Rousseau's law

Ronald Rousseau ronald.rousseau at KH.KHBO.BE
Sat Feb 23 02:35:27 EST 2002

Dear Jonathan,

In his Contrat Social J.J. Rousseau gives, as an example, the number of people
that should form 'a government'. He does that by taking the square root (racine
carrée in French)of the number of people that form the state (l'état). So,
indeed, according to this example, in a population of size n the number of high-
visibility members stands as the square root of n.


Book III, chapter 1.


> Dear SIGMETRICS list members:
> I wonder if one of you might be able to help me out with a small
> bibliographical question, about "Rousseau's law."
> In his article "American Philosophy Today" (Review of Metaphysics 46,
> no. 4, June 1993), Rescher mentions in a footnote "the principle
> known in the social sciences as Rousseau's Law, which maintains that
> in a population of size n the number of high-visibility members
> stands as [the square root of n]." Rescher cites another work of his
> own, Scientific Progress (1978), which is also cited by Diodato in
> his Dictionary of Bibliometrics (1994): "[The formula stating that]
> the volume of really 'important' production stands as the square root
> of the total production ... is in fact a rather well known formula in
> the study of elites ... Such a relationship was initially mooted by
> Jean Jacques Rousseau ..." Diodato also cites Zipf's Human Behavior
> and the Principle of Least Effort (1949): "This statement that is so
> frequently imputed to J. J. Rousseau seems to evade specific
> reference although its sense is apparent in his Contrat Social."
> Of course, the relationship between the size of a population and its
> square root is remarked upon by Price in Little Science, Big Science
> (1963). Price does not mention Rousseau; yet, in an article in IP&M,
> Nicholls (1988) notes that Price's law has its roots in Rousseau's
> law, which had "long been known in the social sciences."
> My (two-part) question is: Who was responsible for the first
> imputation of Rousseau's law to Rousseau? What evidence is there for
> believing that Rousseau was indeed responsible for expressing
> Rousseau's law?
> Thanks,
> Jonathan

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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