Reference health
Square Root Voting System, Optimal Threshold and $$ \uppi $$ π
1 of 24 checkable references need attention · checked 2026-08-07
At the dated check, the references listed below either did not resolve in Crossref or DataCite, or carried a retraction notice. Each one is shown with the registry record that put it there.
22 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.
References needing attention
does not resolve to a known work10.2307/2317945
The 23 checked references that resolve
resolves10.1177/1465116505057814
A Utilitarian Assessment of Alternative Decision Rules in the Council of Ministers
resolves10.1007/s00355-006-0171-6
On the voting power of an alliance and the subsequent power of its members
resolves10.1016/S0261-3794(96)00055-8
The weighted voting rule in the EU's Council of Ministers, 1958–1995: Intentions and outcomes
resolves10.1016/S0165-4896(98)00011-0
Minimizing the mean majority deficit: The second square-root rule
resolves10.1088/0305-4470/24/6/016
Riemann-Liouville fractional integration and reduced distributions on hyperspheres
resolves10.1016/S0176-2680(02)00101-5
Inequality among EU citizens in the EU's Council decision procedure
resolves10.1177/1465116504040446
A Priori versus Empirical Voting Power in the EU Council of Ministers
The 22 references without a DOI — listed, not checked
no DOI — not checkedAde, F. (2006). Decision making in Europe: Were Spain and Poland right to stop the constitution in December 2003? (Preprint 2006), from
http://congress.utu.fi/epcs2006/docs/D3_ade.pdf
no DOI — not checkedAndjiga, N.-G., Chantreuil, F., & Leppeley, D. (2003). La mesure du pouvoir de vote. Mathematical Social Sciences, 163, 111–145.
no DOI — not checkedBaldwin, R. E., & Widgrén, M. (2004). Winners and losers under various dual majority rules for the EU Council of Ministers. CEPR Discussion Paper No. 4450, Centre for European Policy Studies, Brussels 2004, from
http://www.cepr.org/pubs/dps/DP4450.asp
no DOI — not checkedBanzhaf, J. F. (1965). Weighted voting does not work: A mathematical analysis. Rutgers Law Review, 19, 317–343.
no DOI — not checkedHosli, M. O. (2008). Council decision rules and European Union constitutional design. AUCO Czech Economic Review, 2, 76–96.
no DOI — not checkedKirsch, W., Słomczyński, W., & Życzkowski, K. (2007). Getting the votes right. European Voice, 3–9, 12.
no DOI — not checkedKirsch, W. (2007). On Penrose’s square-root law and beyond. Homo Oeconomicus, 24, 357–380.
no DOI — not checkedKirsch, W. (2010). The distribution of power in the Council of Ministers of the European Union. In M. Cichocki & K. Życzkowski (Eds.), Institutional design and voting power in the European Union (pp. 93–107). Farnham: Ashgate Publishing Group.
no DOI — not checkedKurth, M. (2007). Square root voting in the Council of the European Union: Rounding effects and the jagiellonian compromise, (Preprint math.GM 0712.2699).
no DOI — not checkedLeech, D., & Machover, M. (2003). Qualified majority voting: The effect of the quota. In M. Holler, et al. (Eds.), European Governance, Jahrbuch für Neue Politische Ökonomie (pp. 127–143). Mohr Siebeck: Tübingen.
no DOI — not checkedLeech, D., & Aziz, H. (2010). The double majority voting rule of the EU reform treaty as a democratic ideal for an enlarging union: An appraisal using voting power analysis. In M. Cichocki & K. Życzkowski (Eds.), Institutional design and voting power in the European Union (pp. 59–73). Farnham: Ashgate Publishing Group.
no DOI — not checkedMachover, M. (2010). Penrose’s square root rule and the EU Council of the Ministers: Significance of the quota. In M. Cichocki & K. Życzkowski (Eds.), Institutional design and voting power in the European Union (pp. 35–42). Farnham: Ashgate Publishing Group.
no DOI — not checkedMoberg, A. (2010). Is the double majority really double? The voting rules in the Lisbon Treaty. In M. Cichocki & K. Życzkowski (Eds.), Institutional design and voting power in the European Union (pp. 19–34). Farnham: Ashgate Publishing Group.
no DOI — not checkedMorriss, P. (1987) Power: A philosophical analysis (2nd ed. 2002). Manchester UP: Manchester.
no DOI — not checkedPenrose, L. S. (1952). On the objective study of crowd behaviour. London: H.K. Lewis & Co.
no DOI — not checkedPöppe, Ch. Die Quadratwurzel, das Irrationale und der Tod, Spektrum der Wissenschaft, August 2007, pp. 102–105.
no DOI — not checkedPukelsheim, F. (2007). Der Jagiellonische Kompromiss. Neue Züricher Zeitung, 20 Juni 2007.
no DOI — not checkedPukelsheim, F. (2010). Putting citizens first: Representation and power in the European Union in institutional design and voting power in the European Union. In M. Cichocki, & K. Życzkowski (Eds.), (pp. 235–253). Farnham: Ashgate Publishing Group
no DOI — not checkedSłomczyński, W., & Życzkowski, K. (2004) Voting in the European Union: The square root system of penrose and a critical point. preprint cond-mat.0405396.
no DOI — not checkedSłomczyński, W., & Życzkowski, K. (2006). Penrose voting system and optimal quota. Acta Physica Polonica B, 37, 3133–3143.
no DOI — not checkedSłomczyński, W., & Życzkowski, K. (2007). From a toy model to the double square root voting system. Homo Oeconomicus, 24, 381–399.
no DOI — not checkedSłomczyński, W., & Życzkowski, K. (2010). Jagiellonian compromise—an alternative voting system for the Council of the European Union. In M. Cichocki & K. Życzkowski (Eds.), Institutional design and voting power in the European Union (pp. 43–57). Farnham: Ashgate Publishing Group.
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