A measure of a priori voting power of a member in a set (assembly, union or group) was introduced by Lionel Penrose in 1946 and rediscovered by Banzhaf in 1965. Henceforth, one may speak of the Penrose-Banzhaf (power) index. In order to satisfy the principle of one man, one vote, Penrose also made clear that the voting power of each nation in a federal assembly of nations, like the Eurpean Union (EU), should be proportional to the square root of the number of citizens entitled to vote. We call this the rule of Penrose. We present the power distribution among the different countries of the European Union for several periods with constantly changing decision rules and shall see that Penrose’s rule is frequently violated.