Chapter 4.3, Problem 1ES

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 $\left\{6:4,3,2,1\right\}$.

a. What is the quota?

b. How many voters are in this system?

c. What is the weight of voter B?

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

e. Is $\left\{A,D\right\}$ a winning coalition?

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

g. I-low many coalitions can be formed?

h. How many coalitions consist of exactly two voters?