If you’ve ever heard someone list problems in academia, citation-counting is usually near the top. Hiring and tenure committees want easy numbers to judge applicants with: number of papers, number of citations, or related statistics like the h-index. Unfortunately, these metrics can be gamed, leading to a host of bad practices that get blamed for pretty much everything that goes wrong in science. In physics, it’s not even clear that these statistics tell us anything: papers in our field have been including more citations over time, and for thousand-person experimental collaborations the number of citations and papers don’t really reflect any one person’s contribution.

It’s pretty easy to find people complaining about this. It’s much rarer to find a proposed solution.

That’s why I quite enjoyed Alessandro Strumia and Riccardo Torre’s paper last week, on Biblioranking fundamental physics.

Some of their suggestions are quite straightforward. With the number of citations per paper increasing, it makes sense to divide each paper by the number of citations it contains: it means more to get cited by a paper with ten citations than by a paper with one hundred. Similarly, you could divide credit for a paper among its authors, rather than giving each author full credit.

Some are more elaborate. They suggest using a variant of Google’s PageRank algorithm to rank papers and authors. Essentially, the algorithm imagines someone wandering from paper to paper and tries to figure out which papers are more central to the network. This is apparently an old idea, but by combining it with their normalization by number of citations they eke a bit more mileage from it. (I also found their treatment a bit clearer than the older papers they cite. There are a few more elaborate setups in the literature as well, but they seem to have a lot of free parameters so Strumia and Torre’s setup looks preferable on that front.)

One final problem they consider is that of self-citations, and citation cliques. In principle, you could boost your citation count by citing yourself. While that’s easy to correct for, you could also be one of a small number of authors who cite each other a lot. To keep the system from being gamed in this way, they propose a notion of a “CitationCoin” that counts (normalized) citations received minus (normalized) citations given. The idea is that, just as you can’t make anyone richer just by passing money between your friends without doing anything with it, so a small community can’t earn “CitationCoins” without getting the wider field interested.

There are still likely problems with these ideas. Dividing each paper by its number of authors seems like overkill: a thousand-person paper is not typically going to get a thousand times as many citations. I also don’t know whether there are ways to game this system: since the metrics are based in part on citations given, not just citations received, I worry there are situations where it would be to someone’s advantage to cite others less. I think they manage to avoid this by normalizing by number of citations given, and they emphasize that PageRank itself is estimating something we directly care about: how often people read a paper. Still, it would be good to see more rigorous work probing the system for weaknesses.

In addition to the proposed metrics, Strumia and Torre’s paper is full of interesting statistics about the arXiv and InSpire databases, both using more traditional metrics and their new ones. Whether or not the methods they propose work out, the paper is definitely worth a look.