Chapter 17.1, Problem 31PS

In voting method among three candidates, the outcomes are reported as:

$\begin{array}{cccccc}\left(\text{ABC}\right)& \left(\text{ACB}\right)& \left(\text{BAC}\right)& \left(\text{BCA}\right)& \left(\text{CAB}\right)& \left(\text{CBA}\right)\\ \text{8}& \text{4}& \text{3}& \text{0}& \text{2}& \text{5}\end{array}$

Determine the winner, if any, using the voting methods in Problems $29-34$.

Borda count method