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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Jena Economic Research Papers ; No. 2012,045

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis ; Cooperative Games ; Institutions: Design, Formation, Operations, and Impact
• Subject: electoral systems ; simple games ; weighted voting games ; square root rule ; Penrose limit theorem ; Penrose-Banzhaf index ; institutional design ; Wahlsystem ; Gruppenentscheidung ; Kooperatives Spiel ; Machtindex ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Kurz, Sascha ; Napel, Stefan
• Event: Veröffentlichung
• (who): Friedrich Schiller University Jena and Max Planck Institute of Economics
• (where): Jena
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/70142
• Last update: 10.03.2025, 11:44 AM CET