Jagiellonian Compromise

The Jagiellonian Compromise is a voting system for two tier voting bodies originally proposed in 2004 [1] for the Council of the European Union as a way of achieving "one person, one vote" within the Union.

Reaction and explanation

The Compromise was analyzed by various authors[2][3][4] and received attention in the popular press.[5] The system is based on the square root law of Penrose, which implies that a priori voting power defined by the Penrose–Banzhaf index of a member of a voting body is inversely proportional to the square root of its size. Hence the number of votes obtained by a representative of a state j with population N_j is proportional to \sqrt{N_j} . Jagiellonian Compromise is based on a single criterion only. Decision of the Council of the Union of M Member States is taken if the sum of the weights of States voting in favour of a given proposal exceeds the qualified majority quota q equal to

q = \frac12 \cdot\left(1 + \frac{\sqrt{\sum_{i=1}^M N_i}}{\sum_{i=1}^M \sqrt{N_i}}\right)

For a generic distribution of population among M States of the Union the optimal threshold q_* decreases with M as q_* \approx 1/2 +1/\sqrt{\pi M} .[6]

See also

References

  1. ↑ Słomczyński, Wojciech; Życzkowski, Karol (2004). "Voting in the European Union: The square root system of Penrose and a critical point" (pdf). Preprint arXiv:cond-mat/0405396: 5396. arXiv:cond-mat/0405396. Bibcode:2004cond.mat..5396Z.
  2. ↑ Kirsch, Werner (2013). "The Distribution of Power in the Council of Ministers of the European Union (Chapter 6)". In Marek A. Cichocki, Karol Życzkowski. Institutional Design and Voting Power in the European Union. Ashgate Publishing, Ltd. ISBN 9781409499954. Retrieved 11 March 2013.
  3. ↑ Pukelsheim, Friedrich. Putting citizens first: Representation and power in the European Union in Institutional Design and Voting Power in the European Union ed. M. Cichocki, Ashgate, Farnham 2010, pp. 235-254
  4. ↑ E. Ratzer. On the “Jagiellonian compromise” – voting in the European Union, http://www.inference.phy.cam.ac.uk/ear23/voting/voting.pdf
  5. ↑ Highfield, Roger (14 July 2004). "The EU constitution is 'unfair', according to game theorists". The Telegraph (UK). Retrieved 11 March 2013.
  6. ↑ Życzkowski, Karol; Słomczyński, Wojciech (26 March 2012). "Square root voting system, optimal threshold and \pi ". Voting Power in Practice Symposium (London School of Economics) 20–22 March 2011 (archived at Cornell University Library) (pdf). arXiv:1104.5213v2.