Annals of Operations Research

, Volume 215, Issue 1, pp 137–163 | Cite as

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

Article

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.

Keywords

Electoral systems Simple games Weighted voting games Square root rule Penrose limit theorem Penrose-Banzhaf index Institutional design 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.University of BayreuthBayreuthGermany
  2. 2.Public Choice Research CentreTurkuFinland

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