Chapter 2, Problem 61E

Consider the generic weighted voting system $\left[q:w_1,w_2,\mathrm{...},w_N\right]$. (Assume $w_1\ge w_2\ge \mathrm{...}\ge w_N$).

a. Find all the possible values of q for which no player has veto power.

b. Find all the possible values of q for which every player has veto power.

c. Find all the possible values of q for which $P_i$, has veto power, but $P_{i+1}$ does not.

(Hint: See Exercise 60.)