The math department is voting for a new department chairperson. The candidates are Jenkins (J), Peterson (P), and Thomas (T). The results of the election are summarized in the preference table below.
$\begin{array}{l|lll}
\text { Number of votes } & 5 & 3 & 4 \
\hline \text { First choice } & \text { T } & \text { J } & \text { P } \
\text { Second choice } & \text { J } & \text { P } & \text { T } \
\text { Third choice } & \text { P } & \text { T } & \text { J }
\end{array}$

The winner is determined by the plurality-with-elimination method. Suppose the election is declared invalid, and that a reelection is held. If the voters in column 2 change their vote from JPT to PJT, is the monotonicity criterion violated?
A) Yes
B) No

Question

The math department is voting for a new department chairperson. The candidates are Jenkins (J), Peterson (P), and Thomas (T). The results of the election are summarized in the preference table below.
$\begin{array}{l|lll}
\text { Number of votes } & 5 & 3 & 4 \
\hline \text { First choice } & \text { T } & \text { J } & \text { P } \
\text { Second choice } & \text { J } & \text { P } & \text { T } \
\text { Third choice } & \text { P } & \text { T } & \text { J }
\end{array}$

The winner is determined by the plurality-with-elimination method. Suppose the election is declared invalid, and that a reelection is held. If the voters in column 2 change their vote from JPT to PJT, is the monotonicity criterion violated?
A) Yes
B) No

Quizplus · Accepted Answer

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

The Math Department Is Voting for a New Department Chairperson