Cumulative advantage in popularity

Why can one song become a runaway hit while an equally good one is never heard?

You have surely had the experience: a song you love goes nowhere, and another one — no better, sometimes visibly worse — is suddenly everywhere. The tempting explanation is that you have poor taste, or that someone with a marketing budget put a thumb on the scale.

But suppose neither is true. Suppose the songs really are equally good, and nobody is buying anyone's attention. Could the gap still open? And if it could, what exactly is doing the work?

Let us start with the smallest honest assumption we can make about listeners. Not that they are foolish — only that they are busy, that there are more songs than anyone can sample, and that when choosing what to sample they glance at what other people have already chosen. Do you find that assumption unreasonable? I do not. It is what a play count, a chart position, or a "trending" label is for.

Now watch what that one habit does. If some fraction of the next listener's choice is driven by the current count, then a song's chance of being played next rises with how often it has already been played. Write that as a rule and it becomes stark: the growth of the count is proportional to the count itself. What kind of growth is that? Not steady addition — that would be a straight line. A quantity whose increase is proportional to its current size grows exponentially. Ten plays earn eleven, eleven earn twelve and a bit, and the gap between two songs widens by multiplication rather than by subtraction.

So ask the sharp question: what is being multiplied? Not quality — we assumed the songs were equal. What gets multiplied is whatever happened to be in the count when the copying began. And in the first hour, the count is essentially noise: who happened to log on, which friend posted first, which song sat at the top of a list. Exponential growth is indifferent to the meaning of its seed. Feed it a rounding error and it will amplify a rounding error just as faithfully as it would amplify genius.

Is this only a story, or has anyone caught it happening? It has been caught. Salganik, Dodds and Watts built an artificial music market in 2006: about fourteen thousand participants, forty-eight unknown songs, and eight parallel "worlds" that were identical except that each ran its own independent download counts, plus a control world where listeners saw no counts at all. Same songs, same start, same population. If quality alone decided, the eight worlds should have produced roughly the same ranking. They did not. Showing the counts made success both far more unequal — the winners won bigger — and far less predictable: a song that came first in one world could land near the bottom in another. In a later variant the experimenters inverted the displayed ranks, and the falsehood largely made itself true.

Notice what the control world tells us, though, because it stops the argument from becoming too cynical. Quality was not irrelevant. The very best songs rarely finished at the bottom and the very worst rarely finished at the top. What social influence did was widen the range of fates available to everything in the broad middle — which is where nearly all songs live. Quality sets a band; cumulative advantage decides where inside the band you land.

One last step. Does the mechanism need the specific number to be visible? No — it only needs any signal that correlates with past success: a chart, an algorithmic recommendation trained on plays, a friend's playlist, a radio rotation chosen from last week's sales. Each is a different pipe carrying the same feedback. That is why the effect is hard to design away; you would have to hide the past from the present entirely.

Two misreadings are worth heading off.

The first is that this makes popularity meaningless. It does not. It makes popularity a poor measurement instrument — a hit tells you reliably that many people heard the song, and only weakly that it was better than its neighbours. Merton named the general pattern the Matthew effect in 1968, after the verse about those who have being given more; the same arithmetic shows up in citation counts, follower counts and wealth.

The second is that the amplification is a distortion added on top of an otherwise fair process. It is not an add-on. Copying others is often the correct strategy for an individual: with thousands of songs and one evening, sampling what others liked is a sensible shortcut. The pathology is emergent, not personal. Each listener behaves reasonably and the aggregate still manufactures inequality out of noise.

And a caution on prediction. Because the seed is noise, the outcome is not merely hard to forecast in practice — it is unforecastable in principle from the properties of the song. That is a stronger and stranger claim than "experts are bad at picking hits," and it is the part of the finding that has held up best.

• Preferential attachment in networks, and why it produces power-law distributions of links.
• Whether recommendation systems can be tuned to sample the middle of the band deliberately.
• Information cascades, where people rationally ignore their own signal in favour of the crowd's.

Every term the collection defines is gathered in the glossary.