work. But we aren't fully rational and mentally we tend to get odds and percentages quite wrong.

"Why do you care so much about HBD?"

Everybody sure acts like they care about human biodiversity. The big difference is I try to think about this fascinating topic with the critical care it deserves.

I can't speak for Sailer, but as someone who shares that interest, I'll answer as though you had asked me.

Because interesting things happen at the margins.

It sticks out to you because the zeitgeist is assimilatory as far as race, gender, other woe-begotten classes go. But that's not real. Life happens far from equilibrium.

I'm not seeing the high school coach in that hypothetical as very realistic.

First, many/most HS coaches will never have a player go onto to NFL success in their whole careers, yet still have be viewed as successes.

Second, this view of the coach is more as a selector than a shaper. You are modelling the coach like a stock analyst. The analyst tries to pick stocks that will go up but he himself has no influence on the price. Reality is the coach probably views himself as shaping his players hence his fears of being wrong are very odd. Since most or all HS players will not go onto the NFL, the coach being wrong is unlikely to be noticeable. The coach being right will result in lots of bragging rights, but unless the coach has a long track record of producing many NFL players, most people will say maybe the coach had a good insight or maybe he was just lucky. Of course if the coach does have a track record of producing NFL players that would make him more of a shaper of great players which ruins your model where great players are born with the right genes and coaches are just trying to spot them.

Most HS coaches worry about academic eligibility. Bad grades filter out many athletes.

White high school football players with NFL potential these days typically have fathers carefully managing their careers, including picking their high school based on the coach and the opportunity and transferring them to a more amenable school if the coach isn't featuring the son in the manner the father wishes.

For example, say the high school coach wants to play the son at cornerback as maximizing the team's chance of winning, but the father thinks cornerback is a dead end for white boys, so he wants him to play safety on defense, a position where he's more likely to get college scholarship offers.

If the son was black, however, the father would likely agree with the coach that his son playing cornerback is ideal both for the team in the short run and for his son's long term future, since there are no statistical prejudices against blacks playing cornerback in the NFL.

Sounds like you've argued yourself into Brown.v.Board of Education. You're saying that since white fathers and coaches never see a white NFL cornerback, they subconsciously assume it's not a viable option for their sons and steer their kids towards other positions like quarterback. But for every one quarterback there are two cornerbacks so actually rejecting cornerback limits the opportunities for players.

I've long pointed out that a certain amount of statistical discrimination is rational, a position Tyler came to this month. Decisionmakers have to balance off the chance of Type I and Type II errors, so it can make sense for, say, football coaches confronted with a white player who appears to be a world class cornerback to to assume that they are making a mistake an overrating him.

In our culture in 2018, there are extreme sanctions against making mistakes that are bad for blacks, but virtually none for making mistakes that are bad for whites as a group. So, we are more likely to see mistakes negatively affecting, say, white cornerbacks than black quarterbacks.

That seems fair considering the history of blacks in this country.

That’s the $64K question about affirmative action programs ... when has enough time gone by (and enough quotas engineered) such that justice has been served and the programs should be abolished? Unfortunately the discussions of this question are usually high on emotion and low on rationality, see for example Ta-Nehisi Coates.

Perhaps instead of using standard identity politics topics, we should use something like veterans' status? With some sort of 'intent to treat' control like people who were waved off vs those who were waived in, medically?

Nobody in our culture much cares about discrimination against left handers so that can provide an interesting non-politicized case study. For example, no lefthander has been allowed to play catcher in Major League Baseball since the 1980s.

Everybody who is anybody in baseball agrees that it must be perfectly rational to discriminate against lefthanded catchers, but nobody seems to agree on the precise reason why.

Bill James, for example, says that any lefthander with a strong enough throwing arm to be an MLB catcher would get filtered off into being a pitcher, so no harm done.

Others say it would be harder for a lefty to throw to third, but nobody seems interested, despite the vast number of sabermetricians these days, in counting whether catchers throw more to third or to first, where lefties would have the advantage.

My guess is that it's mostly dumb prejudice. But lefthanders are not a Protected Class in 2018, so nobody much cares.

A followup to Tyler's hypothetical, that society would get fantastic tennis players but not as good CEO's as it could have.

Think about this in another culture, the USSR. Such a place produced amazing chess players, because the gov't deemed that something the country should compete on in international circles, but probably wouldn't do great Magic the Gathering players. Talented chess players get lots of 'green lights' to keep going. Magic players get lots of red lights. People who like playing competitive table top games can making a living from the first but not the second.

Forest from the trees here, it isn't enough to just say all companies have hired the best possible CEO from the available candidates. What type of 'green lights' do we give people on a CEO track that has nothing to do with us having great CEOs?

Mark Twain was way ahead of this discussion, in Captain Stormfield's Visit to Heaven: "“Did you ever see Napoleon, Sandy?”
“Often—sometimes in the Corsican range, sometimes in the French. He always hunts up a conspicuous place, and goes frowning around with his arms folded and his field-glass under his arm, looking as grand, gloomy and peculiar as his reputation calls for, and very much bothered because he don’t stand as high, here, for a soldier, as he expected to.”
“Why, who stands higher?”
“Oh, a lot of people we never heard of before—the shoemaker and horse-doctor and knife-grinder kind, you know—clodhoppers from goodness knows where that never handled a sword or fired a shot in their lives—but the soldiership was in them, though they never had a chance to show it. But here they take their right place, and Cæsar and Napoleon and Alexander have to take a back seat. The greatest military genius our world ever produced was a brick-layer from somewhere back of Boston—died during the Revolution—by the name of Absalom Jones. Wherever he goes, crowds flock to see him. You see, everybody knows that if he had had a chance he would have shown the world some generalship that would have made all generalship before look like child’s play and ’prentice work. But he never got a chance; he tried heaps of times to enlist as a private, but he had lost both thumbs and a couple of front teeth, and the recruiting sergeant wouldn’t pass him. However, as I say, everybody knows, now, what he would have been,—and so they flock by the million to get a glimpse of him whenever they hear he is going to be anywhere. Cæsar, and Hannibal, and Alexander, and Napoleon are all on his staff, and ever so many more great generals; but the public hardly care to look at them when he is around. Boom! There goes another salute. The barkeeper’s off quarantine now.”"

Napoleon believed in "careers open to talent." He just barely qualified for the military academy under the ancien regime as a marginal aristocrat from marginal Corsica.

Many of Napoleon's marshals would not have become generals before the Revolution; in general he was well-served by his talented underlings.

In contrast, the British Army let rich guys buy commissions and discriminated against non-aristocrats in the Army (less so in the Navy) due to fear of military coups if generals weren't part of the aristocratic class. Britain was lucky to have gotten one land warfare genius in Wellington; his underlings, often his in-laws, were not very competent relative to Napoleon's underlings.

