Power in the US Legislature

Using a standard model of the US legislative system as a monotonic simple game, we look at rankings of the four types of players – the president, the vice president, senators, and representatives – induced by power indices. We show that regardless of the power index used, the president is always ranked above the other players, and a senator is always ranked above the vice president and a representative. For most power index rankings, including the Banzhaf and Shapley-Shubik power indices, the vice president is ranked above a representative, however, there exist power indices ranking a representative above the vice president. Our results apply to more general yes-no voting systems.