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

Sascha Kurz () and Stefan Napel

Annals of Operations Research, 2014, vol. 215, issue 1, 137-163

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 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. Copyright Springer Science+Business Media New York 2014

Keywords: Electoral systems; Simple games; Weighted voting games; Square root rule; Penrose limit theorem; Penrose-Banzhaf index; Institutional design (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (15)

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Working Paper: Heuristic and exact solutions to the inverse power index problem for small voting bodies (2012)
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DOI: 10.1007/s10479-012-1293-0

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