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Square Root Voting System, Optimal Threshold and \( \uppi \)

  • Karol ŻyczkowskiEmail author
  • Wojciech Słomczyński
Chapter

Abstract

The problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favor of the square root voting system, in which voting weights of member states are proportional to the square root of their population. It is known that the voting power of every member state is approximately equal to its voting weight, if the threshold \(q\) for the qualified majority in the voting body is optimally chosen. We analyze the square root voting system for a generic ‘union’ of \(M\) states and derive in this case an explicit approximate formula for the level of the optimal threshold: \(q\simeq 1/2+1/\sqrt{\pi M}\).

Keywords

European Union Member State Vote System Small State Large State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of PhysicsJagiellonian UniversityKrakówPoland
  2. 2.Center for Theoretical PhysicsPolish Academy of SciencesWarszawaPoland
  3. 3.Institute of MathematicsJagiellonian UniversityKrakówPoland

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