Given the weighted voting system [8: 5, 4, 3], which of the coalitions given are minimal winning coalitions?
A) {A, B, C}
B) {A, B}
C) {B, C}
D) There are no minimal winning coalitions.

Question

Quizplus · Accepted Answer

In order for a coalition to be a minimal winning coalition, it must have enough voting power to win (in this case, a total of 8 or more votes), but no subset of that coalition can also win on its own. 
Option A has a total voting power of 12, which is too much and the subsets {A, B} and {B, C} can also win on their own, so it is not a minimal winning coalition. 
Option B has a total voting power of 9, just enough to win, and no subset of {A, B} has enough voting power to win on their own, so it is a minimal winning coalition. 
Option C has a total voting power of 7, which is not enough to win, so it is not a winning coalition. 
Option D is not correct, as there is at least one minimal winning coalition (option B).

Given the Weighted Voting System [8: 5, 4, 3], Which