Solicited Review: Cumulative Advantage by Mark Schaefer

Mark Schaefer asked me to review his latest book, Cumulative Advantage. It’s a book based on the sociological work of Dr. Robert Merton as well as a series of other sociologists on the phenomenon of cumulative advantage. In the most basic terms, those who have advantage continue to benefit from it at a faster rate than those who do not. It’s a concept embedded in many cliches and tropes: the rich get richer, virtuous cycles, success begets success.

The book is divided into five major themes – initial advantage, the seam, sonic boom, reaching up, and constancy, as his blueprint for how to leverage the power of cumulative advantage.

Initial advantage is what it sounds like – finding opportunities to be an early adopter, to gain some initial cumulative advantage that can be parlayed into greater opportunities.

The seam is an encouragement to find opportunities for disruptions in your marketplace.

Sonic boom is all about using social proof to amplify advantage.

Reaching up is about leveraging the power of your network as well as mentors to achieve more.

Constancy is about creating more bodies of work for greater chances at visibility.

That’s the book, and it was an enjoyable, fast read. Each of the chapters has some ideas for how to implement his framework.

Let’s Talk About The Math

Let’s dig into the single most important part of Mark’s book, which you’ll find at the bottom of page 20 in the hardcover edition. It’s from this 2005 academic paper, “Cumulative Advantage as a Mechanism for Inequality: A Review of Theoretical and Empirical Developments“, by Thomas DiPrete and Gregory Eirich of Columbia University:

This is Dr. Merton’s basic model of cumulative advantage. When you dig into the rest of the paper, further research on the topic explains how this version is good, but incomplete. Let’s decode it, since it’s essential to understanding cumulative advantage as a concept. I’ve marked five different sections of Merton’s formula that was used to describe the “Matthew effect” – aka the rich get richer effect.

Point 1 is cumulative advantage, the advantage an individual has over all time.

Point 2 is looking at current advantage, advantage that an individual accrued previously.

Put together, the left-hand side of the equation is an attempt to predict the likelihood of new advantage based on existing advantage.

Point 3 is actions taken by the individual times their current advantage. This is where the idea of the rich get richer comes from – you carry forward your advantages from the past into your present activities.

Point 4 is a beta distribution of resources brought to a problem. A beta distribution is a mathematical way of talking about diminishing returns; you can only throw so many resources at a problem before you run into limits.

Point 5 is stochastic shocks. This is the fancy way of expressing luck, either in disruptions you take advantage of, or just plain lucky breaks.

Put it all together and this formula essentially says that your cumulative advantage is a combination of advantage you’ve earned in the past plus resources you bring to the problem, plus luck.

And when you read Mark Schaefer’s interpretation, you see this play out in the book; Mark has written Cumulative Advantage based on Merton’s model. Initial advantage is point 2 and part of point 3, the advantage you bring with you. The seam is point 5 – stochastic shocks, aka opportunities to take advantage of, disruptions. Sonic boom and reaching up are point 4, the resources you bring to your situation. And constancy is embedded in the gamma value in point 3, the activities you do.

When you look at Mark Schaefer’s Cumulative Advantage, it all makes sense.

But…

This particular 2005 study went much further, incorporating newer sociological research. And this is where we get into the really important stuff.

Path and Status

Merton’s model doesn’t account for two very important things: path and status. Path is what happened and when in the journey to cumulative advantage; the sum total of stochastic shocks – luck – means that good things happening early on have a strong influence on the advantage you bring with you. It’s better to get lucky earlier than later.

But something even more critical was introduced in later research: the concept of status. Status implies the traits we bring with us: internal resources, as opposed to external resources. What might those be? Things like our race, gender, sexual orientation, religious upbringing, our upbringing in general, how attractive we are – vital factors and sometimes factors completely out of our control.

When we follow the researchers’ expansion of Merton’s model, it becomes this, as seen a few pages later in the 2005 paper:

Points 1 through 3 are the same – cumulative and current advantage. Where we see changes are in points 4 through 6. In the old point 4, above point 6, we see a change – not the resources brought in the moment, but resources brought in the moment that are impacted by past resources. The rich get richer – the more money you bring, the greater effect your past resources have on your present situation. That’s an important distinction – that our legacy, our history impacts our present. Decisions made in the past affect the present – our path.

