On Ehrhart Polynomials and Probability Calculations in Voting Theory
In voting theory, analyzing how frequent is an event (e.g. a voting paradox) is, under some specific but widely used assumptions, equivalent to computing the exact number of integer solutions in a system of linear constraints. Recently, some algorithms for computing this number have been proposed in social choice literature by Huang and Chua  and by Gehrlein ([12, 14]). The purpose of this paper is threefold. Firstly, we want to do justice to Eug`ene Ehrhart, who, more than forty years ago, discovered the theoretical foundations of the above mentioned algorithms. Secondly, we present some efficient algorithms that have been recently developed by computer scientists, independently from voting theorists. Thirdly, we illustrate the use of these algorithms by providing some original results in voting theory.
|Date of creation:||2006|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 02 23 23 35 47
Fax: (33) 2 23 23 35 99
Web page: http://crem.univ-rennes1.fr/
More information through EDIRC
|Order Information:|| Postal: CREM (UMR CNRS 6211) - Faculty of Economics, 7 place Hoche, 35065 Rennes Cedex - France|
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.:
- William Gehrlein, 2004. "Consistency in Measures of Social Homogeneity: A Connection with Proximity to Single Peaked Preferences," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(2), pages 147-171, April.
- Pierre Favardin & Dominique Lepelley, 2006.
"Some Further Results on the Manipulability of Social Choice Rules,"
- Pierre Favardin & Dominique Lepelley, 2006. "Some Further Results on the Manipulability of Social Choice Rules," Social Choice and Welfare, Springer, vol. 26(3), pages 485-509, June.
- Pierre Favardin & Dominique Lepelley & Jérôme Serais, 2002. "original papers : Borda rule, Copeland method and strategic manipulation," Review of Economic Design, Springer, vol. 7(2), pages 213-228.
- William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer, vol. 19(3), pages 503-512.
When requesting a correction, please mention this item's handle: RePEc:tut:cremwp:200610. 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: (CODA-POIREY Hélène)
If references are entirely missing, you can add them using this form.