Abstract
In certain bodies, like the Council of the EU, the member states have a voting weight which depends on the population of the respective state. In this article we ask the question which voting weight guarantees a ‘fair’ representation of the citizens in the union. The traditional answer, the square-root law by Penrose, is that the weight of a state (more precisely: the voting power) should be proportional to the square-root of the population of this state. The square root law is based on the assumption that the voters in every state cast their vote independently of each other. In this chapter we concentrate on cases where the independence assumption is not valid.
This chapter was originally published in Homo Oeconomicus 24 (3/4), 2007.
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Notes
- 1.
The current voting system in the Council is based on the treaty of Nice. It has additional components to the procedure described above, which are irrelevant in the present context. For a description of this voting system and further references see e.g. Kirsch (2012).
- 2.
The electoral college is not exactly a heterogeneous voting system in the sense defined below, but it is very close to it.
- 3.
We label the states using Greek characters and the voters within a state by Roman characters.
- 4.
Although this is the central idea of representative democracy this idealization may be a little naive in practice.
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Acknowledgments
It is a pleasure to thank Hans-Jürgen Sommers, Duisburg-Essen, and Wojciech Słomczyński and Karol Życzkowski, Krakow, for valuable discussions. The author would also like to thank Helmut Hölzler, Göttingen, for pointing out a notational inconsistency in a previous version of the chapter.
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Kirsch, W. (2013). On Penrose’s Square-Root Law and Beyond. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_20
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