Some suggestions:
(1) Estimate the total number of papers P published per year y, Py, rather than
the number of researchers.

(2) Start with the Thompson-Reuters-ISI-indexed (or SCOPUS-indexed) subset.

(3) For Py, sample the web (Google Scholar) to see what percentage of it is
freely available (OA).

Our latest rough estimate with this method, using a robot, is about 20%.

(Using estimates of the number of researchers, if the margin of error for the
total is 1M - 10M then the margin of error for the percentage OA would be 10% -
100%, which is too big. Using known, published papers as the estimator also
eliminates the multi-author problem.)

Cheers, Stevan

On 2011-12-31, at 6:25 PM, Arthur Sale wrote:

      I am trying to get a rough estimate of the number of active
      researchers in the world. Unfortunately all the estimates seem to be
      as rough as the famous Drake equation for calculating the number of
      technological civilizations in the universe: in other words all the
      factors are extremely fuzzy.  I seek your help. My interest is that
      this is the number of people who need to adopt OA for us to have
      100% OA. (Actually, we will approach that sooner, as the average
      publication has more than one author and we need only one to make it
      OA.
 
To share some thinking, let me take Australia. In 2011 it had 35
universities and 29,226 academic staff with a PhD. Let me assume that this
is the number of research active staff. The average per institution is
835, and this spans big universities down to small ones. Australia
produces according to the OECD 2.5% of the world’s research, so let’s
estimate the number of active researchers in the world (taking Australia
as ‘typical’ of researchers) as 29226 / 0.025 = 1,169,040 researchers in
universities. Note that I have not counted non-university research
organizations (they’ll make a small difference) nor PhD students (there is
usually a supervisor listed in the author list of any publication they
produce).
 
Let’s take another tack. I have read the number of 10,000 research
universities in the world bandied about. Let’s regard ‘research
university’ as equal to ‘PhD-granting university’. If each of them have
1,000 research active staff on average, then that implies 10000 x 1000 =
10,000,000 researchers.
 
That narrows the estimate, rough as it is, to
         1.1M  < no of researchers < 10M
I can live with this, as it is only one power of ten (order of magnitude)
between the two bounds. The upper limit is around 0.2% of the world’s
population.
 
Another tactic is to try to estimate the number of people whose name
appeared in an author list in the last decade. Disambiguation of names
rears its ugly head. This will also include many non-researchers in big
labs, some of them will be dead, and there will be new researchers who
have just not yet published, but I am looking for ball-park figures, not
pinpoint accuracy. I haven’t done this work yet.
 
Can we do better than these estimates, in the face of different national
styles?  It is even difficult to get one number for PhD granting
universities in the US, and as for India and China @$#!
 
Arthur Sale
University of Tasmania, Australia
 
 
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