 Pictured person
 Published
 Mon Jul 23 2012
 Number of discussion paper

2012045
 keyword(s)

electoral systems
institutional design
PenroseBanzhaf index
Penrose limit theorem
simple games
square root rule
weighted voting games
 abstract

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 PenroseBanzhaf index by hillclimbing 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.
 article pub. typess JER
 Research article
 article languages JER
 Englisch
 JELClassification for JER
 C61  Optimization Techniques; Programming Models; Dynamic Analysis ; C71  Cooperative Games ; D02  Institutions: Design, Formation, and Operations