laborers. Four candidates are running the election: A, B, C and D, Trb proportio

Question

laborers. Four candidates are running the election: A, B, C and D, Trb proportion of each group in the population are the following: ants, bankers, and preferences and the merch Students Bankers Laborers Merchants 30% 10% 35% 25% (Best) ABC (Worst) D D A a. Which candidate wins under plurality rule? (2 points) b. Which candidate wins under a runoff system? (2 points) c. Say that the bankers get to choose the election system. The bankers can choose either to hold the election by the Borda count, approval voting (top two), or approval voting (top three). Which election system among these three choices will the bankers choose? (2 points)

Explanation / Answer

a.

Plurality rule describes the circumstance where a candidate polls more vote than any other but less than 50% vote.

Under Plurality rule, C wins as 35% of the people prefer C and there is no one who says C is the worst.

b.

if no candidate gets more than 50% of the vote, do a second round.

Here, the first round led to the results:

A 30%, B 10%, C 35% and D 5%

So under the “Plurality with a Runoff” rule, we would go to a second round (since no candidate got 50% or more in the first round),

The top two vote getters in the first round C and A going up against each other in the second round with B and D are eliminated.

In the 2nd round, bankers and merchants must change their votes, since their favourite candidates have been eliminated. They have to choose between C and A

Students

Bankers

Laborers

Merchants

30%

10%

35%

25%

A

C

C

A

C

A

A

C

In this example, both bankers and merchants switch their votes for A and C In the second round so A wins the run off since A defeats C by 55% to 45% in the run off round

c.

In borda count: Everyone ranks every candidate. For each voter, a candidate is given a score: The top candidate gets N, the second candidate gets N – 1, and so on. The candidate with the highest total score wins.

We can calculate the Borda score for each of the candidates as follows:

BS(A) = 3 × .30 + 2 × .25 + 1 ×.10 + 0 × .35 = 1.5
BS(B) = 3 × .10 + 2 × .65 + 1 × 0 + 0 × .25 = 1.6
BS(C) = 3 × .35 + 2 × .10 + 1 × .55 + 0 × 0 = 1.8
BS(D) = 3 ×. 25 + 2 × 0 + 1 ×. 35 + 0 × .40 =1.1

The candidate with the highest Borda score wins. So Candidate C wins.

Approval voting: if there are four candidates, A, B, C, and D, and a bankers have a strict preference order, preferring B to C to A to D, then the following are the voter's possible sincere approval votes:

·         vote for B, C, A and D

·         vote for B, C, and A

·         vote for B and C

·         vote for B

·         vote for no candidates

Approval voting top 2 : for A = 30 + 25 = 55%, for B = 10 +30 +35 = 75%, for C = 35 + 10 = 45%, D = 25%

so B wins

Approval for top 3 : for A = 30 + 25 + 10 = 65%, for B = 10 + 30 +35 = 75%, for C =35 + 10 + 30 +25 = 100%, for D = 25%

so C wins

Approval voting is similar to the Borda count method. Hoever, the process of finding out the winner is much simpler with Approval Voting. Also, one more advantage of approval voting is that addition or removal of candidates does not change the points total of other candidates. So Bankers should choose approval voting method.

Students

Bankers

Laborers

Merchants

30%

10%

35%

25%

A

C

C

A

C

A

A

C

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