Volume 69, 2018
Political Philosophy
Constantinos N. Tsiantis
Pages 411-416
The Mathematical Law of the Athenian Participatory Democracy
The representation of a population is not a conventional subjective choice, neither does it depend upon ideal and non-ascertained statistical conditions. The mathematic law that we present solves this problem and can become a foundation for the political-social sciences: If a population of size N is constituted by m groups of citizens and each group possesses percentage wi (i=1, 2,… m) of the entire population (w1+ w2+… + wm =1), then the minimum number of citizens n (sample) that have to be selected from all the population groups (n = n1+ n2+… + nm, where ni>0) for the representation of the entire population is given by the relation:
This relationship explains the size of the Parliament in the Athenian Democracy, hence its name. It has been successfully tested in statistical sampling and may be tested in other areas as well.