Final answer:
To find the smallest value of q for which all three players have veto power, set up an inequality where p3 is greater than or equal to p1 + p2. The smallest value of q is equal to p3.
Step-by-step explanation:
In a weighted voting system, each player has a certain number of votes, and different players may have different weights assigned to their votes. In this case, we have three players, indicated as p1, p2, and p3. We are given that p2 has veto power, meaning their vote alone can block a decision, while p3 does not have veto power.
To find the smallest value of q for which all three players have veto power, we need to find a value of q such that p3 has veto power as well. This means that p3's votes should be greater than or equal to the sum of p1's and p2's votes. We can set up an inequality as follows:
Since p2 already has veto power and p1 and p2 have the same number of votes, the smallest value of q for which all three players have veto power is equal to p3's weight. Therefore, q = p3.