Over Time, Citations Get More Uneven

In an earlier post, I compared the distribution of citations within Journal of Philosophy, 1976 and Philosophical Studies, 2009. And I noted that although the two ended up in similar places, they got there in different ways. Journal of Philosophy was largely relying on some hugely cited papers; while the distribution of citations in Philosophical Studies was more even. And I suggested that this was part of a trend in the discipline towards more egalitarian citation practices.

In Facebook comments on this post, Ben Blumson and Peter Michael Gerdes suggested an alternative explanation. Perhaps the citations are more unbalanced in Journal of Philosophy, 1976 because the longer a journal is out, the more a consensus builds up around what the great papers are in it, and the more those papers (and those papers only) get cited. In effect, I was seeing an age effect, and viewing it as a cohort effect.

So I looked at the data, and it looks like they were very largely correct. All the points below come from investigating the citations to papers in Journal of Philosophy, 1976.

I broke the citations up into those appearing before and after 1995. In fact more of the citations come after 1995, which was surprising. (That might be due to Web of Science’s coverage getting more comprehensive in recent years.) We can then calculate a Gini coefficient for the citations before and after 1995. (We usually do Gini coefficients for things like income or wealth, but the same idea can be used for citations; think of each cite to an article as a bit of wealth that article gets.)

The numbers ended up being:

  • For citations before 1995, Gini is 0.83.
  • For citations after 1995, Gini is 0.92.

Now both of these numbers are really high, but that’s largely because I included the book reviews, which basically get 0 citations, in the mix. But the second number is much higher. Note that Gini goes on a 0-1 scale, so going from 0.83 to 0.92 is going half way to a situation where only one article gets all the citations; it’s a big jump.

Here’s another way to look at the data. I broke down the articles into those that had (across all 40 years) the 10 highest citation counts, and the rest of the articles. (There are about 130 of them, though many are discussion notes or book reviews.)

  • Among the 10 highest cited articles, 72% of citations came after 1995.
  • Among the rest of the articles, 47% of the citations came after 1995.

So there’s a pattern here. And while it’s only one year, it isn’t surprising.

So I made a mistake here, though I think it’s an interesting mistake. I noticed that within any given year, the citations were getting more evenly spread the closer we got to the present. (That is, the Gini coefficient was going down over time.) I thought that was a cohort effect; it was something about how people interact with post-2000 journals as opposed to how they interact with pre-2000 journals. But it is more plausible that it is an age effect; it is something about how people interact with 20+ year-old journals as opposed to how they interact with younger journals.

It’s easy to confuse cohort effects and age effects. Lots of people look at voting data and conclude that people get more conservative as they get older. This isn’t, on the whole, true. It’s just that, in recent years in the English speaking world, each generation has been less conservative than the one that came before it. This hasn’t always been true; the boomers are much much more conservative than people who could remember the Great Depression. And historically the graph of voting pattern vs age had an inflection point around the time it got to people born in 1930. (That’s too small a group now to show up in the graphs.) And it isn’t true in modern day France, for example. (In the recent election, old folks did largely vote for Fillon, but Le Pen’s support was relatively constant across age groups.)

I’ve made the opposite confusion here; seeing something that really is an age effect as a cohort effect. Thanks to Ben and Peter for pointing this out.

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