Step-by-step explanation:
In a weighted voting system [q1, q2, ..., qn], each voter i has a weight wi assigned to them and the total weight required for a winning decision is W.
The possible values of q that can be used in a weighted voting system are integers such that:
1 ≤ qi ≤ wi for all i = 1, 2, ..., n and
W/2 < Σqiwi ≤ W
In the given system [8, 4, 1], the weights assigned to voters are not given. So, we cannot determine the possible values of q without knowing the weights. We need to know the weights assigned to the voters and the total weight required for a winning decision (W), in order to determine the possible values of q.