With one qualification. Napoleon said "I would rather have a general who was lucky than one who was good."

Note also that Napoleon was making a virtue out of a necessity. Many aristocrats had been hanged from Paris's lanterns, had fled abroad, or were of questionable loyalty. So Napoleon may also have acted -- in part -- out of fear of a military coup, but from above, not below.

Thank you for that!

Though his distaste for Jane Austen is well-known, she had a similar eye: "If I had ever learnt, I should have been a great proficient."

I love that Twain put his mind to imagining heaven, even just in the service of a joke. The other day I was asking my husband something about heaven, and dogs - since I think people now would just as soon be reunited with their dogs in heaven, as loved ones - and the implication of this for all the other animals, blah blah.

He cut me off (he's quick with the filter): "There's a reason Christians don't think too closely about heaven."

Assume two candidates of equal ability for a position, one from a discriminated group and one not. Why hire the candidate from the discriminated group (there's the risk she won't be accepted as an equal by other employees)? What if the candidate from the discriminated group were willing to accept compensation well below that which would be acceptable by the candidate from the non-discriminated group. Wouldn't a rational employer choose the candidate from the discriminated group (assuming there is no legal impediment to paying the lesser compensation)? Historically, that's how members of the discriminated group were employed, blacks in particular. Indeed, today Mexicans are willing to accept lower compensation and work longer hours and, hence, have little difficulty finding employment. Of course, this blog post focuses on potential CEOs, not labor, but the same dynamics apply: she must first be hired before she can prove herself to be CEO material. Economists such as Thomas Sowell have argued that's why anti-discrimination laws, though well-intended, have the perverse effect of keeping blacks out of potential CEO positions: they don't get hired in the first place, not when another candidate with equal ability from a non-discriminated group can be hired at the same compensation. The counter argument is that the candidate from the discriminated group who accepts lesser compensation will forever be pegged as the lesser candidate and will never rise to the position of CEO.

Your post, I think, is not internally consistent. If the employer is rational, why would he pay less to the worker from the discriminated group? Because that's the market rate due to discrimination by irrational employers. The workers are 'willing' to take lower wages. OK so rational employer is savy enough to exploit society's irrational prejudice and get a good worker on the cheap.

BUT now anti-discrimination law says he has to pay the same wages for the same work done by workers who are not the targets of discrimination. Now he won't hire the discriminated worker, because, why? He can't pay him lower wages? But if he hires from the non-discriminated pool he will have to pay higher wages nonetheless. Is your employer rational or is he not. If he isn't then your model has no rational employers in the economy which means you can't count on rationality to save the day.

The more subtle issue here that Tyler is raising is multiple gatekeepers and imperfectly rational decision makers. Say to get to CEO of a big company, you have to pass through 99 'gates'. Those gates include events in school, getting your first jobs, promotions, various programs possibly even social groups (country clubs, being on the boards of high end charities, etc.). Let's say those decision makers are mostly rational, mostly trying to make the best choices, but slightly influenced by prejudices from the larger culture. In any one decision, they are 99% likely to make the 'rational' choice but also liable to falter here and there.

For any one gate, the process will look pretty good. The decisions made will look almost perfect as if they were made by some purely rational AI. The rate of discrimination will be so low it would be impossible to prove as it would almost appear to be statistical noise. Even if you could prove it, it would be rare you'd have a case. 99 out of 100 times you'd still pass this gatekeeper if you were the best choice!

However these effects build up with each gate. By the time you get closer to the CEO the pool of potential candidates has a lot of people missing because they got shot down along the way. (In WWII they got the loss rate of B-17's bombing Europe down to 7%, but for a pilot hoping to survive the 25 missions that still wasn't very good. Taking a 7% risk 25 times means your odds of getting shot down are much higher).

Near the top of the chain there may be no discrimination at all. Choosing the right CEO is a high stakes decision and companies might employ the best, most unbiased, search and selection methods. Nonetheless the best that can be done at that point is achieve 100% rationality in the last gates. That doesn't alter what happened at all the previous gates and their impact.

A recent very popular president was discriminatory in the abstract but not in the particular. That made a big impression on me. My observation is that the president's attitude about discrimination reflected that of the general population. Cowen's approach here turns the abstract into the abstract. It works in theory but doesn't work in practice. Real people make real choices about who they hire. I'm a realist. Given an incentive to hire someone from a discriminated group, such as lower compensation, and the rational employer will discriminate against the discriminated group by hiring someone from the discriminated group.

Not really following you there. How was Obama "discriminatory in the abstract but not in the particular'? That doesn't even sound like a coherent idea. If someone is discriminatory in the abstract, that sounds like you will then be able to point to particular discriminatory acts he or she did. Otherwise that's a bit like me saying I'm a fitness buff in the abstraction but I don't do any particular exercise.

Your view of discrimination sounds pretty unrealistic to me, at least for 2018. Your view sounds a bit like Archie Bunker ("I'll don't want a black doctor treating me!"). Reality is most discrimination was never so blatant and binary. Most of the time it is much more subtle, not so much a gatekeeper who just shuts the door on one group but one who applies a bit more or less scrutiny depending upon which group the applicant is from.

"If the employer is rational, why would he pay less to the worker from the discriminated group? Because that's the market rate due to discrimination by irrational employers."

You are forgetting the premise of this whole gedanken-experiement: that the groups are statistically distinct with respect to the salient attributes. Discrimination, while perhaps unjust, is rational. Unassailably rational. That's what makes this discussion interesting.

Rational here is a heroic assumption. How does the 'rational employer' magically know that a marginalized group that is paid 20% less for the same job is really just as good and therefore a great bargain? Most decisions are made absent a lot of critical information. Most managers look at what the average does and tries tweaking that a little bit and then observes the results. Often it isn't even easy to observe the results. In many large organizations a 'good employee' means one all the other employees say is good. There's no easy way to directly link her output with the larger organization's performance. Absent all this critical information the 'rational employer' often takes on the rules of thumb of society as the best information out there.

No need for heroics or magic.

"Is really just as good" flouts the stated premise in the original framing, which was, "on average, for this category, less good."

"Often it isn't even easy to observe the results." Yes, someone mentioned that below. The difference between this hypothetical and the poker playing scenario. Firms compete against one another as do poker players. But we have less confidence in attributing success and failure to constituent decisions.

You lost to a girl because you tried to play her like a fool and she wasn't is more salient (and more useful) than Comcast's declining subscribers hip being due to the image their installers in urban markets give off to prospective customers.

I'm reminded now of a story about John Von Neumann being queried about the new field of game theory by a colleague in a taxi. "So, like chess?" "No, chess is not a game, it's just a well defined computation." He was interested in life. The Comcast question, not the poker thing.

There's also the example of chess, which is one of Cowen's favorites. Female grandmasters like Polgar look like extreme outliers of talent.

