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MA111 Chapter 1 - Section 4: Plurality With Elimination: Summary of Election Results

In an election with 4 candidates (A, B, C, D), candidate B is initially eliminated because they received the fewest first-place votes. Votes are redistributed to fill in gaps from eliminating B. Candidate C is then eliminated for having the fewest votes, and votes are again redistributed. Finally, candidate D wins with a majority of votes over candidate A.

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82 views1 page

MA111 Chapter 1 - Section 4: Plurality With Elimination: Summary of Election Results

In an election with 4 candidates (A, B, C, D), candidate B is initially eliminated because they received the fewest first-place votes. Votes are redistributed to fill in gaps from eliminating B. Candidate C is then eliminated for having the fewest votes, and votes are again redistributed. Finally, candidate D wins with a majority of votes over candidate A.

Uploaded by

shawnsherwood
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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MA111 Chapter 1 Section 4: Plurality with Elimination

A) Add the numbers on top of each column:


24 + 14 + 13 + 8 + 6 + 1 = 66
B) Majority = 50% + 1
66/2 + 1 = 34 votes
C) B has the least number of 1st place votes
with 8, so eliminate candidate B

Summary of Election Results

ROUND 1
Plurality Winner = A with 24/66 votes
Not a Majority Winner
Eliminate Candidate B with 8 1st place
votes
Create adjusted preference schedule.
D) Eliminate B and use the transitive property to shift
votes up in each column to fill in the gaps ROUND 2
Plurality Winner = A with 24/66 votes
Original Preference Schedule: Note a Majority Winner
Column 1 (24): A > B > C > D A > C > D Eliminate Candidate C with 20 1st place
Column 2 (14): D > C > B > A D > C > A votes
Column 3 (13): C > B > D > A C > D > A Create adjusted preference schedule
Column 4 (8): B > D > C > A D > C > A
Column 5 (6): C > D > A > B C > D > A ROUND 3
Column 6 (1): C > D > B > A C > D > A Plurality Winner = D with 42/66 votes
Candidate D has a majority
Finally, condense all common columns. Candidate D declared Plurality with
Elimination winner
New Preference Schedule:
A > C > D: Col 1 (24) = 24 votes Final Ranking:
1st = Candidate D
D > C > A: Col 2 (14) + Col 4 (8) = 22 Votes
2nd = Candidate A
C > D > A: Col 3 (13) + Col 5 (6) + Col 6 (1) = 20 votes 3rd = Candidate C
4th = Candidate B

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