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We use simplicial complexes to model weighted voting games where certaincoalitions are considered unlikely or impossible. Expressions for Banzhaf andShapley-Shubik power indices for such games in terms of the topology ofsimplicial complexes are provided. We calculate the indices in several examplesof weighted voting games with unfeasible coalitions, including the U.S.Electoral College and the Parliament of Bosnia-Herzegovina.

Weighted simple games and the topology of simplicial complexes