Applying integer programming techniques to find minimum integer weights of voting games

Using concepts from computer science and mathematics I develop three algorithms to find the minimum integer weights for voting games. Games with up to at least 17 players can be solved in a reasonable amount of time. First, coalitions are mapped to constraints, reducing the problem to constraint optimization. The optimization techniques used are Gomory's all-integer simplex algorithm and a variant of the popular integer programming method branch and bound. Theoretical results include that minimum integer weights are not unique and a confirmation of a prior result that minimum integer weights are proportional to a priori seat share. Thus, these algorithms can be useful for researchers evaluating the differences between proportional bargaining models and formateur models. The running times of the different algorithms are contrasted and analyzed for potential improvements.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Strauss, Aaron B., 1980-

Advisor dc:contributor.advisor

• Stephen Ansolabehere.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/18019

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/18019