The Plurality-with-Elimination Election Method

The Plurality-with-Elimination Election Method
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  • 0:02 Introduction to Plurality
  • 0:56 Plurality Method
  • 1:54 Elimination
  • 3:39 Monotonicity Criterion
  • 5:41 Lesson Summary
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

When a run-off is needed in an election, do all the voters have to return to the polls? In the plurality with elimination election method, the run-off can happen instantly. This lesson explains how.

Introduction to Plurality

Can you imagine how it would feel to have spent years of your life and a lot of money to run for an elected position? You come down to the final day, Election Day, and you wait! You wait and wait for the results. Finally, the results are in and there is a need for a run-off (which means that another vote must be held excluding one or more of the original candidates). No one has actually won the race. How disappointing that would be!

Using the plurality with elimination, instant run-offs can be conducted to find a winner without the need for further voter participation. So, how does this work? How can you have an instant run-off without anyone needing to revote? That is what we will discuss in this lesson.

Plurality Method

So, in the plurality method, voters are asked to select their number one choice to win an election. In plurality with elimination, voters are asked to add to this information by indicating second, third, fourth (and so on) places for all candidates. They must rank every candidate.


This ranking method of voting results in a preference schedule that indicates the number of votes each possible combination of preference received. Above is an example of a preference schedule in a race with five candidates: Brown, Jones, Taylor, Smith and Rowe. In this schedule, we can see that Brown and Jones both received 22 votes for first place. There is no clear winner, so a run-off would be required. Luckily, we already have everything we need for the run-off without having to have a re-vote.


In an instant run-off, or plurality with elimination, the candidate with the fewest first place votes is eliminated from the results with his or her votes going to the second choice candidate for those voters. This process is continued until there are only two candidates remaining - one with the most votes; this is called a majority (having more than 50% of the votes is a majority).

In our example, Taylor received the fewest number of votes so he will be eliminated. The column that shows Taylor as first will shift up, with each candidate moving one closer to the top. In each column, Taylor is removed and all candidates below will shift up to accommodate the space. Notice how the first two columns of results now match with Brown being the first choice and Smith, Jones and Rowe following. We can combine these columns to indicate that 39 voters preferred this order.


Round 3 of the elimination would remove Smith from the preference schedule because he received the fewest number of first place votes. Here is the preference schedule after eliminating Smith.

round 3

At this point, we can see that Brown has 39 first place votes, Rowe has a total of 39 first place votes and Jones has only 22 first place votes. In the final round of elimination, Jones will be removed.

The final preference schedule will look like this.

round 4

Adding up the first place rankings for each candidate we see that Brown has a total of 61 first place votes and Rowe has a total of 39 first place votes. Brown wins the election.

Monotonicity Criterion

All methods of voting must be checked for fairness. The monotonicity criterion is a fairness standard that states if a candidate wins an election, then altering the original votes to give that candidate more votes, without altering any other outcomes, will still result in that candidate winning.

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