Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


2016 | 26 | 2 | 31-52

Article title

Dimension, egalitarianism and decisiveness of European voting systems

Content

Title variants

Languages of publication

EN

Abstracts

EN
An analysis of three major aspects has been carried out that may apply to any of the successive voting systems used for the European Union Council of Ministers, from the first one established in the Treaty of Rome in 1958 to the current one established in Lisbon. We mainly consider the voting systems designed for the enlarged European Union adopted in the Athens summit, held in April 2003 but this analysis can be applied to any other system. First, it is shown that the dimension of these voting systems does not, in general, reduce. Next, the egalitarian effects of superposing two or three weighted majority games (often by introducing additional consensus) are considered. Finally, the decisiveness of these voting systems is evaluated and compared.

Year

Volume

26

Issue

2

Pages

31-52

Physical description

Contributors

  • Departament de Matemàtiques, Universitat Politècnica de Catalunya, Spain
author
  • Departament de Matemàtiques, Universitat Politècnica de Catalunya, Spain
  • Departament de Matemàtiques, Universitat Politècnica de Catalunya, Spain

References

  • BERTINI C., FREIXAS J., GAMBARELLI G., STACH I., Comparing power indices, Journal of Game Theory Review, 2013, 15 (2), 1340004.
  • BERTINI C., FREIXAS J., GAMBARELLI G., STACH I., Some open problems in simple games, Journal of Game Theory Review 2013, 15 (2), 1340005.
  • CARRERAS F., Elementary theory of simple games, Working Paper MA2-IT-01-00001 of the Polytechnic University of Catalonia, 2001.
  • CARRERAS F., A decisiveness index for simple games, European Journal of Operational Research 2005, 163, 370.
  • CARRERAS F., FREIXAS J., Complete simple games, Mathematical Social Sciences, 1996, 32, 139.
  • CARRERAS F., FREIXAS J., A power analysis of linear games with consensus, Mathematical Social Sciences, 2004, 48, 207.
  • CHAKRAVARTY S.R., MITRA M., SARKAR P., A course on cooperative game theory, Cambridge University Press, 2015.
  • CHEUNG W.S., NG. T.W., A three-dimensional voting system in Hong Kong, European Journal of Operational Research, 2014, 236, 292.
  • COLEMAN J., Control of collectivities and the power of a collectivity to act, [in:] Social Choice, B. Lieberman (Ed.), Gordon and Breach, New York 1971, 269.
  • DUBEY P., On the uniqueness of the Shapley value, International Journal of Game Theory, 1975, 4, 131.
  • DUSHNIK B., MILLER E.W., Partially ordered sets, American Journal of Mathematics, 1941, 63, 600.
  • FELSENTHAL D.S., MACHOVER M., The Treaty of Nice and qualified majority voting, Social Choice and Welfare, 1941, 18, 431.
  • FREIXAS J., The dimension for the European Union Council under the Nice rules, European Journal of Operational Research, 2004, 156, 415.
  • FREIXAS J., PONS M., Hierarchies achievable in simple games, Theory and Decision, 2010, 68, 393.
  • FREIXAS J., PUENTE M.A., A note about games-composition dimension, Discrete Applied Mathematics, 2001, 113, 265.
  • FREIXAS J., GAMBARELLI G., Common internal properties among power indices, Control and Cybernetics, 1997, 26 (4), 591.
  • FREIXAS J., MARCINIAK D., A minimum dimensional class of simple games, TOP Official Journal of the Spanish Society of Statistics and Operations Research, 2009, 17, 407.
  • FREIXAS J., MARCINIAK D., PONS M., On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices, European Journal of Operational Research, 2012, 216, 367.
  • FREIXAS J., MARCINIAK D., Egalitarian property for power indices, Social Choice and Welfare, 2013, 40, 207.
  • GAMBARELLI G., Political and financial applications of the power indices, Springer, 1991.
  • GAMBARELLI G., Power indices for political and financial decision making. A review, Annals of Operations Research, 1994, 51, 163.
  • ISBELL J.R., A class of simple games, Duke Mathematics Journal, 1958, 25, 423.
  • JERESLOW R.G., On defining sets of vertices of the hypercube by linear inequalities, Discrete Mathematics, 1975, 11, 119.
  • KILGOUR D.M., A formal analysis of the amending formula of Canada’s Constitution, Act. Canadian Journal of Political Science, 1983, 16, 771.
  • KURZ S., NAPEL S., Dimension of the Lisbon voting rules in the EU Council: a challenge and new world record, Optimization Letters, 2016, 10, 1245.
  • MASCHLER M., PELEG B., A characterization, existence proof, and dimension bounds for the kernel of a game, Pacific Journal of Mathematics, 1966, 18, 289.
  • OWEN G., Multilinear extensions of games, Management Science, 1972, 18, 64.
  • OWEN G., Game Theory, Fourth Ed. in Emerald Group Publishing Limited, 2013.
  • PELEG B., Voting by count and account, [in:] Rational Interaction, R. Selten (Ed.), Springer Verlag, 1992, 45.
  • SHAPLEY L.S., A value for n-person games, [in:] Contributions to the Theory of Games II, A.W. Tucker, H.W. Kuhn (Eds.), Princeton University Press, 1953, 307.
  • SHAPLEY L.S., Simple games. An outline of the descriptive theory, Behavioral Science, 1962, 7, 59.
  • SHAPLEY L.S., SHUBIK M., A method for evaluating the distribution of power in a committee system, American Political Science Review, 1954, 48, 787.
  • TAYLOR A.D., Mathematics and Politics, Springer Verlag, New York 1995.
  • TAYLOR A.D., ZWICKER W.S., A characterization of weighted voting, Proceedings of the American Mathematical Society, 1992, 115, 1089.
  • TAYLOR A.D., ZWICKER W.S., Weighted voting, multicameral representation, and power, Games and Economic Behavior, 1993, 5, 170.
  • TAYLOR A.D., ZWICKER W.S., Simple Games. Desirability Relations, Trading, and Pseudoweightings, Princeton University Press, 1999.
  • Treaty of Accession. Negotiations on accesion by the Czech Republic, Estonia, Cyprus, Latvia, Lithuania, Hungary, Malta, Poland, Slovenia and Slovakia to The European Union, Chapter 2. The Council, Article 12. Transitional Measures, Article 26, Brussels, April 3rd 2003.
  • Treaty of Nice. Conference of the Representatives of the Governments of the Member States, Brussels, February 28th 2001. Treaty of Nice amending the Treaty on European Union, the Treaties establishing the European Communities and certain related Acts. EU document CONFER 4820/00, 2001.
  • WEYMARK J.A., Generalized Gini inequalities indices, Mathematical Social Sciences, 1981, 1, 409.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.desklight-e1e2603c-976e-440b-bc14-eabcda8c0bef
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.