(Cross-posted from Telescopic turnip.)

I’ve come together with the fact that humans will never find the truth about culture-war issues. We just can’t help it. I tried checking the facts, listening to the other side, examining the social context, deconstructing the power dynamics. I tried mistake theory, conflict theory, critical theory, but the result is usually the same: after checking all the evidence, I come to the conclusion that my favourite political tribe is always right, and everyone else is an idiot. What a coincidence, the ultimate truth is whatever is most popular in my personal social circle!

This is unfortunate, because the prospect of stuff like social justice is actually pretty great. Everybody agrees that it’s better when society is fair. But social justice is a calibration problem, and a hard one: there’s only one way to be fair, and infinitely many ways to be unfair. To calibrate society, we need a unbiased bird-eye view of it, and that’s where we suck. The human brain is utterly incompetent at this task. Our perception of what is fair is tuned differently for different people. It’s becoming increasingly clear that people carry different genetic variants biasing their brains in different directions, so we may never be able to agree with each other. Did you know that there are documented cases of people turning into conservative authoritarians after brain trauma? Like, you have a car accident, and when you wake up, women must obey their husbands and Infowars makes sense. I have no doubt these patients can come up with very sound arguments about why they changed their mind. How are we supposed to balance the power imbalances in these conditions!?

A culture-wars riddle

In last resort, I’d like to try something different. Here is a culture-wars riddle. It’s like your typical math riddle, except it’s a sociological one. The argument is deliberately hidden and you have to come up with it yourself. Maybe (maybe) it will make it easier to put your existing opinions aside and have a fresher look at the issue. Let’s give it a try.

There is a phenomenon, related to [thunder noise] the gender pay gap, that I came across during my usual peregrinations on the information superhighways. I think this phenomenon is important and more people should take it into consideration. But I won’t tell you what it is. Instead, you will have to guess. Doesn’t that sound extremely fun?

Behold, the riddle:

  • This takes place in a fictional world where there is no gender wage discrimination. All employers calculate wages with an algorithm that doesn’t take gender into account.
  • A man and a woman do the exact same job, in an identical way. They work the same days, always start work at 9 am and leave at 5 pm and everything they do in between is the same. The provide the exact same value to their employers.
  • Yet the man gets a higher salary than the woman. There is no other form of compensation than salaries.
  • The difference is due to gender, but not due to discrimination from employers. There is something they do differently outside of work that leads to a wage difference. That thing has no effect on how they work, or when they work.

How is it possible?

(I will add that the phenomenon in question exists in real life, it has been measured in several Western countries and it’s sizeable.)

Forced curiosity

My hope is that the riddle format forces you to approach the problem with curiosity. It is much harder to find the solution if you come with a soldier mindset. This is not steel-manning as a rhetorical device; this is steel-manning because that’s how you solve the puzzle.

Note that this is still a controversial, culture-wars issue. It’s possible that I am simply wrong, as well as all the researchers who claimed to find evidence. In that case, if you still find the solution, you are in a perfect position to understand how I ended up being wrong, and you can correct me in the most effective way.

Some ground work

Did you find a plausible hypothesis? This is where the fun begins! Now you can go to your favourite academic search engine (e.g.) and look up some carefully-chosen keywords, to find if your hypothesis is supported by actual observations of the world. I found eight studies specifically about the mystery phenomenon. Among these eight studies, one was conducted in France and is published in the Quarterly Journal of Economics. Once you’ve found the study, take the first name of the first author (with the capital letter) and compute the SHA256 hash. Here is what you should find:

5dfcf9ef1fb1ecbce32fefe37ae99aff68832a7e2ac74f52daa5a1bcd8038118

No, I will not give the solution, but you can discuss as much as you want in the comments. I can give hints.

Edit: Richard Kennaway found the solution in the comments

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This is unfortunate, because the prospect of stuff like social justice is actually pretty great. Everybody agrees that it’s better when society is fair.

Hmm, I don’t think this is true…

But social justice is a calibration problem, and a hard one: there’s only one way to be fair, and infinitely many ways to be unfair.

Ok, now this is definitely not true.

I didn't expect that. Do you think there are cases where an unfair society is better than a fair society?

John has $100 and Jill  has $100 is worse but more fair than John has $1,000 and Jill has $500.

