A county consists of four districts, A, B, C, and D, whose populations are 90 thousand, 40 thousand, 30 thousand, and 20 thousand, respectively. Each district has one representative in the County Council, and casts a number of votes equal to the population (in tens of thousands) of his/her district; thus the district A representative casts 9 votes, the district B representative casts 4 votes, the district C representative casts 3 votes, and the district D representative casts 2 votes. 12 votes must be cast in favor of a motion in order to pass it. (This is in fact the same weighted voting system, [12: 9, 4, 3, 2], considered in question HW1 above, for which you have already found the Banzhaf power distribution.) Required:
According to Banzhaf, which district or districts have a percentage of actual power which is less than their percentage of the total county population?