Chapter 17.1, Problem 41PS

Twelve people serve on a board and are considering three alternatives: $\text{A, B}$and $\text{C}$. Here are the choices followed by vote:

$\begin{array}{cccccc}\left(\text{ABC}\right)& \left(\text{ACB}\right)& \left(\text{BAC}\right)& \left(\text{BCA}\right)& \left(\text{CAB}\right)& \left(\text{CBA}\right)\\ 2& 4& 2& 1& 2& 1\end{array}$

Determine the winner, if any, using the voting methods in Problems $39-44$.

Borda count method