Optimization Letters

, Volume 10, Issue 6, pp 1245–1256 | Cite as

Dimension of the Lisbon voting rules in the EU Council: a challenge and new world record

  • Sascha Kurz
  • Stefan Napel
Original Paper


The Lisbon voting system of the Council of the European Union, which became effective in November 2014, cannot be represented as the intersection of six or fewer weighted games, i.e., its dimension is at least 7. This sets a new record for real-world voting bodies. A heuristic combination of different discrete optimization methods yields a representation as the intersection of 13,368 weighted games. Determination of the exact dimension is posed as a challenge to the community. The system’s Boolean dimension is proven to be 3.


Simple games Weighted games Dimension Real-world voting systems Set covering problem Computational challenges  

Mathematics Subject Classification

90C06 05B40 91B12 91A12 



The authors thank two anonymous referees for constructive suggestions. The usual caveat applies.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Physics, and Computer ScienceUniversity of BayreuthBayreuthGermany
  2. 2.Department of EconomicsUniversity of BayreuthBayreuthGermany
  3. 3.PCRCUniversity of TurkuTurkuFinland

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