1.4 The Plurality-with Elimination Method

• Other names for the Plurality-with-elimination method

- Instant runoff voting (in the present)

- Hare method

- Plurality with Elimination

The Plurality-with Elimination Method

• Steps:1) Count the first place votes for each candidate. If a

candidate has a majority of the first-place votes, that candidate is the winner.

2) Cross out the names of the candidates (or candidates if there is a tie) with the fewest first-place votes

3) Move other candidates up and count the number of the first-place votes again. If a candidate has a majority votes, that candidate is the winner. Otherwise, continue the process of crossing names and counting the first-place votes.

Example 1: 37 VOTERS, need 19 votes for majority winner

Number of voters

14 10 8 4 1

1st choice A C D B C

2nd choice B B C D D

3rd choice C D B C B

4th choice D A A A A

Number of voters

14 10 8 4 1

1st choice A D D D D

2nd choice D A A A A

Number of voters

14 10 8 4 1

1st choice A C D D C

2nd choice C D C C D

3rd choice D A A A A

4th choice

Step 1: No one receives 19 votes, so eliminate B and rewrite the table

Step 2: No one with 19 votes yet, so eliminate C and re-write the table

Step 3: D has 23 votes so D is the winner

Example 2

Number of votes

7 8 10 4

1st choice A B C A

2nd choice B C A C

3rd choice C A B B7 8 10 4

1st A C C A

2nd C A A C

C now has 18 first place votes so C is the winner!

29 people votes, need 15 votes for majority winner

Example 3: Similar to example 2. However, 4 people voted for A decided to vote for C. What is the outcome?

Number of votes

7 8 10 4

1st choice A B C A

2nd choice B C A C

3rd choice C A B B

7 8 10 4

1st B B C C

2nd C C B B

Therefore: B is the winner with 15 votes

Number of votes

7 8 10 4

1st choice A B C C

2nd choice B C A A

3rd choice C A B B

How could this happen?

The Monotonicity Criterion

• If X is a winner of an election and in a re-election, the only changes in the ballots are changes that favor X (and only X), then X should remain a winner of the election.

Who is the winner under Plurality with Elimination Method?

#1)

#2)

10 6 5 4 2

1st A B B C D

2nd C D C A C

3rd B C A D B

4th D A D B A