Price and Rousseau

Ronald Rousseau ronald.rousseau at KH.KHBO.BE
Sat Feb 23 03:04:30 EST 2002

Dear SIGMETRICS members,

May I quote from "Introduction to Informetrics":


Price (1971,1976) states that, if there are N sources in a 'bibliography' then
the square root of N of the top sources will have 50% of the items. This
phenomenon is related to the occurrence of invisible colleges, i.e. the
hierarchical elites in fields. As it is with the 80/20 rule 'Price's law' too
is 'too simple', as was already shown by Allison et al. (1976) and Nicholls

Then follows the formulation and main results of the articles Leo Egghe and I
wrote about this.

On p.377 we further wrote:

Price's square root law is sometimes called 'Rousseau's law (J.J. not R.!) as
J.J. Rousseau mentions this explicitly in his 'Contrat Social' concerning the
size of the 'elite' ('elite' refers here to participating in the government).
More information about this early sociometric statement can be found in Zipf
(1949) and Rescher (1978).


Price, D.J. de Solla (1971). Some remarks on elitism in information and the
invisible college phenomenon in science. JASIS, 22, 74-75.
Price, D.J. de Solla (1976). A general theory of bibliometric and other
cumulative advantage processes. JASIS, 27, 292-306.
Allison, P.D., Price, D.J. de Solla, Griffith, B.C., Moravcsik, M.J. and
Stewart, J.A. (1976). Lotka's law: a problem in its interpretation and
application. Social studies of Science, 6, 269-276.
Nicholls, P.T. (1988). Price's square root law: empirical validity and relation
to Lotka's law. IP&M, 24, 469-477.
Egghe, L. (1986). On the 80/20 rule. Scientometrics, 10, 55-68.
Egghe, L. (1987). An exact formulation of Price's law for the law of Lotka.
Scientometrics, 11, 81-97.
Egghe, L. and Rousseau, R. (1986). A characterization of distributions which
satisfy Price's law and consequences for the laws of Zipf and Mandelbrot.
Journal of Information Science, 12, 193-197.
Zipf, G.K. (1949). Human behavior and the principle of least effort. Addison-
Wesley, Cambridge.
Rescher, N. (1978). Scientific progress. A philosophical essay on the economics
of research in natural science (Blackwell, Oxford).

See also:
Glänzel, W. and Schubert, A. (1985). Price distribution. An exact formulation
of Price's 'square root law'. Scientometrics, 7, 211-219.

Ronald Rousseau
dr. mathematics, dr. information science
KHBO - Industrial Sciences and Technology
Zeedijk 101    B-8400  Oostende   Belgium
Honorary Professor Henan Normal University (Xinxiang, China)
E-mail: ronald.rousseau at
web page:

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