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March 17, 2006

a steep popularity curve

The following may be very elementary, but I'm just trying to figure it out for myself. ...

Websites often exhibit a pattern in which a few sites are far more popular than the rest. See, for example, this graph by Daniel Drezner and Henry Farrell, which plots the number of incoming links to each blog versus its popularity rank.

The graph shows enormous inequality. That is a bit counter-intuitive; we might expect that given millions of choices, people would distribute their interest evenly across the whole web. However, we want to know what's going on in the most popular nodes of a network such as the blogosphere. Therefore, we visit those nodes and comment on them, thereby making them even more popular. In other words, network traffic tends to concentrate.

Clay Shirky thinks that blogs fall in a power-law distribution, so that the line above can be plotted as y=axk. Drezner and Farrell think the line is lognormal. That's better news. A lognormal distribution is less steep, so it suggests that unknown websites sometimes gain popularity; the pattern is not perfectly self-reinforcing. In any case, the data clearly show a huge tilt toward top-ten sites.

Some factor must cause mass attention to focus on certain targets rather than others. That factor could be quality, but it could also be precedence--older sites will tend to beat newer ones. For instance, I can't believe that Instapundit is orders of magnitude better than the average blog, but it is older.

Along similar lines, I observed recently that college applicants want to attend competitive universities, so that they can be exposed to other bright students and gain the reputational advantage of a degree from an institution that is known to be hard to get into. Thus we might expect the number of applications to follow a power-law distribution, with a few universities receiving overwhelming interest. But I don't think that's the case. The reason, surely, is that admission to a college (unlike access to a website) is selective. If you want to get into your "best" option, then you must apply to institutions to which you have a reasonable chance of being admitted. If everyone applied to Yale (currently the university with the lowest acceptance rate), then most would waste their application fee. I cannot find a table with the number of applications per institution. But I suspect that the number of applicants/per places does not vary enormously between the most competitive college in America and the nearby branch of the state university, especially if one could control for quality of education. People do tend to prefer already popular institutions; but that preference is countered by their fear of being rejected. [Yale admits 10% of applicants; University of Maryland--many rungs down the ladder--admits about 20%.]

Posted by peterlevine at March 17, 2006 09:47 AM


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