A group of 12 students have to decide among three types of pizza: sausage (S), mushroom (M), and beef (B). Their preference rankings are shown below. Which choice will the group make if they use the Hare system? $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of students }$
$\begin{array} { l l l l l l }
& 3 & 3 & 2 & 2 & 2 \
\text { First choice } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } & \mathrm { S } \
\text { Second choice } & \mathrm { M } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } \
\text { Third choice } & \mathrm { S } & \mathrm { S } & \mathrm { B } & \mathrm { M } & \mathrm { M }
\end{array}$

Question

A group of 12 students have to decide among three types of pizza: sausage (S), mushroom (M), and beef (B). Their preference rankings are shown below. Which choice will the group make if they use the Hare system? $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of students }$
$\begin{array} { l l l l l l } 
& 3 & 3 & 2 & 2 & 2 \
\text { First choice } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } & \mathrm { S } \
\text { Second choice } & \mathrm { M } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } \
\text { Third choice } & \mathrm { S } & \mathrm { S } & \mathrm { B } & \mathrm { M } & \mathrm { M }
\end{array}$

Quizplus · Accepted Answer

The Hare system works by repeatedly eliminating the option with the least first-choice votes until one option has a majority. In this case, the first round of counting gives each option the following number of votes:

$\begin{array} { l l l } 
\mathrm { B } & 4 \
\mathrm { M } & 3 \
\mathrm { S } & 5 \
\mathrm { None } & 0 \
\end{array}$

Since none of the options have a majority, we eliminate the option with the least number of first-choice votes (which is Mushroom, with 3 votes). We then redistribute the second-choice votes for Mushroom, giving each option the following number of votes:

$\begin{array} { l l l } 
\mathrm { B } & 5 \
\mathrm { M } & 3 \
\mathrm { S } & 6 \
\mathrm { None } & 0 \
\end{array}$

Now Sausage has a majority, and is the winner. Therefore, the best choice according to the Hare system is $\boxed{\textbf{(A) } B}$.

A Group of 12 Students Have to Decide Among Three \quad

A Group of 12 Students Have to Decide Among Three $\quad$