On the other hand, Polgar was a legit top ten in the world, and not that long ago. So it's worth thinking about all the work her father did to remove hurdles that female chess players face.

On the other, other hand, Polgar's well-publicized story has not yet opened up a flood of similarly talented female chessplayers the way that Jackie Robinson was followed by Willie Mays and Hank Aaron. But perhaps another few decades will tell another story.

In contrast, Tiger Woods winning the Masters in 1997 followed by Se Ri Pak (sp?) of South Korea winning the Lady's US Open golf tournament in 1999 caused a flood of South Korean tiger parents both in Asia and in America to enroll their kids in golf lessons.

A few promising Korean male golfers emerged, but on the female side, a flood of Korean young women soon came to dominate the LPGA.

Why the difference? Because golf is something that strongly appeals to some percentage of boys, so it's hard for one culture to tiger parent its way to domination of male golf.

But not many individual girls care that much about golf unless there culture is going through a golf fad like South Korea has been. So it's easier to socially construct dominance for your country in many women's sports than in their male counterpart sports.

What about Asians discriminated against by the Ivy League? The average Asian who can make it through would tend to be of higher talent level than the average non-Asian classmate. And that's what we see.

I'm a bit skeptical. Let me give you a story:

It's 1990 and you're an Asian 'tiger mom'. You are approached by a 'consultant'. He says to you:
"Don't you see the movies? Americans expect Asian kids to be math geniuses. If you want your kid to be successful, you need to show American colleges that she knows math, can play the violin (because classical music is relate to math skill and the violin is the hardest instrument to learn). You better start now before it's too late"

You sign your kid up, but so does everyone in your social circle. A few years later you get approached by another 'tutor'. This time they note that 20% of their students got perfect math SAT scores. They spend the summer in 20-hour a week violin training sessions. They give the edge the other companies don't. You sign up, so does everyone else on your block.

Now it's 2010 and you're a college admissions officer. You have 200 spots to fill. 100 applications come in from Asian names, all have perfect SAT scores, all list near professional violin playing as their hobby. I guess the 'fair' thing is for college to be 50% filled by this pool.

But wait a minute, how many violin players does a college really need or want? A college is a bit like a football team in that you have different players. If you only need one quarterback, you pick the top quarterback applying and ditch the rest. if every father tries to mold his son into a future quarterback, the bar is going to get very high to win a scholarship as a college quarterback. So here you have 100 violin playing SAT superstars and here is an application from someone who was a B+ student, got a decent but nowhere near perfect SAT score, has a Youtube channel where he puts his self-made hiphop music with over 1000 followers, plays basketball and the drums but knows nothing of classical music. Hmmmm should this application really be 'fairly' put behind the 100 other ones?

That works with violin, i.e., a college may only want so many violin players, but it doesn't work with SATs or even with math: Harvard doesn't want a mix of SAT scores, and no college is close to whatever internal cap it might have on people with good quant skills.

I argued on the other thread that I think this is a good reason to distrust any single path. If a group decides they are going to really go crazy on acing a test, I think they will likely do so but it doesn't follow then that colleges should just blindly fill up with that group. All single systems can and will be gamed.

My thinking is instead of affirmative action the optimal policy should be a 'many roads lead to Rome' approach. If everyone tries to use one road, the road doesn't widen, it just backs up with traffic. The trick is there should be multiple roads that don't overlap. If 80% of slots are filled with traditional high SAT/high 'classical' skills 20% should be aimed at other criteria.

Harvard imposed a maximum cap on the number of Jewish students it would take from 1922 to c. 1955, and Yale until 1965. Were the average Jewish students at Harvard and Yale in this era notably better on average than the gentile students? I would imagine so, although I have not read any quantitative studies of this.

I suspect it's akin to the Tiger Mom story I gave above. With the quota, the schools were only going to take the top Jewish applicants until the quota was filled. A Jewish kid, then, could secure a spot at Harvard or Yale by being really good academically. But if every other Jewish kid realized that, then now the competition is on and the bar keeps going up. Needless to say the non-Jewish kid who has a legacy into Yale has no need to worry about such competition.

It isn't that Jewish kids or Asian kids magically get better SAT scores, it's just a path successfully trod by many of them that it has become a road of it's own. My thinking is we should establish mutually exclusive roads. Rather than a Jewish/Asian quota, have a quota on top test scores, a quota on top of the class hs grads, etc.

Interestingly, the impact on campus atmosphere of having a maximum cap on Jews and Asians tends to be the reverse. My late friend Jim Chapin, a vice-chairman of the DSA, was a history instructor at Yale in the mid-1960s. He said the intellectual tenor of the campus sharply changed as soon as the cap on number of Jews admitted was lifted in 1965. The 1965 freshman class was much more intellectual than the 1964 freshman class (in which George W. Bush slipped in) and much more argumentative. (Bush became alienated by the new campus atmosphere.) Chapin attributed a certain fraction of late 1960s campus radicalism to the unleashing of Jewish numbers at top campuses.

In contrast, a teacher at Los Angeles's top prep school, now called Harvard-Westlake, told me in 1981 that they discriminated against Asian applicants with high test scores because Asians tended not to contribute much to class discussions.

Hard to say. It was an anecdote after all. Perhaps it just seemed more argumentative because he associated Jews with arguments and he was on the lookout for that after the quota was lifted. Perhaps the times were getting more argumentative and knocking down the Jewish quotas was one of the first arguments that was one by the new era. In play you also had the shock of the Kennedy assassination receding while the Civil Rights movement was picking up speed and the first Vietnam War skeptics were beginning to find their voice. On the other hand it might have been just what it seemed, lifting the quota let in a lot of Jews who had previously been fighting each other in an academic Battle Royal to score one of the quota seats.

It would be interesting to know just how dramatic lifting the quota was? how Jewish was the next year's class?

Karabel's book probably has the Yale numbers, although it's more focused on Harvard. My friend Jim Chapin said it was an extremely sizable change from 1964 to 1965.

In general, a lot of the Sixtiesness of the Sixties and Seventies has to do with Jewish Liberation. The 1967 Six Days War, for example, greatly boosted Jewish-American self-confidence.

I still don't buy that this could possibly work in the real economy. There is value to be had in not following the crowd so some gatekeepers should always be willing to adopt alternative search strategies.

Consider the simplest example. 10 gatekeepers are looking to find the top 100 people in a population of 10,000. They can statistically discriminate against 5,000 people and lose 10 of the top performers.

What do they gain by doing this? They reduce their search costs by 50%. Each of the 10 screens 5,000 and they try to convince 10 of the 90 best candidates found to come to them.

