Use the following information to answer the Questions
Consider an 11-member committee that must choose one of three alternatives: X, Y, or Z. Their schedule of preferences is shown below. $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of voters }$

$\begin{array} { l c c c }
& 5 & 4 & 2 \
\text { First choice } & \mathrm { Z } & \mathrm { X } & \mathrm { Y } \
\text { Second choice } & \mathrm { Y } & \mathrm { Y } & \mathrm { X } \
\text { Third choice } & \mathrm { X } & \mathrm { Z } & \mathrm { Z }
\end{array}$
-If the Hare system is used, alternative X wins. Could the voters who most prefer Z vote insincerely in some way to change the outcome in a way that would benefit them?
A) Yes, they could switch the ranking of X and Y.
B) Yes, they could switch the ranking of Y and Z.
C) Yes, they could switch the ranking of X and Z.
D) No, X would always win.

Question

Use the following information to answer the  Questions 
Consider an 11-member committee that must choose one of three alternatives: X, Y, or Z. Their schedule of preferences is shown below. $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of voters }$

$\begin{array} { l c c c } 
& 5 & 4 & 2 \
\text { First choice } & \mathrm { Z } & \mathrm { X } & \mathrm { Y } \
\text { Second choice } & \mathrm { Y } & \mathrm { Y } & \mathrm { X } \
\text { Third choice } & \mathrm { X } & \mathrm { Z } & \mathrm { Z }
\end{array}$
-If the Hare system is used, alternative X wins. Could the voters who most prefer Z vote insincerely in some way to change the outcome in a way that would benefit them?
A) Yes, they could switch the ranking of X and Y.
B) Yes, they could switch the ranking of Y and Z.
C) Yes, they could switch the ranking of X and Z.
D) No, X would always win.

Quizplus · Accepted Answer

In the Hare system, whenever a candidate has enough first-choice votes to reach the victory threshold, they are declared the winner. If no candidate reaches the threshold, the candidate with the fewest votes is eliminated and their votes are redistributed according to the voters' second choices. This process continues until a winner is determined.

In this case, X received 5 first-choice votes, which is enough to win since the victory threshold is 6 (which is 50% of the 11 members, rounded up). Therefore, X would always win regardless of how the voters who most prefer Z vote.

However, if X had not received enough first-choice votes to win outright, then the voters who most prefer Z could potentially change the outcome by strategically ranking their choices. The best option for them would be to switch the ranking of Y and Z, which would increase the likelihood of Y being eliminated and their votes being redistributed to Z. Switching the ranking of X and Y or X and Z would not have the same effect. Therefore, the correct answer is B.

Use the Following Information to Answer the Questions \quad

Use the Following Information to Answer the Questions $\quad$