Reference no: EM133067680
Major League Baseball uses "5-3-1 voting" to select the most valuable player (MVP) in each league. Each voter gets to vote for three different players they consider worthy of the award and their first-choice candidate gets 5 points, their second-choice candidate gets 3 points, and their third-choice candidate gets 1 point. Points are then added up across all voters, and the player with the most total points wins the award.
Suppose there are three voters (Neyer, Law, and Phillips) and five MVP candidates (Alex, David, Raffy, Manny, and Mario). The following table shows how each voter ranks the candidates:
|
Rank
|
Neyer
|
Law
|
Phillips
|
|
Best
|
David
|
David
|
Raffy
|
|
Second Best
|
Alex
|
Alex
|
Alex
|
|
Third Best
|
Raffy
|
Raffy
|
Manny
|
|
Fourth Best
|
Manny
|
Manny
|
Mario
|
|
Fifth Best
|
Mario
|
Mario
|
David
|
In addition, candidate Raffy is embroiled in a substance abuse scandal. A verdict on his guilt or innocence will be made public one day before voting for MVP. If Raffy is found guilty, he becomes ineligible for MVP and voters then choose between the remaining four candidates.
(a) Who will win the MVP if Raffy is found innocent?
(b) Who will win the MVP if Raffy is found guilty?
(c) Is "3-5-1 voting" a consistent voting system? If yes, show that it satisfies all three conditions. If no, show which condition is violated.