Chapter 17.2, Problem 54PS

To determine

a)

Is there a majority winner or not and if not, who is the plurality winner for an election with three candidates with the following results:

$\begin{array}{ccc}\left(\text{ACB}\right)& \left(\text{BAC}\right)& \left(\text{CAB}\right)\\ 4& 2& 5\end{array}$

To determine

b)

The runoff winner between second and third choices for an election with three candidates with the following outcomes:

$\begin{array}{ccc}\left(\text{ACB}\right)& \left(\text{BAC}\right)& \left(\text{CAB}\right)\\ 4& 2& 5\end{array}$

To determine

c)

How can the voters who support $\text{C}$ vote insincerely to enable $\text{C}$ to win the election with three candidates with the following outcomes:

$\begin{array}{ccc}\left(\text{ACB}\right)& \left(\text{BAC}\right)& \left(\text{CAB}\right)\\ 4& 2& 5\end{array}$