Obviously, at least one of our 10 gatekeepers is going to come up short on his 10 top candidates he needs to find. So he either tries to bid higher (e.g. scholarships, prestige, higher wages, better healthcare) for the 90 best candidates or he has to admit failure and take a sub-optimal candidate. This incentive exists for all of our gatekeepers.

So how high does a gatekeeper bid? It certainly cannot be more than the opportunity cost of searching the full 10,000 population.

At some point the bidding gets high enough that it makes sense for one gatekeeper to exit the bidding war and just pay the search cost for the bottom 5,000. If the heuristic is simple (e.g. don't interview women), then our one maverick could quite literally search only the bottom 5,000, let the other 9 gatekeepers fight over the top 5,000 and snag 10 candidates for his efforts.

This just wreaks of a highly inefficient market to me. Imagine that instead of people we were looking at securities. You could find an easy heuristic to tell you that some securities were more likely to turn a profit. We would expect people to use it to build mutual funds and then for it be used again build pensions from mutual funds and all the other increasing complex securities. Would some securities be left on the table never bought?

Of course not, competition would bid up the price of the good ones until the expected return on both the good ones (according the heuristic) and the bad ones were equal.

From a market perspective there is no reason this would not happen with people either. Only in a world where gatekeepers need not compete among each other would we not see increasing bids for better prospects.

Certainly this was my experience going through a very explicit set of gatekeepers to reach a good position in the medical community. At every step of the way gatekeepers had various budgets of cash, prestige, amenities, and the like that they routinely used to bid for me to pick them over their competitors.

And when I was gatekeeping, I did the same thing. We had budgets for where we send people to look for candidates, for the people we would send mailings, and everything else. We knew where the top performers were and we basically ignored them. We could more cost effectively acquire better prospects by going after candidates where the competition was lighter.

Likewise, I find it incredible that we would just be stuck with a heuristic forever in the real world. Consider baseball. For years batting average was the dominant heuristic for which players to sign for how much. Then on came Sabermetrics. Somehow the real world managed to exceedingly quickly change from one heuristic to another.

Lastly, it is not like candidates are dumb. I served in the military for a variety of reasons, one of them was that I placed me on the right side of a heuristic. Whenever I come across a gatekeeper in the medical profession who understands the military I get bumped to the right side of the heuristic. Other things, like looking the part or spamming publications, also give candidates agency. If I know that some heuristics are going to go against me regardless, I can change my behavior to place me on top for others. After all if I get a higher return for paying these costs I am more likely to do them. This is particularly true for floor functions where any of several things is sufficient to get you past (e.g. going to an elite school, serving in the military, having 5 years of solid work history all get you the interview).

It is an awfully finicky Just So Story to have an inefficient market where competition does not drive some gatekeepers to change search and bidding strategies, where new heuristics fail to arise, and where candidates cannot offset their weakness on some heuristics by hacking some others. This just looks like a toy model that says nothing about the real world.

Yes. The burden of proof rests very heavily on the discriminationists, and the general rhetorical tactic is to shift that burden.

I note in your comment a sustained discrimination against "she" as a pronoun.

Numerically, perhaps, we can just count on the fact that, although discrimination is the norm, 20% of decision makers discriminate on something besides the coarsest statistic, and they end up making 80% of the smart bets? And all this handwringing may be a nice pass-time, but of no real consequence? Unless we enjoy puzzling.

Don't recall the source but I read a study of Canadian pro hockey players puzzling out why they all had the same birthday (more or less). They were all born extremely close to the same date.

Turns out the Canadian youth hockey leagues had the same cutoff date for placement, so that the closer you were born to that date, the older you were (relative to your peers) in your game cohort. That advantage could be substantial--you could for example be nearly a year older than other players on your team, or on the opposing team.

At young ages, a year brings a giant leap in terms of physical and mental development.

Now, assuming there is no natural phenomenon causing people born near that cutoff date to actually be *better* athletes, the fact that (nearly) all Canadian pros *were* born just before that date suggests there was an immense discriminatory system in place--exactly what Tyler is looking for.

From the very start, your age-advantaged youth hockey player was getting noticed by the coaches, and getting positive feedback for his efforts, and getting special attention and opportunities, and getting status from adults and peers.

Your age-disadvantaged player was getting exactly the opposite.

Except for a couple of things. Notably teams that drafted players born later in the year got more value from them. Contra Cowen, this heuristic did not result in players born earlier in the year actually being better due to years of accrued advantage. Instead players born later in the year were more productive than those drafted near them born earlier in the year.

Cowen is not saying that people have faulty heuristics. He is saying they necessarily become overwhelming and uncorrectable . The hockey data showed that discrimination happened but not it compounded over years. Since that study, several teams have explicitly changed their draft strategies.

I think the salient point is not that teams got more value out of older players (they did), but that equally talented young athletes were shunted out of the system because, through no fault of their own, they were born on the wrong date.

Yes, sports leagues have addressed this. Again, that's not the point. The key is this is a magnificent example of the way small, systematic discrimination over a career can add up to very large consequences.

How many would-be greats never got to the pro level because they had the wrong birthday?

Actually, no. Teams got more value from the younger players. As far has how many superstars were lost, try close to none.

The handicap for this error was that youngest players made up 15% of the league. So we lost around 1/3rd of those players. But 2/3rds remained. Odds of us capturing all the superstars is pretty high. After all, the younger players who did make it to the NHL outperformed their draft peers.

After something like six rounds of discrimination we only lost 1/3rd of the potential players. This suggests that we lost something like 17% of the youngsters each pass. The odds that a "superstar" would be in the bottom 17% early on is very low and that they would repeatedly be in the bottom 17% is lower still.

And even if they were cut, it is not like players lack agency. Many of the ones who missed the cut did things differently - they played college hockey, they switched positions, and they rocked lesser leagues. All of this mitigation is quite possible.

And remember hockey is basically a single pyramid scheme with a monopoly at top. I the real world you have millions of gatekeepers and many more options to try different tacks.

Again, how are people different than stocks this way?

I have a sure fire rule to pick stocks that are going to make money. Great once everyone knows the rule, they bid up the shares that fit the rule until everyone profit margins equalize. At which point the rule is not having a major impact.

Sure small markets can have irrational moments, and they can stay irrational longer than an individual can stay solvent ... but this seems to be exceedingly minor due to truly basic economics. We do not believe poor signal quality results in such compounding losses elsewhere in the economy, why is labor different?

I mean, if anything, I suspect labor is actually less likely to have economy wide heuristics than pretty much any other item in the market.

Ultimately this strikes me as Prisoner's Dilemma. A model which implies some things which are rarely salient in the real world (e.g. actual prisoner's typically solve the dilemma with ease).

One thing to keep in mind is that lower level gatekeepers, such as sport coaches, have multiple roles, such as nurturing young talent but also winning right now. Those tasks are somewhat contradictory and talent can be sacrificed.

