5: The votes are in! For candidates Alice, Bob, Carlos, and Dave, there are 6 ba

Question

5: The votes are in! For candidates Alice, Bob, Carlos, and Dave, there are 6 ballots ranking (Highest-lowest) ABCD, 4 ballots CDAB, 2 ballots DCAB. A) First count these with a Bordo count, assigning 1,2,3,4 points to first, second, third, and fourth preferences. Who wins the election? B) If this had been a plurality and voters had cast just one vote (for their preference), who would win? top C) "Keeping voters" preferences in order, if voters could eliminate their least preferred candidate, then take a second ballot to eliminate again, and so on, who would win the election? Aliu:11x1)+(3x2): 7- 2nd 3

Explanation / Answer

Q5.

A) Assigning 1,2,3,4 points to the first, second, third and fourth preferences, the candidate getting the least score wins.

Points scored by A = 6x1 + 4x3 + 2x3 = 24

Points scored by B = 6x2 + 4x4 + 2x4 = 36

Points scored by C = 6x3 +4x1 + 2x2 = 26

Points scored by D = 6x4 + 4x2 + 2x1 = 34

So, A wins the election having the lowest count of points.

B) If voters had cast just one vote for their top preference, then

Votes obtained by A = 6

Votes obtained by B = 0

Votes obtained by C = 4

Votes obtained by D = 2

So, candidate A would have won here.

C) Keeping voters' preference in order, at the end of the first round of voting, D would get 6 votes for elimination and B would get 6 votes for elimination. So both D and B would get eliminated at the end of the first round.

For the second round, we only have the candidates A and C. Keeping the voting preferences in order, C would get 6 votes for elimination and A would get 6 votes for elimination. So there is a tie between A and C to win the election.

Q1 is not complete, because the data are missing.

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