A football team is voting for a captain based on how many times the captain would have the team would practice per week. The table below shows the number of team members in favor of various numbers of practices per week.
a. If the team is choosing between three captains—Buck, Jim, and Brian—can we use the median-voter theorem?
b. Assume that at the last minute, Buck decides to withdraw from the race. Can we use the median-voter theorem for the race as it stands now?
c. If you can use the median-voter theorem to predict the result without Buck, how many times will the team practice? If you cannot use the theorem, what two answers can you rule out?
d. Assume that two more players join the team before the vote. They both prefer to practice 10 times a week. If you can use the median-voter theorem to predict the result without Buck, how many times will the team practice? If you cannot use the theorem, what two answers can you rule out?