For example, consider the career of quarterback Kurt Warner, who eventually put together a heroic postseason record behind only Joe Montana and Tom Brady. But early in his career, Warner tended to get stuck on the depth chart where he didn't get much experience. He only got to start one year at lowly Northern Iowa. He went undrafted by the NFL, but was impressive at the Packers' training camp. But ...

"Warner was competing for a spot against Brett Favre, Mark Brunell, and former Heisman Trophy winner Ty Detmer. ... After Warner was released, Mariucci told him that he knew Warner had enormous potential but was not ready to be an NFL quarterback yet.

"After his release, Warner stocked shelves at a Hy-Vee grocery store in Cedar Falls for $5.50 an hour."

The Kurt Warner story had a happy ending, but who knows how many that could have been similar did not?

How about non-superstars? What about players slightly above average? By definition the system would want to keep those players as they would increase the average play of the sport, but individually if confronted with a bunch of kids who are bigger and play better, they might have quite reasonably assume hockey wasn't the sport for them.

Sailer's point about Warner might be another type of bias. A tall tree might block out the sun and stunt a perfectly fine tree that just happened to be growing a bit too close to the tall neighbor. Perhaps superstars have a hidden cost by inadvertently stunting the development of talent cross the entire field.

Steve Young got stuck behind Joe Montana before becoming a Hall of Fame quarterback in his 30s. Matt Cassell got stuck behind a Heisman Trophy winner at USC and then behind Tom Brady in New England. When he finally got a chance to start after about 10 years of being a benchwarmer since high school, he won 11 of 15 games.

Jeremy Lin is a famous example of a basketball player who wasn't drafted by the NBA probably due to racial prejudice. He then went on to have a spectacular 7 game stretch. But that mostly turned out to be the much pooh-poohed hot hand and since then he has just been a decent NBA player. But, yeah, racial prejudice probably cost Lin not being, say, a second round draft pick.

Sure there will always be some marginal loss because in no endeavor do we have perfect information, sorting and processing. But for the hockey example we are not talking about a whole bunch of people who are were even near average at each cut.

We are talking about losing the bottom 17% of a disfavored batch each round. It is exceedingly unlikely that any of the better-than-average NHL players are going to fall out of the system before the final cut or two for a simple analysis.

Not only that, but in reality it gets much murkier. If you survive the cut and other people make it in who shouldn't, then the your relative talent position improves. Say everyone perceived to be above the 70th centile moves on past a gatekeeper.

In the discriminated group, 25 (skills uniformly distributed from 75-100) individuals will make the cut. In the favored group 35 (65 - 100) will make the cut.

At the next round we want to keep 30% again. If this step were completely fair, we could completely ignore the impacts of the tier below us - we would end up with 10 from both favored and disfavored groups. But suppose it is not fair again. Say that the disfavored group again has to score 5 points higher to make the cut.

Well their average score is now 87.5 while that of the favored group is 82.5. Over half the burden of discrimination is gone just because they already cleared a higher bar and have a higher mean.

Each subsequent round would do likewise. As you move to ever more elite levels, the disfavored group will have higher means and be more likely to make the cut.

It is only for a very small subset of setups where compounding penalty is seen. This not surprising. Tyler posits a positive feedback system without mitigation or negative feedback in the mix. These are astonishingly rare in science, medicine, sociology, or basically anything else. Any process that does not have healthy doses of "reversion to the mean" takes massive amounts of intervention to prevent it.

I mean think about what it took to maintain Jim Crow. The South had to sell out its politics to one party. It routinely destroyed every other political initiative of Southern voters. It required losing huge amounts of economic development and chasing off large amounts of its talent. It had massive depopulation with the Great Migration. It required undercutting the fight against Communism. It required higher taxes and massive government intrusion into the private sector.

And even that was not positive feedback. The number of lynchings dropped long before the federal anti-lynching bills. The economic circumstances of African Americans improved more during Jim Crow than they did after (where by some measures we have not seen any progress in real dollar terms).

Compounding penalty requires either creative accounting like looking at outcomes in a narrow domain or massive society level commitments. Otherwise there are just so many natural ways that things revert towards a mean it just cannot be sustained.

I can completely buy that some people get dinged by discrimination. I just cannot buy that it always get worse at each filter. People have agency, gatekeepers are not monolithic, and heuristics improve with time and study.

Well it does strike me that the 'age cut off filter' is probably more like a one time event or an event that gets smaller after each pass since kids grow most dramatically when they are young. The model Tyler seemed to be thinking about was the same potency filter applied at each gate.

But why would every gatekeeper at every level keep applying the same heuristic?

Just because some statistic is true in the general population does not mean it is true in previously sorted population.

Take height. If you are looking for NBA level talent it helps to be tall. So for kids basketball the filters are set to look for the taller kids as height helps with a lot of functions of the game.

However, by the time we get to the NBA draft the population has changed. The short guys who are left as draft prospects have some serious compensating skills. I would be willing to bet that the taller kids will be more likely to be better basketball players. Yet when you look at the NBA, average team height does not predict better performance.

Compounding loss with each gate just seems very finicky and easily disrupted by a few contrarians bucking the system.

I would be willing to bet that the taller kids will be more likely to be better basketball players.

I think you meant to say you would bet by the time you get to the NBA draft the shorter players are better. But that demonstrates the point. If the filters were perfect, the short players would be filtered out only to the degree that being shorter is bad. By the time you get to the draft a short player should be on average the same as a taller player and that should cease to be an element you use in your filter. If you are finding short players have an edge, that's a sure sign that previously the filter was overused along the way.

Malcom Gladwell's "Outliers" - he summed up the phenomenon as selection, streaming, and differentiated experience.

Right, Wayne Gretzky, was born January 1961, so that he was always among the oldest boys on his age-group all star teams. He was famous as a child prodigy and given the best coaching available.

My guess is that Canadian boys less favored by the calendar for becoming hockey stars may drift into other sports where the calendar isn't rigged against them (different sports tend to have different age cutoff dates).

For example, what about Larry Walker, the fast, slugging outfielder from Canada who won the 1997 NL MVP award? I bet he could have been a pretty good hockey player. He was born in December 1966, so he would have been a very young 7 year old on his 7 year olds' hockey team.

I looked up Walker's life story. He was set on being an NHL goaltender up through age 16. But he could only get an offer from a junior league with shoddy facilities, so then he decided to concentrate on baseball. Perhaps if he'd been born in January instead of December, he would have been signed by a premiere junior league and we'd be arguing over whether he deserves to be in the NHL hall of fame rather than in Cooperstown's hall of fame.

Lucky break for Walker, he surely got paid a lot more being a pro baseball player vs pro hockey.

NHL players currently seem to make about 80-85% as much as MLB players, so both are very nice jobs.

Totally agree. Although I would wager the gap was larger when Walker played.

