The results of an election are summarized in the preference table below. Suppose the election is declared invalid, and a reelection is held. If the people who voted XYZ in the
Original election change their vote to ZXY, is the monotonicity criterion violated?
A)Yes
B)No

Question

The results of an election are summarized in the preference table below.  Suppose the election is declared invalid, and a reelection is held. If the people who voted XYZ in the
Original election change their vote to ZXY, is the monotonicity criterion violated?
A)Yes 
B)No

Quizplus · Accepted Answer

According to monotonicity criterion, if a candidate gains more first preference votes, then the candidate should not receive fewer overall votes. In this particular case, if the people who voted XYZ in the original election change their vote to ZXY, then ZXY will receive more first preference votes, which makes it impossible for ZYX to lose overall votes. Thus, the monotonicity criterion is not violated. Monotonicity criterion states that if a candidate gains more first place votes, then they should never receive fewer first place votes. In the original election, candidate X received 4 first place votes and candidate Z received 3, so candidate X won. If the people who voted for XYZ change their vote to ZXY, then candidate Z would receive 4 first place votes and candidate X would receive 3 first place votes, which means candidate Z would win. Therefore, the original winner (candidate X) did not lose any first place votes and the monotonicity criterion is not violated.

The Results of an Election Are Summarized in the Preference