2026-09-20T03:24:42Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/180192022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Stephen Ansolabehere.
Strauss, Aaron B., 1980-
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2005-06-02T19:38:47Z
2005-06-02T19:38:47Z
2003
2003
http://hdl.handle.net/1721.1/18019
57224479
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.
Includes bibliographical references (p. 73-76).
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.
by Aaron B. Strauss.
M.Eng.
76 p.
3809395 bytes
3817408 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Applying integer programming techniques to find minimum integer weights of voting games
Thesis
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<Abstract>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.</Abstract>
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