There's no reason to posit a multi-layer compounding of discrimination. If a coin is 51% to come up heads, you bet heads 100% of the time. End of discussion no need to posit some long-reaching tentacle of structural discrimination.

2 points that seem to be missing in this academic discussion. In the real world, any institution with an HR department implements an anti-discrimination stance via a diversity index score; so the fact that despite this the outcomes are not completely diverse indicates something other than ‘hidden’ ( or even unconscious) discrimination. Cf. Harvard. Second, a study showed that most men prefer men to women as their manager. And most women... prefer men to women as their manager.

The simplified "two-sector" model is apparent at times in science - the types of subtle and statistical discrimination that keep women away from CS and math-ier sciences lead to many of the most talented women scientists in the life sciences.

Possible real life example:
Women are 20% more likely to be fired after misconduct than men. Interesting bit of bias here in the financial industry....because if anything you think it should be the opposite. Men, one suspects, are more likely to commit misconduct a 2nd time after getting called out on it than women.

So consider a 'Captain Kirk' model of the highest positions in finance. To get there you will probably have to break or fudge the rules multiple times in your career. If you break or fudge rules, there's a chance any given time you'll get caught. If you get fired, that's a huge setback. But if you just get chewed out then you live to die another day and if the next time you break the rules it happens to win big, you'll be a hero and advance to the next level easier.

What statistical discrimination like that would seem to imply then is that some women may play it safe, be Mr. Spock and do everything by the book....never advance to the top but always be secure in the middle. Women who do try for the top, though, will get filtered out along the way while their corresponding Kirk's get 'extra lives'.

Put are all financial mavens equally likely to avoid getting caught?

Those women make it past the first N times "cheating" are going to be more skilled than the equivalent men who make it through. After all, getting caught and chewed out is still inferior to not getting caught. This suggests that women should be less likely to get caught higher up the food chain evening out some of the initial discrimination.

Likewise, once this insight becomes known it seems like there should be a nice pool of mostly equivalent talent to be had cheaper. Of all the firms on the street are none willing employ those that are caught? Are none willing to pay extra for women who can cheat successfully?

Likewise, are women without agency here? Could they not for instance, develop skills in buck passing, lying, and preemptive accusation?

Lastly, how does this heuristic persist? If managers know women are more likely to get fired it either represents something of real value to the firm or it is something they can change to increase their profits. Once this becomes known, why don't hiring managers change behavior (say by firing more men)?

It again is very special pleading that again and again the discrimination will compound over time. This seems particularly finicky within one firm where senior management would have incentive to actively change the behavior of lower tier actors.

Well the talent on the street is not going to be equivalent talent since in this context you need experience+innate quality. If women get fired more often and firing puts a break on one's career path that becomes a big deal after multiple gates.

Lastly, how does this heuristic persist? If managers know women are more likely to get fired it either represents something of real value to the firm or it is something they can change to increase their profits. Once this becomes known, why don't hiring managers change behavior (say by firing more men)?

Does it change their profits? Recall the old adage about "no one ever got fired for hiring IBM". Suppose men who make it to the 'nth gate' are just as good as women. The process of surviving n-gates is what creates the talent. In that case the pool of unfairly fired women is not a treasure trove of cheap talent for firms to pull from, it is simply people left behind in the race and hiring them is not an advantage.

If the process of surviving gates were responsible for the bulk of talent differences, employers would be no worse off hiring randomly, and those that wasted resources trying to find talent would be disadvantaged. Since we observe that few companies hire randomly, EMH strongly suggests this is not the case.

"employers would be no worse off hiring randomly, " that probably is the case when you're talking about gate 1. Say we're talking 100 steps from mailroom to CEO. It's quite possibly true that hiring randomly for the mailroom is no worse a strategy than trying to hire 'intelligently' with interviews/resumes/transcripts from school etc. (OR once you clear some basic hurdles, like you screen out the people who can't show up for an interview or submit a resume without numerous misspellings and errors hiring the mailroom slots randomly is no worse than any other strategy).

But if a random hiring strategy works, so would a biased one. If a manager hired men more often for the mailroom because he had some notion of men having good 'sorting genes' he gleamed from some men's rights blogger....and his theory is totally wrong there's no more chance the market will demonstrate he is wrong. The mailroom he produces for his company is no more likely to be worse than the firm cross the street whose mailroom hiring is done by a radical feminist or one with a chimp throwing darts at the resume.

Mailroom to CEO is a bit of a fairy tale in business but not so much beginning sales associate to upper management.

No, if talent is the result of being hired, that means after adjusting for experience employers should be able to hire even CEOs randomly.

Interesting angle, it very well may be the case once you get a pool of qualified CEO's, choosing randomly might actually be no better than any other method and all the efforts of selection committees, recruiters, etc. to make the right choice are as useful as active mutual fund managers picking stocks.

You can buy an index. You can't hire one.

Again, if there is significant discrimination at any level, the tax falls even more heavily on employers than candidates, particularly for the most key positions -- the employee may have to find a worse job, the firm may fail entirely and cease to exist. Employers will adjust tactics to compensate and find the "hidden" talent, and on average those that don't will suffer the judgment of markets. (Unless, of course, you don't believe in EMH.)

EEOC isn't the only reason you can't go ten minutes in a corporate management job without a diversity seminar.

In reality, there are not a lot of spurned CEOs running to the tennis market, and the officially mandated quest for diversity probably overcorrects for what discrimination actually does exist.

I do think, though, that the cumulative effect of lowest level filtering may be inordinately responsible for the relative success of more attractive people. Getting a foot in the door can establish a career, and in the absence of experience it always helps if the foot is attached to something easy on the eyes.

To put it another way, suppose the marginal cost of irrational CEO discrimination on company value is 10% across the private sector. That's tantamount to saying the largest companies are leaving tens of trillions of dollars on the floor because they don't understand bias, and so few of them are smart enough to arbitrage it that the effect persists? Is that really likely?

Markets are often wrong, but genuine long-term large-scale arbitrage opportunities are very hard to find.

Of course if the discrimination is rational, there can be no "disadvantage" or "tax" -- if the group tends to lack the traits for success, hiring would have to be irrational to represent them proportionately, and then Tyler's argument amounts to a Marxish conflation of a natural distribution with a social injustice.

In reality, there are not a lot of spurned CEOs running to the tennis market, and the officially mandated quest for diversity probably overcorrects for what discrimination actually does exist.

There is I believe 4 African American CEO's among the Fortune 500 companies. So you're saying absent the bias introduced by diversity initiatives there would only be 3 or 2 African American CEOs?

Why would that surprise anyone? There are a couple billion Indian and Chinese people in the world, and yet the NBA is dominated by the 42M Americans of African ancestry,

And oh, hey, about those Indians...

