Price's law is not intensive

Price's law was proposed in the context of scientific publishing: 

The square root of the total number of authors contribute half of the total number of publications.

It is a more extreme version of Pareto's 20/80 rule, which would state that 20% of authors contribute 80% of the total number of publications (see next post for the relation between the two). Unlike Pareto's rule, however, Price's law is not stable under extension. This is a trivial observation, but I have not yet seen it in the literature, just like I have not seen much empirical evidence for Price's law.

Let us denote by \(N\) the total number of authors and by \(N_p\) the number of "productive" authors (the top authors that provide half of all publications). As the ratio of two extensive quantities, \(p\) should be independent of the system size \(N\): consider ten systems (e.g. the research communities in different countries, different subjects, etc.), each of size \(N\), with the same publication distribution and hence the same \(N_p\). Half of the total number of publications is published by \(10 \, N_p\) contributors, so the overall productivity is \(p' = \dfrac{10 N_p}{10 N} = p\). According to Price's law, it should however be \(p' = p/\sqrt{10}\) ! The situation is similar to having ten identical vessels, all under the same pressure \(p\). If we connect them all together the pressure does not change, although both the volume and energy increase by a factor of ten.

Price's law does have a "convenient" feature: simply by selecting the representative size \(N\) one can obtain any productivity, since \(p = 1/\sqrt{N}\). For instance, the same Pareto distribution that yields the 20/80 rule predicts that 0.7% of causes yield half of the effects. This result is reproduced by Price's law with \(N \simeq 23000\).

Outside of bibliometry, Price's law has been invoked in economics, for instance by Jordan Peterson in (at least) one of his videos. What I find amusing is that it seems to contradict the principle of economies of scale: if there is a connection between the productivity \(p\) and the economic efficiency (and this is the more likely the higher the personnel costs are) then an increase in the size of a company decreases its efficiency. For instance, a chain of ten supermarkets would be less effective than ten independent units, which would be less effective than many small shops. Since the market is supposed to select for efficiency, we should witness fragmentation, rather than consolidation. 

References:

https://subversion.american.edu/aisaac/notes/pareto-distribution.pdf Clear derivation of the 20/80 principle from the general Pareto distribution.

The open data controversy

As of March 3rd, open access publisher Public Library of Science (PLoS) requires authors publishing in one of its journals  to make publicly available all data relevant to the conclusions drawn in their papers.

After the wave of protests (just check #PLoSFail) that PLoS delicately called "an extraordinary outpouring of discussions" or "[a] flurry of interest", the publisher changed its position, see updated original blog post and the more recent explanation. The requirement was downsized from 

"...any and all of the digital materials that are collected and analyzed in the pursuit of scientific advances" 

to

"...if you are providing graphs, it would indeed be helpful to provide the spreadsheet from which you generated the graph. If you think some other form of the data would be useful to other researchers who might want to understand, replicate or build on your work, please do include it. Conversely, if it is usual in publications in this field to provide only the summary information, then that remains sufficient now."

In short, they attempted a revolution before quickly returning to the status quo. Still, it's a good thing they insist on making available the raw data for graphs: squinting at ten superposed curves in log-log scale is hard on the eyes...

As to their more ambitious goal of opening all the relevant data, it is much too early for that, mainly because scientists see their (painfully acquired) data as valuable property, to be converted into publications. Giving it up for free to colleagues (and competitors) is not an economically viable model. A very lucid presentation of this point of view was given by Terry McGlynn, in a (long) blog post.

I am sure a default policy of open access to all scientific data (with reasonable exceptions) would be a Very Good Thing, but we need to work out a way of formally crediting the initial authors. The only solution I see is co-authorship, but that would pose some serious problems:

• Merely collecting the data is not sufficient for authorship. PLOS ONE, for instance, requires active involvement in all stages of the work.
• The original authors might disagree with the conclusions of the second team, or even compete with them by writing their own, separate analysis.
• The number of authors on scientific papers is already quite large; do we need to increase it? This point might be solved, or at least mitigated, by a detailed description of each author's role.

I'm looking further to the development of this story, in particular to the response of the more established journals.

No more access to the APS journals in France

Many (most ?) universities and research institutes in France get access to scientific journals through the Couperin consortium. This year, the consortium failed to reach an agreement¹ with the American Physical Society (publisher of the Physical Review) who increased their 2014 prices by 7.6% with respect to 2013². As a result, our subscription to the Physical Review will stop as of January 1st 2014.

UPDATE 09/01/2014: For the moment, we do have access to the 2014 papers. Couperin will pursue the negotiations until the end of February.

---

<sup>1. Letter from the APS to the Couperin consortium. ↩
2. Letter from the APS to French researchers. The 7.6% is the overall price increase requested from the consortium. For the Paris-Sud University, for instance, the increase would be 28%. ↩</sup>

Which licence for your publication?

Over at Nature, Richard Van Noorden discusses the various choices authors make when publishing in open-access journals, in particular the wide-spread adoption of the 'noncommercial' (NC) and 'no derivative works' (ND) clauses. I can see two interesting points:

1. The possibility of data-mining (requiring bulk downloads)
2. The meaning of "re-use".

As to the first point, I do not know whether the authors are given the choice between 'only individual downloading' and 'bulk downloading' (and I think the distinction would be difficult to implement technically). This looks more like global journal policy.

Re-use seems to cover a lot of very different situations, from "build[ing] on work if [credit is given] to the original author" to "remix[ing]", "tweak[ing]", and reselling for a profit.

• The first type of use is unobjectionable, since that is exactly what publishing is for.
• Forbidding others from making a profit on one's own work (NC) is a reasonable point of view, but it might be at odds with the commonly involved argument that "all this work has been paid for with public funding, so it should be made available with as little constraints as possible".
• Modifying the work is a much more serious problem. In the particular case of scientific publications I cannot see how the 'attribution' clause (BY) can work without the ND one. In a changed version of a paper, what is still by the original author? Can I take an article from a prestigious journal, keep all the data and "slightly" modify the presentation to draw exactly the opposite conclusions (all this while benefiting from the reputation of the original authors and of the journal)?

Episciences Project: open journals

Tim Gowers announces the Episciences project, a series of arXiv overlay journals. The platform will be supported by the CCSD, a French documentation center. More details from Jean-Pierre Demailly in Nature. Terence Tao is also on board.

The scientists above are all mathematicians and it is not clear whether (or when) this initiative will also be extended to other disciplines. [UPDATE (23/01/13): According to the CCSD blog (in French), the platform is open to new or already existing journals in all scientific areas. The launch is scheduled for the first semester of 2013.]