Assignment: 12A Voting: Majority Rule? Student: Lesa Thacker Date: 4/14/16 Time:

Question

Assignment: 12A Voting: Majority Rule? Student: Lesa Thacker Date: 4/14/16 Time: 4:23 AM Instructor: Jame Mccumbee Course: ACTC MAT 146-Bennett 5c-0121 83184 Mathematics, Se For the following preference schedule, answer questions a throughg. A D BCD B Book: Bennett: Using and Understanding First Second DCD D CC Third B BC BA A Fourth C A A A BD 24 18 12 8 7 5 a. How many votes were cast? A total of votes were cast. b. Find the plurality winner. Did the plurality winner also reccive a majority? Explain. O Candidate B is the plurality winner, but not by a majority because B received less than 50% of the first-place votes. Candidate D is the plurality winner, but not by a majority because D received less than 50% of the first-place votes. candidate A is the plurality winner by a majority because A received more than 50% of the first-place votes. o candidate C is the plurality winner, but not by a majority because C received less than 50% of the first-place votes. c. Find the winner by a runoff of the top two candidates. Choose the correct answer below. O Candidate A is the winner of the top-two runoff. O O O Candidate C is the winner of the top-two runof Candidate B is the winner of the top-two runoff. Candidate D is the winner of the top-two runoff. d. Find the winner by a sequential runoff. Choose the correct answer below. O The winner by sequential runoff is A. O The winner by sequential runoff is D. O The winner by sequential runoff is C. O The winner by sequential runoff is B. e. Find the winner by a Borda count. Choose the correct answer below. O Candidate C is the winner by the Borda count. O Candidate D is the winner by the Borda count. O Candidate B is the winner by the Borda count. O Candidate A is the winner by the Borda count.

Explanation / Answer

11.a) The preference schedule compactly summarizes the votes in the election by grouping identical preference ballots together along with a count of how many voters cast each identical preference ballot.

In the given case, the total no. of votes cast = 24+18+12+8+7+5 = 74 votes

11..b) Plurarity winner.

For the Plurality Method, the candidate with the most first place votes wins.

Here D is the Plurality winner, but he doesn't have the majority (majority = 74/2 + 1 = 38 votes)

11.c) Runoff Method

In the runoff method, voters are asked to rank candidates from highest to lowest, highest being their number one choice. This method immediately narrows all the candidates down to only two options. The two candidates with the most first place votes are kept and all the other candidates are removed. The removed candidates’ first place votes go to the remaining candidate that is closest to the top on each voter’s preference schedule. Then the first place votes are tallied again, with a majority winner between the two final candidates.

Here, A and D are the top 2 and B & C are eliminated. The 12 votes of B will go to D & 5 votes of B will go to A. The 8 votes of C will go to D.

Then the position will be as follows:

A = 24 + 5 = 29

D = 25 + 12 + 8 = 45

Hence D will be the winner.

11.d) Sequential runoff

The sequential runoff method is a backward approach of the runoff method. Each candidate’s first place votes are tallied and the one candidate with the least is removed from all schedules. Each preference schedule is refigured, with each remaining candidate keeping their respective rankings. Again the candidate with the least first place votes is removed and this method continues until there are only two final candidates, with a majority winner between the two.

Here C will be eliminated & the votes will be distributed as follows:

A = 24, B = 17, D = 33

In the next step, B will be eliminated

A = 29, D = 45

Hence the winner is D

11.e) Baroda Count

The Borda count has voters rank the candidates in order.

o find the Borda winner, points are assigned to each ranking. A voter’s last choice for a candidate receives a value of 1, a second to last candidate receives a value of 2, a third to last candidate receives a value of 3, and this pattern continuesuntil all candidates on a voter’s schedule have been assigned a point value.

Here the points will be as follows:

A = 24*4 + 18*1 + 12*1 + 8*1 + 7*2 + 5*2 = 158

B = 24*2 + 18*2 + 12*4 + 8*2 + 7*1 + 5*4 = 175

C = 24*1 + 18*3 + 12*2 + 8*4 + 7*3 + 5*3 = 170

D = 24*3 + 18*4 + 12*3 + 8*3 + 7*4 + 5*1 = 237

Hence, D is the winner

Candidate No. of first place votes A 24 B 17 (12+5) C 8 D 25 (18+7)

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