Chapter 4.3, Problem 2ES

In the following exercises that involve weighted voting systems for voters A. B. C. ... the systems are given in the form $\left\{q:w_1,w_2,w_3,w_4,\mathrm{...},w_n\right\}$. The weight of voter A is $w_1$. the weight of voter B is $w_2$. the weight of voter C is $w_3$, and so on.

A weighted voting system is given by $\left\{16:8,7,4,2,1\right\}$.

a. What is the quota?

b. How many voters are in this system?

c. What is the weight of voter C?

d. What is the weight of the coalition $\left\{B,C\right\}$

)?

e. Is $\left\{B,C,D,E\right\}$ a winning coalition?

I. Which voters are critical voters in the coalition $\left\{A,B,D\right\}$?

g. How many coalitions can be formed?

h. How many coalitions consist of exactly three voters?