Power indices expressed in terms of minimal winning coalitions
AbstractA voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley-Shubik index and the Banzhaf value, show the influence of the individual players. We used to calculate them by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the rules of the legislation. We introduce a new way to calculate these measures directly from the set of minimal winning coalitions. This new approach logically appealing as it writes measures as functions of the rules of the legislation. For certain classes of games that arise naturally in applications the logical shortcut drastically simplifies calculations. The technique generalises directly to all semivalues. Keywords. Shapley-Shubik index, Banzhaf index, semivalue, minimal winning coalition, Möbius transform.
Download InfoIf 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.
Bibliographic InfoPaper provided by Óbuda University, Keleti Faculty of Business and Management in its series Working Paper Series with number 1002.
Length: 14 pages
Date of creation: 2010
Date of revision:
Shapley-Shubik index; Banzhaf index; semivalue; minimal winning coalition; Möbius transform.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-06-04 (All new papers)
- NEP-CDM-2010-06-04 (Collective Decision-Making)
- NEP-GTH-2010-06-04 (Game Theory)
- NEP-POL-2010-06-04 (Positive Political Economics)
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statistics
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alexandra Vécsey).
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.