Diversity Math

A model of how bias propagates in the recruiting process

Tech startup teams often suffer from the many limitations of having a monoculture — lack of innovative solutions, lack of empathy to customer needs, simplistic solutions to customer problems where a diverse outlook would have, perhaps, allowed a broader spectrum of possibilities to be considered. Even solutions to hard technical problems very often benefit from an attack by a diversity of approaches that comes from a diversity of outlooks which is harder to achieve in monocultures.

Diversity, though, is a contentious and divisive topic. Discussions are often a futile exercise in talking past each other. Over time people may agree that something needs to be done and hence do something, often anything, with the intention that it’s better than doing nothing.

However, without an understanding of the mechanics of how monocultures propagate it may be hard or even impossible to construct company structures that nurture vibrant diversity as they grow.

How to get at the heart of the problem without drowning in angry verbiage? How to find the Archimedean Lever to change things?

This essay aims to model the process by which, consciously or unconsciously, teams with monocultures grow and self-reinforce. Seeing this in an emotion-neutral model, it is hoped, diversity might be easier to design-in.

A Game

Consider the following mental game. It is well known in mathematical statistics. No math is needed - this will be painless, I promise.

Imagine that we have a large urn with an unknown number of red and blue billiard balls. We reach in and pull out a ball. We look at the color and we put it back with another of the same color. So if we pick a red ball then we put back two red balls, if blue then two blue. That’s it!

As we repeat this many times, the math says, the proportion of red to blue may fluctuate a bit in the beginning but eventually settles down to what it was at the start.

Think about that for a bit — no matter what the proportion at the start — if you play this game you will end up with pretty much the same proportion. This is known as Polya’s Urn Theorem, named after a famous mathematician.

An Interpretation

Consider this process as a model for the hiring process in companies.

The act of replacing one with two is analogous to expanding the team by one via a hiring process. Now whether it is “cultural fit” or “lack of pipeline” or whatever we explain it away to be, the underlying math is very clear.

If we start with all red in the urn, we will continue to always have all red. Simply because we don’t have a way to “attract” a blue — so you’ll always pick a red and you’ll replace it with two red, growing the team of all reds ad infinitum.

Now while the statement of the game here and in Polya’s theorem, uses color as a differentiating attribute, this essay does not imply it to be color of skin.

It stands for ANY attribute that we may consider as the filter, conscious or unconscious — race, gender, age, ethnicity, university and educational background, personality, skill level, experience, type of intelligence, cultural commonality and so on.

So, if we start with a small team that has a monoculture i.e. all members are similar in multiple aspects (age, race, gender, ….) , and if we use the existing team as a hiring filter, then our company will grow with the same or very similar monoculture. Without a change to our hiring filter the monoculture will get reinforced more and more strongly as the team gets larger and larger.

If we want to build a company that attracts a diverse employee demographic, which in turn expands the hiring pool, and makes the culture vibrant, creative and resilient, then we need to do so at the ground floor. AND we need to have hiring be driven by the diversity of the current team, in terms of interviewers, interview styles, filter attributes etc.

The more we use “fit” with the existing team as the primary filter, the closer we look like Polya’s Urn. If the existing team is diverse, diversity propagates; if a monoculture then that propagates. Again diversity is meant in its most general form not any particular section of it.

Caveat

This essay does not mean to suggest that one way is better than the other — that diversity is superior to monocultures — what it does very unequivocally suggest, though, is that initial bias propagates strongly through the hiring process, possibly unknowingly.

The hidden subtext is the larger the company gets the harder it is to change later as we have to effect a far bigger change to make a noticeable difference and confirmation bias makes it harder to recognize opposing viewpoints.

Summary

If we want to create a diverse company, then it is good to think about the implications of the Polya Urn Model of monoculture propagation and design teams to make diversity a default.

Thoughts?