A committee has three members with the system [10: 5, 4, 3, 2, 1]. Which voters are critical in the coalition {A, B, C, E}?
A) A only
B) A and B
C) A and E
D) E only

Question

Quizplus · Accepted Answer

For a voter to be critical in a coalition, the coalition must not have enough votes on its own to make a winning majority. In this case, the coalition {A, B, C, E} has a total of 12 votes (5 from B, 4 from C, and 3 each from A and E). The total number of votes in the system is 25, so a winning majority requires 13 votes.

If we remove both A and B from the coalition, we are left with {C, E}, which has a total of 7 votes, so it is not a winning coalition. Therefore, both A and B are critical in the coalition {A, B, C, E}.

A Committee Has Three Members with the System [10: 5