HW7. In a weighted voting system with four players the winning coalitions are the following: {P1, P2, P3, P4}, {P1, P2, P3}, {P1, P2, P4}, {P1, P3, P4}, {P2, P3, P4}, {P1, P2}, {P1, P3}, {P1, P4}

Step-by-step explanation:

a). Underline the critical player (s) in each winning coalition?

{P1, P2, P3, P4}, {P1, P2, P3}, {P1, P2, P4}, {P1, P3, P4}, {P2, P3, P4}, {P1, P2}, {P1, P3}, {P1, P4}

b). Find the Banzhaf power distribution of the weighted voting system?

12 instances of criticality P1: 6/12 =.5P2: 2/12 = 16.66%P3: 2/12 = 16.66%P4: 2/12 = 16.66%

c). Determine which players, if any, are dictators, and explain briefly how you can tell?

There are no dictators in this weighted voting system, since no one player is alone in a winning coalition; equivalently, no one player has 100% of the power.

d). Determine which players, if any, have veto power, and explain briefly how you can tell?

There are no veto power players, since no player is critical in the grand coalition.

e). Determine which players, if any, are dummies, and explain briefly how you can tell?

There are no dummies, since each player is critical in at least one winning coalition.