Voting Power and Proportional Representation of Voters
Our paper provides a justi cation for the proportional representative (PR) election system for politically diversi ed societies. We employ the Shapley value concept to measure the political power of parties in a parliament. We prove that for the PR system if parties' size add up to 1 and is uniformly distributed, the expected ratio of a party size to its political power converges to 1, and the variance decreases to 0 as the number of parties increases. The rate of convergence is high. An empirical evidence from the Netherlands elections supports our result. Using the Shapley-Owen index we obtain similar result (this time numerically only) for a voting model that takes into account ideological differences between parties and voters.
|Date of creation:||Aug 2012|
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- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
- Lindner, Ines & Owen, Guillermo, 2007. "Cases where the Penrose limit theorem does not hold," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 232-238, May.
- Nicolas Houy & William S. Zwicker, 2013. "The geometry of voting power : weighted voting and hyper-ellipsoids," Working Papers halshs-00772953, HAL.
- Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 37-49, January.
- Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
- Chang, Pao-Li & Chua, Vincent C.H. & Machover, Moshe, 2006.
"L S Penrose's limit theorem: Tests by simulation,"
Mathematical Social Sciences,
Elsevier, vol. 51(1), pages 90-106, January.
- Pao-Li Chang & Vincent CH Chua & Moshe Machover, 2004. "LS Penrose’s limit theorem: Tests by simulation," Working Papers 26-2004, Singapore Management University, School of Economics.
- Raphael Debets, 2008. "Performance Budgeting in the Netherlands," OECD Journal on Budgeting, OECD Publishing, vol. 7(4), pages 1-20.
- Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 485-506, December. Full references (including those not matched with items on IDEAS)
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