Penrose method

The square root law of Penrose is a method of distribution of seats or votes, which can be applied for example to bodies, to which different countries are involved, each uniformly ( as a block ) agree in polls a proposal or reject it.

Thus, every citizen according to the Banzhaf power index has the same voting strength ( power ), regardless of the country from which he comes, must the power indices of the countries within the body proportional to the square root of the population size be ( 1 square-root law ). The theory was developed in 1946 by the British mathematician Lionel Penrose.

In order to obtain such a distribution of power within the committee, the voting weights can be chosen to be proportional to the square root of the size of the population in this method ( 2 square root law ). However, the distribution is transmitted only on the power indices, if a suitable agreement quorum applies to the polls. An approximate formula for the quorum is

Where Ni denotes the population sizes. For the EU, with 27 Member States, it is given by mathematicians with 61.4 percent. A lower quorum leads to larger, higher quorum to smaller power indices of the larger states.

The NGO International Network for a United Nations Second Assembly ( infusa ) assesses the square root method as

The method was proposed for the allocation of seats in a reformed EU Council of Ministers and a Parliamentary Assembly at the United Nations. In the negotiations on the Treaty of Lisbon in 2007, the Polish government vehemently demanded (but ultimately unsuccessful ), this type of power distribution for the Council of Ministers.

The American statistician and political scientist Andrew Gelman rejects a distribution from voting weights according to the square-root law. From a statistical analysis of a large number of real elections, he concludes that the square-root law underlying assumptions are not met at the voting behavior in the real world and an equitable distribution of votes would yield more like a high -0 ,9- law.