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