In the weighted voting system below, the weights represent voters A, B, C, and so on, in that order. Answer parts (a) through (d). A has 16 vote(s). B has 6 vote(s). C has 6 vote(s). D has 6 vote(s). c. Are there any dictators? Yes (t) No weights of the voters? d. Which voter(s), if any, have veto power?

We have four voters with weights: A = 16, B = 6, C = 6, D = 6. (The total weight is 34.) In many weighted voting systems a coalition is winning if the total weight meets or exceeds a quota. (Often this quota is set to be just above half the total weight; in this case a natural choice is 18 votes.) Part (c). Dictatorship A dictator is a voter who can, on his own, form a winning coalition—i.e. his weight alone is enough to reach the quota regardless of how the other votes go. Here, even the largest voter, A, has 16 votes, which is less than 18. Therefore, A cannot decide the outcome by himself, and none of the voters has such power. Answer for (c): No. Part (d). Veto Power A voter has veto power if every winning coalition must include that voter (equivalently, if the voter votes “no,” there is no way for the remaining voters to reach the quota). Let’s check each voter: • Voter A (16 votes): Notice that the coalition B + C + D has 6 + 6 + 6 = 18 votes, which meets the quota without A. So A is not essential for every winning coalition. • Voters B, C, or D (each 6 votes): Consider a coalition like A + C (with 16 + 6 = 22 votes). This coalition wins without B or D. Similarly, A + B wins without C, and so on. Because for every voter there is at least one winning coalition that excludes that voter, none of the voters has veto power. Answer for (d): None of the voters have veto power.