Heuristic and exact solutions to the inverse power index problem for small voting bodies
AbstractPower 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.
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Bibliographic InfoPaper provided by Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics in its series Jena Economic Research Papers with number 2012-045.
Date of creation: 23 Jul 2012
Date of revision:
electoral systems; simple games; weighted voting games; square root rule; Penrose limit theorem; Penrose-Banzhaf index; institutional design;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D02 - Microeconomics - - General - - - Institutions: Design, Formation, and Operations
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