Cumulative advantage = preferential attachment?

April 15th, 2007

The NYT has an article by Columbia’s Duncan Watts entitled Is Justin Timberlake a Product of Cumulative Advantage? on a fascinating experiment on how markets chose popular items.

Conventional marketing wisdom holds that predicting success in cultural markets is mostly a matter of anticipating the preferences of the millions of individual people who participate in them. … The common-sense view, however, makes a big assumption: that when people make decisions about what they like, they do so independently of one another. But 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 reason is that when people tend to like what other people like, differences in popularity are subject to what is called “cumulative advantage,” or the “rich get richer” effect. This means that if one object happens to be slightly more popular than another at just the right point, it will tend to become more popular still. As a result, even tiny, random fluctuations can blow up, generating potentially enormous long-run differences among even indistinguishable competitors — a phenomenon that is similar in some ways to the famous “butterfly effect” from chaos theory.

This isn’t too surprising and is related, partly, to the well known preferentiall attachment concept from the Barabási-Albert (BA) model for scale-free networks. In a graph model, preferential attachment means that the more links a node is, the more likely it is to get new links.

Watts and his collaborators at Columbia created MusicLab as an environment for running experiments to explore the phenomenon as described in this paper in Science:

Experimental Study of Inequality and Unpredictability in an Artificial Cultural Market, Salganik, M.J. and Dodds, P.S. and Watts, D.J., Science, v311, n5762, p854, 2006.

Hit songs, books, and movies are many times more successful than average, suggesting that ‘‘the best’’ alternatives are qualitatively different from ‘‘the rest’’; yet experts routinely fail to predict which products will succeed. We investigated this paradox experimentally, by creating an artificial ‘‘music market’’ in which 14,341 participants downloaded previously unknown songs either with or without knowledge of previous participants’ choices. Increasing the strength of social influence increased both inequality and unpredictability of success. Success was also only partly determined by quality: The best songs rarely did poorly, and the worst rarely did well, but any other result was possible.”

They ran two groups, in one subjects were asked to rate and optionally download music without any knowledge of how popular others found it. The other group was split into eight distinct communities and were also asked to rate and possibly download. Subjects in each community could see how often the songs had been downloaded, a measure of their popularity. The findings were (1) that knowing a song’s popularity effected the rating and (2) the different communities edned up choosing different highly-popular songs.

In all the social-influence worlds, the most popular songs were much more popular (and the least popular songs were less popular) than in the independent condition. At the same time, however, the particular songs that became hits were different in different worlds, just as cumulative-advantage theory would predict. Introducing social influence into human decision making, in other words, didn’t just make the hits bigger; it also made them more unpredictable.

I wonder how well their results can be explained by preferential attachment.