Question

an executive board consists of a president (p) and three vice - presidents (v1, v2, v3). for a motion to pass it must have yes votes from three of the voting members, one of which must be the presidents. a weighted system that could represent this situation is: q : p, v1, v2, v3 where: q = p = v1 = v2 = v3 =

Explanation:

Step1: Determine the quota

Since a motion needs yes - votes from three of the four voting members (president and 3 vice - presidents) and one of them must be the president, the quota $Q$ is 3.

Step2: Assign weights

The president is essential for a motion to pass. So we can assign the president a weight of 2, and each vice - president a weight of 1. This way, if the president votes yes and two vice - presidents vote yes, the sum of the weights is $2 + 1+1=4\geq3$. If the president votes no, even if all three vice - presidents vote yes, the sum of the weights is $1 + 1+1 = 3$ which is not enough as the president's vote is mandatory. So $P = 2$, $V_1=1$, $V_2 = 1$, $V_3=1$.

Answer:

$Q = 3$
$P = 2$
$V_1=1$
$V_2 = 1$
$V_3=1$