“For onto everyone that hath shall be given, and he shall have abundance; but from him that hath not shall be taken away even that which he hath.” Matthew 25:29 King James Version

There is a common effect variously referred to as “the rich get richer,” “cumulative advantage,” “preferential attachment,” “the bestseller effect,” “the Matthew Effect” and the “Yule-Simon Process.” What these various formulations of the same effect are getting at is that the more _____ you have the more _______ you will tend to get. This happens because as humans we tend to like (or want to like) what other people like.

Let’s look at some examples.

Music Popularity

A fascinating experiment concerning how music becomes popular was conducted by researchers at Columbia University about 15 years ago. Over 14,000 volunteers were asked to listen to, download and rate songs by various bands they had never before heard of. One set of participants saw only the names of the songs and the bands. Another set of participants “split into eight parallel worlds” saw the names of the songs and the bands as well as the number of downloads of the previous participants in their “own world.” What happened? In the eight-worlds with social influence, the popular songs were much more popular and the least popular songs were much less popular than the independent condition. And, what ended up being hit songs in each of the eight worlds was different. From the author of the study writing the New York Times Magazine:

In our artificial market, therefore, social influence played as large a role in determining the market share of successful songs as differences in quality.

Fascinating! This suggests that popular musicians become popular based on random variables and luck and quality and talent are may be secondary (how many times have you heard an amazing singer/band at a coffee shop or wedding and wondered why Britney Spears was popular and they weren’t?). Again from the study author:

People almost never make decisions independently — in part because the world abounds with so many choices that we have little hope of ever finding what we want on our own; in part because we are never really sure what we want anyway; and in part because what we often want is not so much to experience the “best” of everything as it is to experience the same things as other people and thereby also experience the benefits of sharing.

The Success of Cities

Why do some cities grow and others languish? It is partly explained by cumulative advantage. From Geoffrey West in his book Scale:

Successful companies and universities attract the smartest people, resulting in their becoming more successful, thereby attracting even smarter people, leading to even greater success and so on, just as wealthy people attract favorable investment opportunities that generate even more wealth which they further invest to get even more wealthy. Hence the catchphrase the rich get richer and its implied, but usually unstated, corollary the poor get poorer to characterize this process

Thus, cities with already great universities and companies and arts will continue to attract even more of the same, with cities with less of these things will languish.

Academic Citations

Sociologist Robert K. Merton looked at how often academic papers were cited by other papers and found that an initial advantage in citations built throughout an academic’s entire career. In other words, academics who get cited a lot get cited even more. As noted in a paper from Carnegie Mellon University: “Totally around 5 million scientific papers have been recorded. Minimum citation number among all these papers is 0. The mean citation number is around 5. There are a few hundred papers with citation numbers greater than 1000. The maximum citation number reaches around 20,000. All these observations demonstrate well the right-skewed and heavy-tailed behaviors of the real network models.”*

Here’s how this works as explained by Nassim Taleb in The Black Swan:

Let’s say someone writes an academic paper quoting fifty people who have worked on the subject and provided background materials for his study; assume, for the sake of simplicity, that all fifty are of equal merit. Another researcher working on the exact same subject will randomly cite three of those fifty in his bibliography. Merton showed that many academics cite references without having read the original work; rather, they’ll read a paper and draw their own citations from among its sources. So a third researcher reading the second article selects three of the previously referenced authors for his citations

These three authors will receive cumulatively more and more attention as their names become associated more tightly with the subject at hand. The difference between the winning three and the other members of the original cohort is mostly luck: they were initially chosen not for their greater skill, but simply for the way their names appeared in the prior bibliography. Thanks to their reputations, these successful academics will go on writing papers and their work will be easily accepted for publication. Academic success is partly (but significantly) a lottery.

Final Interesting Points

Cumulative Advantage typically operates on a power law. It scales and the effects can be modeled mathematically. Here again is Geoffrey West:

[Cumulative advantage] is based on a positive feedback mechanism in which new elements of the system are added with a probability proportional to the abundances of how many are already there. The more there are, the more of that type are going to be added, so more frequent types get even more abundant with increasingly higher probability than less frequent types.

The Matthew Effect obviously also applies to wealth/capital. It usually takes money to make money. Similarly, there is something known as the Banker’s Paradox – which states that the people most in need of money are the greatest credit risks and least likely to obtain a loan. Or, if they do it will be at a rate that is hard to afford. The wealthy – the least credit risks – will not need loans, or will get them for the cheapest amount.

Cumulative advantage applies to movies, bestselling books, restaurants, etc. The effects are likely becoming more pronounced as EVERYTHING seems to have reviews online lately. I recently selected a new refrigerator filter based on popularity!!!!