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

Title data

Kurz, Sascha ; Napel, Stefan:
Heuristic and exact solutions to the inverse power index problem for small voting bodies.
In: Annals of Operations Research. Vol. 215 (2014) . - pp. 137-163.
ISSN 1572-9338
DOI: https://doi.org/10.1007/s10479-012-1293-0

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Abstract in another language

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.

Abstract in another language

electoral systems; simple games; weighted voting games; square root rule; Penrose limit theorem; Penrose-Banzhaf index; institutional design