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Heuristic and exact solutions to the inverse power index problem for small voting bodies

Title data

Kurz, Sascha ; Napel, Stefan:
Heuristic and exact solutions to the inverse power index problem for small voting bodies.
In: Annals of Operations Research. Vol. 215 (2014) Issue 1 . - pp. 137-163.
ISSN 0254-5330
DOI: https://doi.org/10.1007/s10479-012-1293-0

Abstract in another language

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. This paper considers approximations and exact solutions to this inverse problem for the Penrose-Banzhaf index, 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.

Abstract in another language

electoral systems; simple games; weighted voting games; square root rule; Penrose limit theorem; Penrose-Banzhaf index; institutional design

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Faculties > Faculty of Law, Business and Economics
Faculties > Faculty of Law, Business and Economics > Department of Economics
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics IV
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics IV > Chair Economics IV - Univ.-Prof. Dr. Stefan Napel
Profile Fields
Profile Fields > Emerging Fields
Profile Fields > Emerging Fields > Governance and Responsibility
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
300 Social sciences > 320 Political science
500 Science > 510 Mathematics
Date Deposited: 04 Nov 2014 08:38
Last Modified: 03 Nov 2016 07:47
URI: https://eref.uni-bayreuth.de/id/eprint/3263