Many people would think that the second case is more fair. It depends on how these dollars were obtained.

They must work in an environment that does not have competitive labor markets with profit maximizing firms else the firm hiring the man could increase its profits by firing him and hiring the woman.

In the riddle's world, there are indeed competitive labor markets. The firm would hire the woman if they could. It turns out they can't, because of the mystery phenomenon.

That would be true in a perfectly rational, globally-optimized company with perfect visibility into facts.

Consider that there is no statement about the reviews or raises they receive. It is very possible for identical work output to receive different reviews and rewards based on personal traits and relationships. Setting aside gender, taller people also make more and receive higher ratings.

So while you’re 100% correct that it should work that way, it is entirely possible that in a local situation it does not work that way. One hypothesis might be that management is predominantly male, and faced with identical work output, conscious or unconscious bias leads them to pay the man more.

I’m not sure what they author is going for here, but I can say from a lot of firsthand experience that labor markets are anything by rational. So I’d expect the result to rest on irrationality.

A few ideas occur to me, all based on the man having a larger range of employers to choose from.

  1. More men than women migrate to find work.

  2. Men are willing to commute further.

  3. Men are more willing than women to apply for jobs that they do not meet the requested qualifications for.

The briefest Googling suggests that there are studies to support all of these, but I'm not going to search any further for the needle.

These three all look like manifestations of a single characteristic, "initiative", or "get-up-and-go", but neither of those terms is good in a search engine.

The commuting gap is what I was thinking of. Well done!

Er, how exactly does this cause the man and the woman to get different salaries, unless they work at different companies, in different locations? And if so, then, contrary to the stipulations, they’re not doing “the exact same job”!

Maybe there is an aspect of randomness in every salary offer. Sometimes companies will overoffer/underoffer based on their impressions of the candidate. By applying to more places, the men have more opportunities to get lucky with high offers, which they are then likely to accept.

This seems like a stretch, a just-so story. Do you have any concrete reason to believe this to be the case?

I mean, plenty of companies in our world give variable salaries based on interview performance. Once you have that the rest follows.

Another alternative: There could be companies that agree to match your highest competing offer. This also exists in our world and would explain the effect.

The most direct modelisation of the problem does lead to that result without any trickery, that seems like a concrete reason and one you can calculate before looking at the real world. 

Suppose each interview leads to a Measured Competence Score PCS, which is Competence Score * random var pulled from a normal distribution. We suppose men and women have the same Competence Score from the assumptions that they do the same work, but suppose men are going to twice as many interviews as women because have more accepting criteria on where to work. Finally suppose the algorithm for fixing pay is simply MCS multiplied by some constant (which is indeed not directly related to gender). 
It's easy to see that a company received twice as many male candidates and selecting the top x% of all candidates will end up with more male candidates with higher salaries, even though competence and work done is exactly the same.

A very interesting point here is to notice that a smarter employer who realises this bias exists can outcompete the market by correcting for this bias, for example by multiplying MCS of women by a constant (calculated based on the ratio of applicants). He will thus have more competent people for a certain price point than their competitors. In this simple toy model, affirmative action works and makes the world more meritocratic (people are payed closer to the value they provide).

I also note that the important factors here is that interviews lead to variance in measured competence score and there is a disproportion of number of applications per person per gender. It does not seem  to matter if there is only a disproportion of number of applications per gender (eg. in tech if 10% of applications come from women and that accurately reflects the number of applicants, then there will be no average pay difference in the end, and so affirmative action does not help for simple population disproportions, only for applications per person disproportions). In fact, this doesn't need to be corrected by gender. If applicants had to answer how many interviews they were doing total, the  algorithm could directly correct for that per person and again reach an unbiased measurement of competence. 

These three all look like manifestations of a single characteristic, "initiative", or "get-up-and-go", but neither of those terms is good in a search engine.

This feels like a weak classification of those three points. All of those could be explained by "initiative", sure. But you could equally explain 1 & 2 via the fact that women do more childcare, and so are less mobile for labour market purposes. 

When I looked into this question, the paper Gender Differences in Job Search: Trading off Commute against Wage came up, where they point out:

The left panels of Figure IV show that gender gaps in reservation wage and commute grow with age until the age of 40 and then begin to plateau, following a pattern quite similar to that documented in the right panels for the gender wage and commute gaps in the overall working population.

