1. 1.4 The Plurality-with Elimination Method

2. Other names for the Plurality-with-elimination method
- Instant runoff voting (in the present)
- Hare method
- Plurality with Elimination

3. 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.

4. Example 1: 37 VOTERS, need 19 votes for majority winner
Step 1: No one receives 19 votes, so eliminate B and rewrite the table
Number of voters 14 10 8 4 1
1st choice A C D B
2nd choice
3rd choice
4th choice
Number of voters 14 10 8 4 1
1st choice A C D
2nd choice
3rd choice
4th choice
Number of voters 14 10 8 4 1
1st choice A D
2nd choice
Step 3: D has 23 votes so D is the winner
Step 2: No one with 19 votes yet, so eliminate C and re-write the table

5. Example 2 7 8 10 4 1st A C 2nd Number of votes 7 8 10 4 1st choice A B
2nd choice
3rd choice 7 8 10 4
1st A C
2nd
29 people votes, need 15 votes for majority winner
C now has 18 first place votes so C is the winner!

6. Example 3: Similar to example 2
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
2nd choice
3rd choice
How could this happen? 7 8 10 4
1st B C
2nd
Number of votes 7 8 10 4
1st choice A B C
2nd choice
3rd choice
Therefore: B is the winner with 15 votes

7. 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.

8. Who is the winner under Plurality with Elimination Method?
#1)
#2) 10 6 5 4 2
1st A B C D
2nd
3rd
4th