# Voting power and proportional representation of voters

## Author

Listed:
• Artyom Jelnov

()

• Yair Tauman

()

## Abstract

We prove that for the proportional representative election system if parties’ sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power, measured by the Shapley–Shubik index, converges to $$1$$ 1 , as the number $$n$$ n of parties increases indefinitely. The rate of convergence is high and it is of the magnitude of $$\frac{1}{n}$$ 1 n . Empirical evidence from the Netherlands elections supports our result. A comparison with the Banzhaf index is provided. Copyright Springer-Verlag Berlin Heidelberg 2014

## Suggested Citation

• Artyom Jelnov & Yair Tauman, 2014. "Voting power and proportional representation of voters," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 747-766, November.
• Handle: RePEc:spr:jogath:v:43:y:2014:i:4:p:747-766
DOI: 10.1007/s00182-013-0400-z
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File URL: http://hdl.handle.net/10.1007/s00182-013-0400-z

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## References listed on IDEAS

as
1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
2. Nicolas Houy & William S. Zwicker, 2013. "The geometry of voting power : weighted voting and hyper-­ellipsoids," Working Papers halshs-00772953, HAL.
3. 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.
4. Raphael Debets, 2008. "Performance Budgeting in the Netherlands," OECD Journal on Budgeting, OECD Publishing, vol. 7(4), pages 1-20.
5. 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.
6. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
7. 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.
8. 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.
9. 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.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Matteo Migheli, 2016. "Measuring Representativeness in Different Electoral Systems, Using Italian and Dutch Data," Group Decision and Negotiation, Springer, vol. 25(4), pages 723-748, July.

### Keywords

Shapley-Shubik index; Banzhaf index; Voting power; Voting systems; Proportional representation;

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