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. 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.  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 states that if a candidate wins an election, and then the voters who preferred that candidate change their preference to ranking that candidate lower, then the candidate should still win the election.

In this case, if the voters in column 2 change their vote from JPT to PJT, Peterson would win the election instead of Jenkins. However, if those voters changed their vote from JPT to TJP, Thomas would win the election instead of Peterson.

Since the change in voter preference does not violate the monotonicity criterion, the answer is B. The monotonicity criterion is not violated in this scenario because the new vote choice PJT is still a higher preference for Peterson than their original first preference, and Jenkins still receives the lowest number of first-choice votes. Therefore, Peterson's chances of winning can only increase or stay the same, and not decrease.

The Math Department Is Voting for a New Department Chairperson