"India-born CEOs are taking the U.S. by storm"

To put that into perspective, US blacks are less than 1% of the world population, and yet they are ~70% of the NBA. That means they are more than 70x overrrepresented, which is actually larger than their ~10x underrepresentation as CEOs among Americans.

It's not about surprise. Assume the figures are 496 white CEOs of Fortune 500 companies and 4 Africian Americans. That means the rate of Africian Americans is 0.8% with what you describe as a "mandated quest for diversity". You say maybe the 'true' rate should be 2 or 3. So with 'quest for diversity' you get 0.8% and without it 0.4%? Assuming the 'quest for diversity' causes the wrong call to be made 2 out of 500 times that seems amazingly trivial.

No, Tyler already explained why -- at each level of filtering, the pool of blacks gets smaller, but they still face the same statistical hurdle but now with a smaller group. So by the time you get near the CEO level, the pool of black candidates is already tiny.

Meanwhile, blacks are overrepresented in the NBA for the same reason -- the other ethnicities take a bigger hit at every level.

Also, while those are your numbers (I don't claim to know the optimal rational distribution of black or Indian CEOs) diversity mandates do exist and presumably have some effect on the distribution. I don't think anyone can claim to know with any certainty what the optimal distribution is, but because of the levelling effect it's not obvious "1% black" is evidence of discrimination against blacks.

(at least, not irrational discrimination)

I don't know why you believe that the tax is heavier on the corporation than the individual. You might think differently if you were a black or women held back unfairly. Also, you are missing the point of Tyler's argument - that there is some rational discrimination happening - the cost of getting good information at each step is higher than the loss from not optimizing, and that cummulatively, this causes inefficiences/loss for the organization, the people impacted and society.

I explained why -- people rarely cease to exist if they don't get the best job, but corporations fail all the time. Almost by definition, a key position means the prospective employee will have a larger effect on the organization than vice versa, because the organization is putting them in control of the organization's resources. Thus they have a larger incentive to avoid hiring the worse person than the employee has to find the better job.

And again. the cost accumulates for employers too, particularly since an organization that discriminates on one level is more likely to do so at multiple levels, so those that don't gain larger and larger cumulative advantages.

Also, while corporations don't have feelings, their investors do. You might feel differently if you had your life savings invested in a company that went bankrupt because they hired a less-qualified minority candidate to run the company.

The logical flaw is below, where Tyler goes from saying (roughly) the "discrimination is rational" to "the group is disadvantaged -- the group cannot be disadvantaged if the discrimination is rational, we already stipulated they are receiving exactly the correct amount of discrimination at each level.

Each level will apply its own “statistical discrimination” tax, whether intentionally or not. Say for instance there is (mild) statistical discrimination against women at the CEO level. Firms that wish to hire and promote future CEOs will be less likely to seek out women to hire, including at lower levels. This may or may not be conscious bias; for instance the firms may decide to look for certain personality traits that, for whatever reason, are harder to find in women. They’ll simply be making decisions that give them plaudits as good talent spotters.
So say the “Bayesian rational” level of statistical discrimination is a five percent discount. You can get far more than that as the actual effective tax on the disadvantaged group, with everyone in the system behaving in a self-interested manner.

But there is no tax on any specific person (remember, no one was discriminated against!), just a distribution in which they are naturally underrepresented. To call it a "tax" is a misleading appeal to emotion on behalf of a victim that doesn't exist.

You entirely miss the point. The discrimination compounds over each level. So a 5% differential ends up being a 40% differential. The 35% that should have been at the top that are not are severely disadvantaged. And the organization and society are disadvantaged by not being able to better identify the best talent.

Again, you accuse me of missing the point when you do. It doesn't matter whether it's cumulative, it's not a disadvantage, it's a distribution. No one faced any unfair discrimination, but the effect of fair discrimination still results in a certain distribution.

I get that this is not the easiest point to grasp, so consider this example.

Suppose we give 10 people a thousand dollars each to invest. The next year, we come back and give the 9 best performers another two thousand. And so forth. Each year the pool gets smaller and the rewards larger. At the end of the experiment, the incomes will have a distribution that is much different than the initial "fair" distribution, even though we always gave everyone the same amount of money at each level. That's not unfair, that's just the result of the system.

There seem to be a number of comments that miss the point. Tyler's key point is that small levels of bias will accumulate across gatekeepers and result in much larger outcomes in results, i.e., a 5% level of discrimination in the system could result in 40% reduction in the number of woman CEOs. This is completely independent to whether the discrimination is warranted and what women's career aspirations are. Unless managers always have perfect information and always make the firm optimizing choice, I think any model would show that the difference between outcomes and level of bias grows over time. Scott Adams would not have made a career out of Dilbert if managers were perfect rational-decision making machines. It's hard to know how much gatekeepers amplify initital bias, but it's hard to argue that there is no amplification. (Of course, affirmative action can counteract bias amplification. Folks in the comment section seem to believe that affirmative action is far more prevalent than I do. It is really not a thing in the start-up/tech world.) The gatekeeper impact is going to be further amplified by different levels of investment in human capital (mentoring, training, opportunities).

I think the point is even more subtle than that. Assume that gatekeepers have extremely accurate understandings of average racial gaps in performance. Thus gatekeepers in, say, the 100 meter dash coaching business are less likely assume a white sprinter will succeed than a black sprinter, even if they appear equal on all non-racial metrics. If a sprinter needs to get past several successive gatekeepers to become an Olympic finalist, then rational decisionmaking by gatekeepers can make it more harder for a late-maturing white sprinter than a late-maturing black sprinter of equal talent.

This form of rational statistical bias could help account for the extreme imbalance seen in fields where nobody much cares about bias because whites do worse, such as the men's 100m dash in the Olympics and cornerback in the NFL.

I agree that you would expect a greater differential in outcomes, even if the gatekeepers are rational and have good information. The more rational the gatekeeper and the better the information, the less amplification you would see. If gatekeepers had perfect information on racial gaps, the amplification would be negligible, because at that point, the gatekeepers would be able to accurately able to predict who will succeed. I don't see why it couldn't have an impact in the sports examples you give. I would expect that the amplification effect would be far greater in the business world, as performance is much more difficult to measure.

Thus gatekeepers in, say, the 100 meter dash coaching business are less likely assume a white sprinter will succeed than a black sprinter, even if they appear equal on all non-racial metrics.

What exactly are the metrics you use to measure a potential 100 meter dash sprinter other than performance on the 100 meter dash? Likewise if you have two sprinters who are exactly the same in all metrics but one is black and the other is white there is no basis to assume the black one would be better, you've defined your case as one where both are equal.

Sailer's analysis doesn't really work for athletics where you aren't testing for a single isolated trait/ability (100m dash) but a whole set of skills (just about all team sports, in football the ability to run 100m quickly is important but it may mean nothing in terms of the quality of a particular player). There the quality of the player gets harder to measure against the synergy of the overall team.