But the really big changes are at points 4 and 5, which were point 3 in the older model. What this says is that activities, the gamma variable at point 4, are bound with the delta function of status at point 5. Delta function is fancy for change over time – this reflects not just a person’s status now, but how their status has changed over time. Your status – like your race – is inextricably bound to your activities. This means that the activities of someone of the preferred gender, race, sexual orientation, etc. will always outperform the same activities of someone not of the preferred class.

Here’s why cumulative advantage, the sociological concept, is so important. If we want to grow advantage, we need all the components in the formula to maximize our success. Merton’s formula didn’t take into account status and path, and how they interact – in the bigger formula above, status and activities summed together are multiplied by current advantage. Which means that if your status is lower than that of someone else, you have an anchor tied around your foot, and its effects are multiplicative. It’d be like trying to save money and your friend’s bank has a higher interest rate than yours. If you both save the same amount of money, your friend’s money will grow faster than yours.

Cumulative Advantage Is Much More Than Marketing

The concepts of cumulative advantage have a distinguished heritage: they’re about sociologists trying to figure out how to counter the effects of racism and sexism. When you look at the advanced formula, you suddenly begin the grasp just how challenging disadvantages can be.

If you’re working in a society where racism or sexism or bigotry is systemic and endemic – embedded in the culture itself – then if you are a member of the preferred class, you have a bigger status multiplier at point 5 in the advanced formula. That status gives you a massive advantage, even when everything else is equal. You will always outrun other runners in the race, because they all have weights around their legs constantly dragging them down.

Let’s put this in concrete terms using race so you can see just how much status matters to cumulative advantage.

Suppose in year 1, a Black person and White person start out on equal footing except the White person is working in a system where their status – being White – is an advantage. The simplified formulas put into action (minus the beta distribution, etc. for clarity) would look like this:

We see there’s a 2 point advantage in year 1.

Now, let’s look at year 2. All the other conditions – activities, resources, and luck are the same, but they carry through their advantage from year 1.

The gulf between the two has widened by 20x, from 2 to 40 in just a year. Wow. By the end of year 2, with all other factors being equal, systemic racism has disadvantaged the Black person by a 20x multiplier.

Now we move onto year 3. Again, hold everything else constant:

We are now at a point where the gulf has widened another 10x from the previous year. The Black person is now at double the disadvantage compared to the White person.

In the book, Mark talks about some of the work he’s done to try helping in his local community with disadvantaged youth, which is laudable. That brings more resources to the table for an individual. Let’s see what effect that has:

We see Mark lending more resources to the Black person each year, giving them a resource advantage. The nature of systemic racism is that advantage is nullified almost immediately; by year 3, the gap between Black and White is almost the same.

This is one of the many, many reasons minorities object to things like White Savior complexes (which is not what Mark is doing, to be clear) – because not only do they reinforce systemic racism, they also don’t blunt the impact of systemic racism very much, if at all. Our focus must be on dismantling the systemic racism itself.

One of the most common racist insults people lob towards minorities is, “Oh, you just have to work harder, don’t be lazy.” Well, what impact would working harder – generating more activities have?

In this equation, all other things being equal, a Black person working 17% more still isn’t enough to overcome systemic racism’s disadvantage.

Now, what happens if we blunt – not eliminate, just diminish – the effect of systemic racism, changing the status of the Black person to be closer to that of the White person?

What a difference. Just diminishing racism’s impact by one, elevating the Black person’s status by 1, achieves the same effect as that person having to work 17% more.

This is why the concept of cumulative advantage is so important, especially in its expanded form. Once you dig into the mechanics of it, you see just how powerful the path and status variables can be in cumulative advantage – and we didn’t even touch on the resources question, where minorities typically have fewer resources to begin with. Path and status are massive multipliers to cumulative advantage, and it’s why systemic racism, sexism, and bigotry are so damaging.

