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

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Power, Voting, and Voting Power: 30 Years After

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: \(q\simeq 1/2+1/\sqrt{\pi M}\).

This chapter was presented to the Voting Power in Practice Symposium at the London School of Economics, 20–22 March 2011, sponsored by the Leverhulme Trust.

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Author information

Authors and Affiliations

  1. Institute of Physics, Jagiellonian University, ul.Reymonta 4, 30-059, Kraków, Poland

    Karol Życzkowski

  2. Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668, Warszawa, Poland

    Karol Życzkowski

  3. Institute of Mathematics, Jagiellonian University, ul. Lojasiewicza 6, Kraków, 30-348, Poland

    Wojciech Słomczyński

Authors
  1. Karol Życzkowski
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  2. Wojciech Słomczyński
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Correspondence to Karol Życzkowski .

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Editors and Affiliations

  1. Institute of SocioEconomics, Department of Economics, University of Hamburg, Von-Melle-Park 5, Hamburg, 10146, Germany

    Manfred J Holler

  2. Department of Political Science and, Contemporary History, University of Turku, Assistentinkatu 7, Turku, 20014, Finland

    Hannu Nurmi

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Życzkowski, K., Słomczyński, W. (2013). Square Root Voting System, Optimal Threshold and \( \uppi \) . In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_30

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  • DOI: https://doi.org/10.1007/978-3-642-35929-3_30

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