$$\begin{array}{l}
\text { The results of an election are summarized in the preference table below. }\
\begin{array} { l | c c c c }
\text { Number of votes } & 15 & 2 & 20 & 10 \
\hline \text { First choice } & \mathrm { X } & \mathrm { X } & \mathrm { Z } & \mathrm { Y } \
\text { Second choice } & \mathrm { Y } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } \
\text { Third choice } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } & \mathrm { Z }
\end{array}
\end{array}$$ (a) Using the pairwise comparison voting method, determine the winner. (b) If candidate X drops out and the votes are recounted, does this election violate the irrelevant alternative criterion?

Question

$$\begin{array}{l}
\text { The results of an election are summarized in the preference table below. }\
\begin{array} { l | c c c c } 
\text { Number of votes } & 15 & 2 & 20 & 10 \
\hline \text { First choice } & \mathrm { X } & \mathrm { X } & \mathrm { Z } & \mathrm { Y } \
\text { Second choice } & \mathrm { Y } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } \
\text { Third choice } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } & \mathrm { Z }
\end{array}
\end{array}$$ (a) Using the pairwise comparison voting method, determine the winner. (b) If candidate X drops out and the votes are recounted, does this election violate the irrelevant alternative criterion?

Quizplus · Accepted Answer

The Answer of $$\begin{array}{l}
\text { The results of an election are summarized in the preference table below. }\
\begin{array} { l | c c c c } 
\text { Number of votes } & 15 & 2 & 20 & 10 \
\hline \text { First choice } & \mathrm { X } & \mathrm { X } & \mathrm { Z } & \mathrm { Y } \
\text { Second choice } & \mathrm { Y } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } \
\text { Third choice } & \mathrm { Z } & \mathrm { Y } & \mathrm { X } & \mathrm { Z }
\end{array}
\end{array}$$ (a) Using the pairwise comparison voting method, determine the winner. (b) If candidate X drops out and the votes are recounted, does this election violate the irrelevant alternative criterion?

(A) Using the Pairwise Comparison Voting Method, Determine the Winner