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