Overcoming Cumulative Advantage

One of the biggest questions I had going into the book, and didn’t really get an answer to until I dug into the mathematics in the source papers, was how we can negate someone else’s cumulative advantage.

In the world of marketing, how do you mitigate a competitor who has so much more advantage than you?

In the world of people, how do you help someone who’s disadvantaged not stay locked in disadvantage?

Let’s review the variables. There’s existing advantage, activities, status, resources, and luck.

We cannot diminish someone’s existing advantage. We can’t turn back time or take away what has happened in the past.

Relying on luck is a terrible strategy, and as we see in the formula, luck is additive, not multiplicative.

Resources have finite limits, as expressed by the beta distribution in the formula. You’ll hit diminishing returns at some point – and because resources are additive, you’d need more and more to counter a competitor’s ever-multiplying advantage.

No, the only leverage point you really have to overturn the status quo is to change either status or activities, because those have multiplicative effects.

A competitor with a multiplicative advantage will always beat someone with an additive advantage over time.

For example, suppose you want to outrank a competitor in SEO, but they have an advantage. They’ve got content and years of reputation and rank. Can you diminish their status? Not through any white hat tactics, no. So the only variable you have left is to massively outwork them, create massive multipliers of valuable content at a crazy pace to outrank them. Companies can do this, can scale activities if it’s a strategic priority. The challenge will be, with finite resources, which battles do you pick to scale against a competitor that has accumulated advantage?

In the world of people, how do you help a minority that’s at a disadvantage? There are finite limits to how much they can work too, so the only lever you have there for sustained change is to break the status variable. How do we do that? By breaking systemic discrimination, dismantling it at every point possible. If we want BIPOC people to achieve equality, we have to break system racism. If we want women to achieve equality, we can only do so by breaking systemic sexism. If we want LGBTQ+ people to achieve equality, we have to break systemic bigotry. Giving someone a temporary boost with resources or luck will not fix the problem because the system multiplies status against that boost.

What’s an example of breaking a systemic discrimination problem? For this, we look to the example shared by Malcolm Gladwell in Outliers, when the Berlin orchestra, seeking to hire a new first violinist, was forced to put up a screen for auditions because one of the candidates was a relative of the conductor and they wanted to rule out nepotism. Prior to that point, the orchestra had hired only men, on the biased belief that men were better musicians. After the auditions, the orchestra staff took down the screen to reveal they had hired a woman instead. That audition screen blocked the ability of the orchestra staff to discriminate – it broke the system itself.

We have that opportunity today. With so many systems like hiring, performance reviews, etc. being made digital, we can add safeguards to our systems that inhibit biases. For example, in choosing which candidates to interview, HR software should not display personally identifying information to avoid biases like “that person’s name sounds Black” or “that’s a woman’s name”. Allowing screening of resumes only on experience and credentials without the ability to bring biases into the process will change the hiring pool dramatically.

Conclusion

Mark’s book is a good introduction to the topic of cumulative advantage, and it’s filled with fun anecdotes and relatively little math. It’s an important work in that it introduces many more people to the concept of cumulative advantage, and what its implications are, and for that, you should read it. It’s available wherever books are sold, like on Amazon.

Once you’ve read it and you’ve decided you want to dig in further, start hitting up Google Scholar and other academic resources to read the latest research sociologists have put into the topic, and then start planning how to build your own cumulative advantage and negate the advantage of competitors. Mark’s book intentionally shies away from the more complex mathematics, but to really operationalize cumulative advantage, you’ll want to delve deeper into the specifics of how it works and perhaps even build your own model from the research.

And as you learn more about cumulative advantage, give thought to how you can help end things like systemic discrimination, forces that make our overall society worse, rather than better. How could you use your talents, your resources – your own cumulative advantage – to level the playing field more and build a more equitable society for everyone?

FTC Disclosure: Mark sent a copy of the book for free for review purposes, along with a pound of bacon. The Amazon link is an affiliate link for which my company, Trust Insights, earns a small commission if you make a purchase.

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