Heuristic and exact solutions to the inverse power index problem for small voting bodies
Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system which induces a power distribution as close as possible to a desired one. The paper considers approximations to this inverse problem for the Penrose-Banzhaf index by hill-climbing algorithms and exact solutions which are obtained by enumeration and integer linear programming techniques. They are compared to the results of three simple solution heuristics. The heuristics perform well in absolute terms but can be improved upon very considerably in relative terms. The findings complement known asymptotic results for large voting bodies and may improve termination criteria for local search algorithms.
|Date of creation:||23 Jul 2012|
|Date of revision:|
|Contact details of provider:|| Postal: Carl-Zeiss-Strasse 3, 07743 JENA|
Phone: +049 3641/ 9 43000
Fax: +049 3641/ 9 43000
Web page: http://www.jenecon.de
More information through EDIRC
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.:
- Laruelle,Annick & Valenciano,Federico, 2011.
"Voting and Collective Decision-Making,"
Cambridge University Press, number 9780521182638, April.
- 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.
- 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.
- Laruelle, Annick & Widgren, Mika, 1998.
"Is the Allocation of Voting Power among EU States Fair?,"
Springer, vol. 94(3-4), pages 317-39, March.
- Annick Laruelle & Mika Widgrén, 1998. "Is the allocation of voting power among EU states fair?," Public Choice, Springer, vol. 94(3), pages 317-339, March.
- Laruelle, Annick & Widgren, Mika, 1996. "Is the allocation of voting power among EU states fair?," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996022, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.
- Leech, Dennis, 2002. "Power Indices As An Aid To Institutional Design : The Generalised Apportionment Problem," The Warwick Economics Research Paper Series (TWERPS) 648, University of Warwick, Department of Economics.
- Noga Alon & Paul Edelman, 2010. "The inverse Banzhaf problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 371-377, March.
- Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
- Deineko, Vladimir G. & Woeginger, Gerhard J., 2006. "On the dimension of simple monotonic games," European Journal of Operational Research, Elsevier, vol. 170(1), pages 315-318, April.
When requesting a correction, please mention this item's handle: RePEc:jrp:jrpwrp:2012-045. 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: (Markus Pasche)
If references are entirely missing, you can add them using this form.