If you want to explain it via "initiative", I think you have to have an explanation for why this change occurs (and it does seem like its generating the majority of the effect), whereas an increase in the time spent taking care of children feels like a better explanation for the data. Sadly from a quick ctrl-F I don't think the authors determined whether women/men involved were parents, but I may be wrong. 

Yes, that could be a factor.

I'm a bit confused by the details of the thought experiment.

  • When you say "a fictional world where gender wage discrimination doesn’t exist", that could mean either:
    • Hiring managers don't take gender as a direct input on hiring in such a way that the distributions P(pay|gender) = P(hire) if the applicant is equal otherwise. In this case, intervening variables (such as height) might make men paid more than women on average, since they are on average taller and people who are taller are paid more for whatever reason.
    • Gender doesn't have any population level effect on pay, i.e. the population distributions P(pay|gender) and P(pay) are equal. In this case, differences between genders that matter for hiring (such as educational attainment) would necessitate that people of different genders be paid different amounts (so that the difference in educational attainment is balanced out by the explicit gender preference in pay).
  • When you say "negotiate the salary the same way", it could mean:
    • Negotiation strategy does not depend on gender (but may depend on, e.g. disposition, in which case we can have intervening variables again)
    • The people being compared in the thought experiment are forced to employ a fixed negotiation strategy (in which case people with different circumstances or dispositions will apply for different jobs).

It's the second option in both cases (e.g. P(pay|gender) and P(pay) are equal). In addition, since they do the same work with the same productivity, it's assumed that they have the same circumstances and dispositions.

Not a fan of the format - I suspect I've seen some of the studies you're referring to, but in this case the puzzle is distracting from your intro, and the more interesting point that you yourself are struggling with stepping outside the culture wars.  I'd love to hear more about how you found alternate voices, and how you're convincing your brain to down-weight the models that most of the people around you are supporting.

One of the issues with culture war dynamics lies in people having a lot of certainty for their views with very little evidence for their views. The real world is very complex.

Your riddle shows one dynamic that leads to higher pay for men but it's just one of many factors.

If you for example read the moral mazes sequence it provides you with one mechanism that likely reduces the number of women in top management positions.

In the real world, some people are trying to counter perceived biases and overcorrect. 

It's really hard to know what factors go into why a certain job pays women differently than men but as humans, we love to feel like we know what goes on. We like to pretend that we can easily generalize effects over a large number of different examples.

Two possibilities:

  • The company figured out that men consume less health care than women, and adjusted their salaries to account for it
  • The company has a defined-benefit pension plan, and realized that this costs more to provide to women because women live longer. So they adjusted salaries to account for the difference in costs

Nice try, but it's neither. To clarify, the company doesn't take gender into account when calculating the wages.

Maybe the company is discriminating on some property that is not gender itself but is due to gender. Based on the description it would have to be something that does not affect the employees' work.

One possibility is that the company pays sole breadwinners more to help them support their families, and men tend to be sole breadwinners more often due to differing preferences/abilites/cultural expectations of the genders.

My thoughts were

  • Education - men might invest more in education outside of the job - which is factored into future value.
  • Socializing - men might socialize more with potential business partners/customers.

I tried mistake theory, conflict theory, critical theory, but the result is usually the same: after checking all the evidence, I come to the conclusion that my favourite political tribe is always right, and everyone else is an idiot.

Seriously? Doesn't sound like you did a good job there. Maybe your identity is a bit on the large side? Having a "favorite political tribe" is sus already, and "always right" is a dead giveaway that your evidence checking was thorough enough. 

Yeah, there was a bit of hyperbole, but overall when I see what gets in my RSS feed, it's clear that it tends to converge on a particular kind of people and I have to spend a lot of energy finding contradictory sources. On topics like the gender pay gap, I find that one "side" is basically always wrong, and it's hard to tell if it's just because they are really always wrong, or because of my confirmation bias. Also, by "favourite political tribe" I just mean that there are tribes with which I disagree more often than others. I don't think anybody really likes every tribe equally.

My guess: the woman was hired later than the man and hasn't been promoted/given raises as much.

I interpreted the second bullet point to mean that's not the case.