Chapter 17.2, Problem 52PS

To determine

a)

Whether there is a majority winner in the election of three candidates. If not, then check who is the winner by the plurality method when $10$ votes added in each list of the following voter preferences:

$\begin{array}{ccc}\left(\text{ABC}\right)& \left(\text{BCA}\right)& \left(\text{CBA}\right)\\ \text{5}& \text{3}& \text{3}\end{array}$

To determine

b)

The winner by using the pairwise comparison method when $10$ votes added in each list of the following voter preferences:

$\begin{array}{ccc}\left(\text{ABC}\right)& \left(\text{BCA}\right)& \left(\text{CBA}\right)\\ \text{5}& \text{3}& \text{3}\end{array}$

To determine

c)

Whether the ordering for the choices for candidates in part (b) is transitive or not when $10$ votes added in each list of the following voter preferences:

$\begin{array}{ccc}\left(\text{ABC}\right)& \left(\text{BCA}\right)& \left(\text{CBA}\right)\\ \text{5}& \text{3}& \text{3}\end{array}$