Voters' power in voting games with abstention: Influence relation and ordinal equivalence of power theories
The influence relation was introduced by Isbell [Isbell, J.R., 1958. A class of simple games. Duke Math. J. 25, 423-439] to qualitatively compare the a priori influence of voters in a simple game, which by construction allows only "yes" and "no" votes. We extend this relation to voting games with abstention (VGAs), in which abstention is permitted as an intermediate option between a "yes" and a "no" vote. Unlike in simple games, this relation is not a preorder in VGAs in general. It is not complete either, but we characterize VGAs for which it is complete, and show that it is a preorder whenever it is complete. We also compare the influence relation with recent generalizations to VGAs of the Shapley-Shubik and Banzhaf-Coleman power indices [Felsenthal, D.S., Machover, M., 1997. Ternary voting games. Int. J. Game Theory 26, 335-351; Freixas, J., 2005a. The Shapley-Shubik power index for games with several levels of approval in the input and output. Dec. Support Systems 39, 185-195; Freixas, J., 2005b. The Banzhaf index for games with several levels of approval in the input and output. Ann. Operations Res. 137, 45-66]. For weakly equitable VGAs, the influence relation is a subset of the preorderings defined by these two power theories. We characterize VGAs for which the three relations are equivalent.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- R J Johnston, 1978.
"On the measurement of power: some reactions to Laver,"
Environment and Planning A,
Pion Ltd, London, vol. 10(8), pages 907-914, August.
- R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
- Dominique Lepelley & N. Andjiga & F. Chantreuil, 2003. "La mesure du pouvoir de vote," Post-Print halshs-00069255, HAL.
- Edward M. Bolger, 2002. "Characterizations of two power indices for voting games with r alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 709-721.
- Josep Freixas & William S. Zwicker, 2003. "Weighted voting, abstention, and multiple levels of approval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 399-431, December.
- Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
- 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.
- Lawrence Diffo Lambo & Joël Moulen, 2002. "Ordinal equivalence of power notions in voting games," Theory and Decision, Springer, vol. 53(4), pages 313-325, December. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:64:y:2008:i:1:p:335-350. 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: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.