The hypothetical sport of Major League Calvin ball uses what is known as a 5€“3€“1system to vote for the league€™s Most Valuable Player (MVP) in each league. In a 5€“3€“1system, each voter gets to vote for three different players they consider worthy of the award. Their first-place candidate gets 5 points, their second-place candidate gets 3points, and their third-place 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 arethree voters€”Neyer, Law, and Phillips€”and five potential candidates for the award€”Alex, David, Raffy, Manny, and Mario. The table below shows how each voter ranks the candidates. Raffy is embroiled in a substance abuse scandal. The €œguilty€ or €œinnocent€ verdict will come out the day before voting, and a guilty verdict will ban him from being voted on as an MVP and all players ranked below him on a given voter€™s ballot will be €œbumped up€ one spot on that ballot.

a. Who will win the MVP if Raffy is found innocent?
b. Who will win the MVP if Raffy is found guilty?
c. What problem with consistent aggregation does this illustrate?

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Rank Best Second Best Third Best Fourth Best Fifth Best Never David Alex Raffy Manny Mario Law David Alex Raffy Manny Mario Phillips Raffy Alex Manny Mario David