Voting games with abstention : A probabilistic characterization of power and a special case of Penroseâ€™s Limit Theorem
In general, analyses of voting power are performed through the notion of a simple voting game (SVG) in which every voter can choose between two options: 'yes' or 'no'. Felsenthal and Machover (1997) introduced the concept of ternary voting games (TVGs) which recognizes abstention alongside. They derive appropriate generalizations of the Shapley-Shubik and Banzhaf indices in TVGs. Braham and Steffen (2002) argued that the decision-making structure of a TVG may not be justified. They propose a sequential structure in which voters first decide between participation and abstention and then between yes or no. The purpose of this paper is twofold. First, it compares the two approaches and shows how the probabilistic interpretation of power provides a unifying characterization of analogues of the Banzhaf (Bz) measure. Second, using the probabilistic approach we shall prove a special case of Penrose's Limit Theorem (PLT). This theorem deals with an asymptotic property in weighted voting games with an increasing number of voters. It says that under certain conditions the ratio between the voting power of any two voters (according to various measures of voting power) approaches the ratio between their weights. We show that PLT holds in TVGs for analogues of Bz measures, irrespective of the particular nature of abstention.
|Date of creation:||00 Nov 2005|
|Date of revision:|
|Contact details of provider:|| Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)|
Fax: +32 10474304
Web page: http://www.uclouvain.be/core
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer, vol. 18(3), pages 431-464.
- 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.
- MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
- Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer, vol. 21(3), pages 399-431, December.
When requesting a correction, please mention this item's handle: RePEc:cor:louvco:2005078. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alain GILLIS)
If references are entirely missing, you can add them using this form.