A weighted voting system with voters P1, P2, P3, P4, and P5 is given by [q | 11, 6, 4, 2...

A weighted voting system with voters P₁, P₂, P₃, P₄, and P5 is given by [q | 11, 6, 4, 2, 1].

a. If a supermajority is required to pass a measure, what is the quota q?

b. List all two-person coalitions and their weights. Are there any two-person winning coalitions?

c. List all four-person coalitions and their weights. Which voters are critical in each winning coalition?

d. Is P₅ a dummy? Explain.