  We investigate systems of indirect voting based on the law of Penrose, in
which each representative in the voting body receives the number of votes
(voting weight) proportional to the square root of the population he or she
represents. For a generic population distribution the quota required for the
qualified majority can be set in such a way that the voting power of any state
is proportional to its weight. For a specific distribution of population the
optimal quota has to be computed numerically. We analyse a toy voting model for
which the optimal quota can be estimated analytically as a function of the
number of members of the voting body. This result, combined with the normal
approximation technique, allows us to design a simple, efficient, and flexible
voting system which can be easily adopted for varying weights and number of
players.

Physics and Society