Voting power on a graph connected political space with an application to decision-making in the Council of the European Union

Abstract We analyze the problem of computing Banzhaf and Shapley power indices for graph restricted voting games, defined in a particular class graphs, that we called line-clique. A line-clique is model uni-dimensional political space which voters with same bliss point are connected vertices clique then other arcs connect nodes consecutive cliques. The interest to this comes from its correspondence spatial game: has been proposed used by analysts understand nations’ behavior outcome bargaining process within EU Council. Broadly speaking, computation index game strongly #P-complete, as it includes enumeration all winning coalitions. Nevertheless, show special coalitions can be enumerated dynamic programming, resulting pseudo-polynomial algorithm proving only weakly #P-complete. After implementing our new algorithms finding they very fast practice, Council, application previous research compiled large data set concerning positions outcomes. will test whether an effect on outcome, more precisely, nations favored their weight position influence advantages. Using linear regressions, see unrestricted not capable any predictive property, but are. statistic evidence shows combination network source affects advantage country.