The Inverse Relationship of Equality of Outcome vs Opportunity

Rationally speaking, it’s easier to frame a question well than to resolve the question. But all too often even framing the question well never really happens. In this post I’m going to frame the question of equality of outcome vs opportunity for women in the work place, using the now famous Jordan Peterson vs Cathy Newman interview as my backdrop.

In Cathy Newman’s interview with Jordan Peterson she used the fact that there are only 7 women running the top FTSE 100 companies as support for the idea that women are still being dominated and excluded by men. To her, this was proof of that fact. To Peterson, it was not. (And I note that to Newman, the fact that Peterson didn’t see it that way was essentially proof that Peterson must be sexist for ignoring the evidence.)

Let’s formulate this issue mathematically, not to determine who was right but to make the question more solid as to what we’re asking in the first place. Then, without ever even knowing the answer as to who is right, I’ll illustrate how just understanding the question well is useful to us.

The Interest Gap and Equality of Outcome

To make the numbers easy, let’s pretend that there are only 100 men and 100 women in the world. Let’s say that in this world of 200 people, we only need 5 CEOs for the FTSE 100. (Or rather FTSE 5?) And let’s pretend the FTSE 100 CEOs consist of 4 men and 1 woman. This means that only 1 in 5 women are FTSE 100 CEOs, clearly favoring men as CEO. So far, clearly Newman is right that there is a lack of equality of outcome here. Women are underrepresented and thus do get less of a voice in how the FTSE 100 are run.

Peterson makes the claim that there are fewer women seeking to be CEOs in the first place. So let’s pretend he’s right and model that by having 5 of the 100 women want to be CEOs and 20 of the 100 men wanting to be CEOs.

So here is the question: if you’re a woman interested in being a CEO, is your chances of being a CEO any different than a man’s?

Let’s do the math:

A woman that wants to be a CEO has a 20% chance of becoming one (i.e. 1 in 5). Likewise, a man that wants to be CEO also has a 20% chance of becoming one. (i.e. 4 in 20.) So, at least in this hypothetical world, men and women have equal chances of becoming a CEO should they want to strive for that position. So here we have a case of equality of opportunity — both genders have a 20% chance of becoming a CEO.

Put another way, even though there are significantly fewer women as FTSE 100 CEOs, it’s still true that if you are a woman that wants to be a CEO your chances are exactly equal to that of a man’s.

Now to be clear, this was just a hypothetical example to help illuminate the question, so remember that we can’t draw any conclusions in real life using this example.

The Inverse Relationship Between Equality of Outcome vs Opportunity

But here is where things get interesting. Let’s say that we decide to adjust things somehow such that we get more women as FTSE 100 CEOs so that women have a strong voice in how businesses are run.

Let’s even give the men the nod still and say that 2 out of the 5 FTSE 100 CEOs are now women. Now we have something close to equality of outcome (as close as I can get with an odd number of CEOs) but how did this affect equality of opportunity?

Well, now a woman that wants to be a CEO has a 2 in 5 chance (or 40% chance) of becoming a CEO and a man has a 3 in 20 chance (or 15% chance of becoming a CEO). Note that now it’s considerably better, if you want to be a CEO, to be a woman now.

In short, unless the level of interest of men and women to be a FTSE 100 CEO happens to be identical, by adjusting for equality of outcome we automatically also negatively impact equality of opportunity. You can’t make both fair simultaneously.

Asking the Right Question

Given this math, the first question we should probably want to ask is: what is the actual real life disparity between men and women wanting to be CEOs?

I confess, I have no idea and probably most of you reading this don’t know either. So we can’t conclude anything about the real world using my math above.

But we can use it to illustrate the problem of trying to solve both the problem of equality of outcome and equality of opportunity simultaneously. So if you have to choose between one or the other, which is more important to you and why?

This brings me to my most important point: that there is not a single all encompassing definition of ‘fair.’ “Fair” is a term that simultaneously maps to multiple competing moral priorities. This is why we should be careful using “but it’s not fair” arguments without considering all possible understandings of “fair” for a given situation.

Other Points to Consider

There is obviously a lot more to this debate than this one single simplified point. Peterson raised issues around differences between men and women on the big five personality traits (i.e. Openness, Agreeableness, Conscientiousness, Extroversion, and Neuroticism — the word that got James Damore in trouble.) Is Peterson correct that women tend to be more agreeable and that agreeable people tend to get promoted less? And even if he is correct, is Newman correct that we ought not to organize society in such a way that agreeable people are less likely to be promoted? And how, exactly, would we organize society instead? For that matter, is it possible we’re socializing younger girls to not want to be CEOs in the first place? All of these are fair related questions.

These are just a taste of the wide variety of other factors that have to be considered that are completely unrelated to the inverse relationship of equality of outcome to equality of opportunity. So we have not even come close to exhausting all relevant arguments surrounding this debate. But we have seen that forming a question well can teach us something useful even if we never know the answer to the question.

Bruce is a Master's student specializing in Machine Learning and Artificial Intelligence at the Georgia Institute of Technology.