The results of an election are summarized in the preference table below.
$\begin{array}{l|lcccc}
\text { Number of votes } & 5 & 12 & 7 & 14 & 10 \
\hline \text { First choice } & \mathrm{Z} & \mathrm{Z} & \mathrm{X} & \mathrm{X} & \mathrm{Y} \
\text { Second choice } & \mathrm{X} & \mathrm{Y} & \mathrm{Y} & \mathrm{Z} & \mathrm{Z} \
\text { Third choice } & \mathrm{Y} & \mathrm{X} & \mathrm{Z} & \mathrm{Y} & \mathrm{X}
\end{array}$

Suppose the election is declared invalid, and a reelection is held. If the people who voted $\mathrm { XYZ }$ in the original election change their vote to $\mathrm { ZXY }$, is the monotonicity criterion violated?
A) No
B) Yes

Question

The results of an election are summarized in the preference table below.
$\begin{array}{l|lcccc}
\text { Number of votes } & 5 & 12 & 7 & 14 & 10 \
\hline \text { First choice } & \mathrm{Z} & \mathrm{Z} & \mathrm{X} & \mathrm{X} & \mathrm{Y} \
\text { Second choice } & \mathrm{X} & \mathrm{Y} & \mathrm{Y} & \mathrm{Z} & \mathrm{Z} \
\text { Third choice } & \mathrm{Y} & \mathrm{X} & \mathrm{Z} & \mathrm{Y} & \mathrm{X}
\end{array}$

Suppose the election is declared invalid, and a reelection is held. If the people who voted $\mathrm { XYZ }$ in the original election change their vote to $\mathrm { ZXY }$, is the monotonicity criterion violated?
A) No
B) Yes

Quizplus · Accepted Answer

The monotonicity criterion is not violated because the winner remains the same (Z) even after the change in votes.

The Results of an Election Are Summarized in the Preference