Are Weighted Games Sufficiently Good for Binary Voting?

Binary “yes”–“no” decisions in a legislative committee or shareholder meeting are commonly modeled as weighted game. However, there noteworthy exceptions. E.g., the voting rules of European Council according to Treaty Lisbon use more complicated construction. Here we want study question if lose much from practical point view, restrict ourselves games. To this end, invoke power indices that measure influence member binary decision committees. More precisely, compare achievable distributions games with those reasonable superset It turns out deviation is relatively small.