Penrose square root law

In the mathematical theory of games, the Penrose square root law, originally formulated by Lionel Penrose, concerns the distribution of the voting power in a voting body consisting of N members. It states that the a priori voting power of any voter, measured by the Penrose–Banzhaf index ${\displaystyle \psi }$ scales like ${\displaystyle 1/{\sqrt {N}}}$.

This result was used to design the Penrose method for allocating the voting weights of representatives in a decision-making bodies proportional to the square root of the population represented.