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.
[1][2][3] It states that the a priori voting power of any voter, measured by the Penrose–Banzhaf index
Assume for simplicity that the number of voters is odd, N = 2j + 1, and the body votes according to the standard majority rule.
that the vote of a given voter is decisive The same approximation is obtained for an even number N. A mathematical investigation of the influence of possible correlations between the voters for the Penrose square root law was presented by Kirsch.
[3] Penrose law is applied to construct Penrose-like systems of two-tier voting, including the Jagiellonian Compromise designed for the Council of the European Union.