How game theory can help us understand why diversity is hard

Diversity is pretty much about three things: How people interact, who is rewarded by institutions, and the differences in our starting points, including the social networks and resources into which we’re born.

There’s of course a lot of context and nuance in these three categories, and they don’t represent everything. But they cover a lot of the big challenges that have proven frustratingly resistant to interventions thus far. Today, I want to zoom in on interactions and see if game theory can be of any help.

Game theory is a mathematical approach to understanding strategic interactions. These are situations involving two or more people where each person’s best move depends on what the other person does. If you’re thinking about chess or football, you’re on the right track (to be clear, this is now the most I’ve thought about either). The core idea is that they’re situations where there’s no obvious, universal, context-free best move. Instead, whether you should, say, sacrifice a pawn depends on how you think the other person will respond.*

At first, game theory can feel like a great way to suck the air out of things that should be fun, like playing games and talking to people (emphasis on “should”). But taking the time to pull apart the specific dynamics of a complex interaction, inspect them all, and then put them all back in can help us get a clearer understanding of the key strategic dilemmas that are giving rise to certain outcomes. And, once we know more about those dilemmas, we can then think about interventions to change them. See? It’s so fun.**

One of my favorite game theoretic models is called Exit, Voice, and Loyalty, which is about what a person should do if an organization does something they don’t like. The idea comes from the economist Albert O. Hirschman’s 1970 book, Exit, Voice, and Loyalty: Responses to Decline in Firms, Organizations, and States.

The key here is “decline”. Suppose a company you work for adopts a policy you don’t like. According to Hirschman, you have three options: exit (quit your job), voice (speak up), or loyalty (keep your grievances to yourself and keep working). You can formalize this, and add in the company’s possible responses. The version below is modified from the one I know best, which is originally for political contexts (a citizen choosing whether to leave a country), and developed by my former professor Bill Clark and his coauthors.

I want to emphasize that models are meant to be simplifications of reality, not reality itself. Of course, there’s a lot more we could build into this to map to more specific circumstances, but it’s useful to start with the simplest version.

This is the structure of the game. This is also a great caption.

The game begins when something bad is going on in the company you work for, and then it’s played from left to right. First, in response to this bad thing, you can choose exit, voice, or loyalty. If you choose exit or loyalty, the game ends — you either leave or keep your grievances to yourself and carry on. If you choose voice, the game continues. Voice in this model can refer to any method of speaking up — from sending an email to meeting with your manager or HR, to staging a walkout or strike.

To keep the model simple, we assume that you choose the “right” level of voice the first time around, which is the maximum level you are comfortable with in the hopes of change. You can imagine a version of the game where this iterates or escalates: you might first try sending an email, then ask for a meeting, then go on strike. But, the underlying dynamics are largely the same, so we just collapse these steps into one for analytic tractability, which is a wonderful social science way of saying “making it easier”.

If you choose voice, the company can respond or ignore you. If they respond, we assume you just get what you want, and things carry on in the company with a new status quo. If they ignore you, you’re back to choosing — stay under the shitty conditions after having incurred whatever cost may have come from using voice, or leave?

So, should you speak up? We can see it a little more clearly by adding possible outcomes:

This is the game with payoffs and some assumptions.

To solve games like this, we use something called backwards induction, which means … inducing backwards. We start from the last possible decision branch: suppose the employee has used voice, and the company has ignored them. The best option for the employee depends on how bad the situation is at a company, and whether they have a credible exit option. Let’s suppose the exit option is better than the shitty status quo at the company. This means the best move for the employee is to leave. Thus, the company loses this talent.

Working back one step: If the company knows the talent is going to leave, they can weigh their options: would they rather lose the talent and keep the status quo, or change the status quo and keep the talent? This depends on how valuable the particular employee is to the company compared to the status quo. Let’s suppose they are unwilling to change the status quo, even if they do have a positive value for the talent. This means their best move is ignore the employee.

Working back one more step: If the employee knows they are just going to be ignored by the company, at which point they’d leave anyway, then the best move is to leave in the first round and save themselves a whole bunch of energy and time trying to get the status quo to change. So, the best move for the employee is to just leave the company without trying to change anything.

And that’s a story we see over and over again in pipeline and turnover problems in companies in the US (and everywhere).

Now, all of this depends on a handful of assumptions: The employee has a credible exit option, the company is committed to its status quo more than it would prefer to keep talent, and voice is costly.

We can imagine adjusting all of these for different scenarios. For example, suppose you’re a non-cis-male person or a person of color, perhaps voice is more costly for you because, as research shows, you’re more likely to be perceived as “difficult” than your white, cis-male counterparts. Or, perhaps your voice is less likely to be taken seriously. Then we see these groups even more likely to exit.

But now assume you don’t have an exit option — turns out, that can hit these same populations harder as well. If you can’t afford to quit your job, it means you also can’t afford to speak up. And this means the shitty status quo continues. (This also explains why we may have seen more #MeToo activity in some industries and communities (mainly white women) than others.)

This has all been insanely abstract. It applies to anything — from a concrete policy, like family leave or job-sharing, to an aggressive, hostile culture or a culture where disagreement is seen as disengagement. This has already gone on too long, so maybe I’ll unpack this more in the future, but for now it’s pretty cool (I think) that we can see mathematically why there are both pipeline problems and situations where it’s irrational to speak up about a harmful status quo. I like to think this is a little bit of mathematical support for the importance of allyship, too, which we’ll talk about in a future article.

By the way! I was supposed to do ten of these, and this is the tenth! In my original article I said I’d do 14 if I felt like they were going “well” — which is something I deliberately, if hypocritically, did not define. I am not sure any of this is going well, but I don’t think we’ve really solved anything yet, so I’m going to keep going to 14. (And I want to get better at this, and it’s the best I’ve got for now for now.)

Thanks, as ever, for reading!

*Or, if you’re like me, it depends on how extremely bored you are, which in addition to being generally a lousy chess strategy, also moves us to the domain of decision theory, which is when your best move doesn’t depend on what other people do, and instead is about optimizing over some set of options; in my case, I am optimizing over causing something to f*cking happen.

**It is dawning on me that I say some version of “SEE I TOLD YOU THIS WAS FUN ISN’T THIS FUN” in every article. This is what psychologists call “trying too hard.”