Heuristic and exact solutions to the inverse power index
problem for small voting bodies
Volume 6
Jena Economic Research Papers
2012-07-23
2012
2007
2012-045
electoral systems
simple games
weighted voting games
square root rule
Penrose limit theorem
Penrose-Banzhaf index
institutional design
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.
jportal_jpjournal_00000016
2012-07-23T06:32:33.923Z
2012-07-23T06:32:20.872Z