"(Of course, affirmative action can counteract bias amplification. Folks in the comment section seem to believe that affirmative action is far more prevalent than I do. It is really not a thing in the start-up/tech world.)"

Granting that statement to be true - a handful of commenters have wondered, if affirmative action was less of a thing, or entirely absent, in the the rest of the world, would it be more of a thing in the tech world?

Is there any way to lower Tyler's initial, Bayesian 5% "bias"? Hopefully no one here thinks that a world run by the sort of people drawn to HR, even if they were armed with "perfect information," is a thing devoutly to be wished.

I can't imagine how less affirmative action elsewhere would encourage more affirmative action in tech. I don't think tech cares what non-tech companies are doing one way or another.

They don't have to care if it reduces the number of people who want to work in tech because affirmative action gives them better opportunities elsewhere.

Funny idea here that oganizations should care about things other than their own sucess. Why?

"if (mild) discrimination at several rungs of the ladder kept me from rising to the penultimate rung, I’d have ZERO chance of attaining the top rung, not merely a small chance"

But remember, we stipulated the discrimination wasn't against your type, it was against a trait you lack, which happens to be less common in your type. Other people of your type who do have the trait did get the job, your type is just less likely to have it, and you didn't.

So in this example, you failed to get the job because you were not well-suited to it by that trait. The system did exactly what it was supposed to do -- what a capitalist society needs it to do to give us the historically ridiculous living standards we take for granted. That it results in a distribution in which your type is increasingly less represented at higher levels is not a bug, it's a necessary feature, much as the process of achieving the NBA needs to filter out shorter, less athletic people from the NCAA and elsewhere to give us a showcase of the best basketball players.

That is not the premise. The premise is that a particular trait is less common in my type, but it is unknown whether or not I personally have that trait. Say this trait occurs 4% in males and 2% in females. If the system equally promoted everyone equally with the trait, at the end, you'd have 2x as many males as females. If you can't readily measure the trait, you'll be far more likely to promote males than females at every step. At the end, you may end up with 20x males as female. In this case, there are many females just as well suited, maybe better suited, to do the job as the males that succeeded. This is the bug, and it hurts everyone (other than the males that might not have been promoted in a fairer system). It significantly harms the non-promoted women and it harms the overall capitalistic society for not optimizing its resources. If the ability to measure the trait is easy, such as running speed or lifting power, the end distribution will be close to fair. But if the trait is difficult, it will be very sub-optimal.

If the system equally promoted everyone equally with the trait, at the end, you'd have 2x as many males as females.

Nope, that's Tyler's whole point, you don't end with twice as many males, you end up with as much 99% males depending on how many iterations you go through.

Wave 1: 100 applicants, 50 male 50 female. Male odds are 2:1, so 30 positions go to 20 males, 10 females.

Wave 2: 30 applicants, 20 male 10 female from Wave 1, for 15 positions. What is the number of positions that go to females? Male odds are still twice as good as female, but now pool is also 67% male, so the 33% of females who got to Wave 1 positions now face another 33% hurdle to achieving Wave 2 positions, meaning we should expect to find women in (33% of 33%) = ~11% of positions, and males in ~89%. So let's round up the ladies and say 2 women, 13 men.

Wave 3: 15 candidates, 7 positions. 13 of the candidates are men, only 2 are women. The men are still twice as likely to get the job as a given woman. A woman's likelihood is now 33% of 33% of 33%, or about 4%.

And now you see why there are essentially no women in the NBA, MLB, or NFL even though women are only slightly smaller and faster than men on average.

There's no bug, this is exactly what's supposed to happen, and it hurts no one (indeed, it helps everyone!). It's just counterintuitive because the math does not work out the way one might expect at first glance.

Actually I guess that's not quite right... if we give males a 5% advantage on each level as in Tyler's example, we have an increase of men at a given level N of (1.05)^N (and for women a reciprocal decline), so after 7 iterations there are 1.41 men for every .71 women.

In your example the advantage would be (3/2)^N vs the reciprocal, so only after 4 iterations are men are 96% of the total (5 vs .2).

No. That's not the right analysis. It's not that at every stage, you are 2x as likely to promote a male to a female. It's that males are 2x as likely to have a trait as women in this case. The optimal result is that you would have 2x as many men. Not 20x as many men. I'm not disputing that a system that was the result of fully rational choices could end up highly lopsided. My argument is that such a lopsided result is not the optimal outcome, even though it came about from rational choices. The QWERTY keyboard is not the optimal keyboard, even though the reasons for its development were perfectly rational. Just because a process is rational does not mean that the outcome is optimal. (And for the record, I'd highly dispute that the system is free of all prejudice and that all actors act rationally. But that is an entirely different topic.)

No, the optimal result is the one in which the best candidates are picked, not the one that satisfies someone's notions of social justice -- and if a market process isn't rational EMH means someone will arbitrage it.

If blacks weren't wildly over-represented in the NBA, the results wouldn't be the best players and few people would bother to watch.

BTW, QWERTY inefficiency is mostly a myth. That's why even today relatively few people use DVORAK, ABCDE or other alternatives.
Contrary to popular belief, the QWERTY layout was not designed to slow the typist down,[5] but rather to speed up typing by preventing jams. Indeed, there is evidence that, aside from the issue of jamming, placing often-used keys farther apart increases typing speed, because it encourages alternation between the hands.[14] There is another origin story in the Smithsonian that the QWERTY keyboard was made for telegraph operators and has this layout to make it easy for the telegraph operator to work.[14][15][16] (On the other hand, in the German keyboard the Z has been moved between the T and the U to help type the frequent bigraphs TZ and ZU in that language.) Almost every word in the English language contains at least one vowel letter, but on the QWERTY keyboard only the vowel letter "A" is located on the home row, which requires the typist's fingers to leave the home row for most words.
Several alternatives to QWERTY have been developed over the years, claimed by their designers and users to be more efficient, intuitive, and ergonomic. Nevertheless, none have seen widespread adoption, partly due to the sheer dominance of available keyboards and training.[55] Although some studies have suggested that some of these may allow for faster typing speeds,[56] many other studies have failed to do so, and many of the studies claiming improved typing speeds were severely methodologically flawed or deliberately biased, such as the studies administered by Dvorak himself before and after World War II.[citation needed] Economists Stan Liebowitz and Stephen Margolis have noted that rigorous studies are inconclusive as to whether they actually offer any real benefits,[57] and some studies on keyboard layout have suggested that, for a skilled typist, layout is largely irrelevant – even randomized and alphabetical keyboards allow for similar typing speeds to QWERTY and Dvorak keyboards, and that switching costs always outweigh the benefits of further training on whichever keyboard you already use.

The exception is apparently chording, but that's different than typing.

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