2012/02/28 by Sascha Kurz, Kurz, Sascha, Stefan Napel +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #90C10 #91A12 #91B12 #Combinatorics (math.CO) #Diffusion and Search Dynamics #FOS: Mathematics #Game Theory and Voting Systems #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1202.6245
openalex publication_date 2012/02/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Power indices are mappings that quantify the influence of the members of a\nvoting body on collective decisions a priori. Their nonlinearity and\ndiscontinuity makes it difficult to compute inverse images, i.e., to determine\na voting system which induces a power distribution as close as possible to a\ndesired one. This paper considers approximations and exact solutions to this\ninverse problem for the Penrose-Banzhaf index, which are obtained by\nenumeration and integer linear programming techniques. They are compared to the\nresults of three simple solution heuristics. The heuristics perform well in\nabsolute terms but can be improved upon very considerably in relative terms.\nThe findings complement known asymptotic results for large voting bodies and\nmay improve termination criteria for local search algorithms.\n