Penrose method

The Penrose method is a method, devised in 1946 by Professor Lionel Penrose, for allocating seats or votes in legislatures based on the square root of the population of the representative's district or state.

This choice is motivated by the Penrose square root law,which states that in any voting body the voting power of each member measured by the Penrose-Banzhaf index is inversly proportional to square root of the number of voters. This implies that if in a two-tier voting system the voting power of each representative scales like square root of the population he represents, the voting power of a single citizen in each member state is equal.

The voting system of Penrose has been proposed as a method for apportioning representation in a United Nations Parliamentary Assembly, and for voting in the Council of the European Union.

Recently, the Penrose method became revitalised, as it was proposed by Sweden in 2003 (negotiations on the Amsterdam Treaty) and Poland in 2007 (the June 2007 summit on the Treaty of Lisbon) as method of computing voting power of each state in the European Union. With modern computers, it is simple to calculate the threshold percentage which constitutes an optimal level of qualified "majority", at which the voting powers of all citizens in any member state are equal.The level of the optimal threshold,(about 61.6% for EU-27) decreases with the number of the member states.This system is reffered to as the "Jagiellonian Compromise" http://th-www.if.uj.edu.pl/acta/vol37/pdf/v37p3133.pdf] [Physics World 2006; 19(3):35-37.] .

Many bodies already follow a similar method even though they do not refer to it as such; for example, in the Bundesrat of Germany, vote allocation can be approximated as 2.01+Square_root (1.24 * land's population in millions). However, this agreement with the Penrose method is accidental; therefore 4 (5 without constraints) out of 16 Bundesländer have one vote less than they ought to have according to the Penrose method. Still, it is an example where political processes converge to game theoretical results.

The UN proposal

According to INFUSA, "The square-root method is more than a pragmatic compromise between the extreme methods of world representation unrelated to population size and allocation of national quotas in direct proportion to population size; Penrose showed that in terms of statistical theory the square-root method gives to each voter in the world an equal influence on decision-making in a world assembly". Fact|date=June 2007

Under the Penrose method, the 14 most populous nations get fewer seats than they would under one man, one vote; the other nations get more seats.

References

ee also

*List of countries by population

* Penrose, L., The elementary statistics of majority voting, J. of the Royal Statistical Society, 109 (1946) 53-57.

* [http://th-www.if.uj.edu.pl/acta/vol37/pdf/v37p3133.pdf Penrose Voting System and Optimal Quota] published by W. Slomczynski & K. Zyczkowski in Acta Physica Polonica BVol. 37, No. 11, November 2006, page 3133

* [http://www.ceps.be/Article.php?article_id=360 article] by W. Kirsch at Center for European Policy Studies

* many more references at the web page of American Mathematical Society [http://www.ams.org/featurecolumn/archive/weighted6.html here] .