Heuristic and Exact Solutions to the Inverse Power Index Problem for Small Voting Bodies

16 Pages Posted: 3 Dec 2013

See all articles by Sascha Kurz

Sascha Kurz

University of Bayreuth

Stefan Napel

University of Bayreuth

Date Written: December 2, 2013

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. This paper considers approximations and exact solutions to this inverse problem for the Penrose-Banzhaf index, 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

JEL Classification: C71, C63

Suggested Citation

Kurz, Sascha and Napel, Stefan, Heuristic and Exact Solutions to the Inverse Power Index Problem for Small Voting Bodies (December 2, 2013). Annals of Operation Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2362235

Sascha Kurz (Contact Author)

University of Bayreuth ( email )

Universit├Ątsstr. 30
Lehrstuhl f├╝r Wirtschaftsmathematik
Bayreuth, Bavaria D-95440
Germany
+49 921 55 7353 (Phone)
+49 921 55 7352 (Fax)

HOME PAGE: http://www.wm.uni-bayreuth.de/index.php?id=sascha

Stefan Napel

University of Bayreuth ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

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