1.4 The Plurality-with Elimination Method

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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 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

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!

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

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 C D 2nd 3rd 4th