# Ranking Candidates: Recursive & Extended Ranking Methods

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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.

If you have ever wondered who would come in second place in an election (or third or fourth), this lesson will give you two ways - the recursive and extended methods - to determine just that information.

## Recursive and Extended

Hello, and welcome to this lesson on recursive and extended ranking methods for candidates. Sometimes it is really easy to tell who the winner of a race is. There is a clear front runner, and everyone knows that person will win. But, is it enough just to announce the top spot in an election? Is it ever necessary to indicate the rankings of all the other candidates?

One scenario in which ranking (at least for the first few positions) is important is a beauty pageant. The contestants and the audience are interested to know how each candidate ranked in comparison to the others, and naming the runners-up is important as well.

Another place that ranking candidates can come in handy is private club officer elections. Many clubs have people who are interested in being an officer simply run for a place. The person with the most votes is elected president; however, the second-place person becomes vice president, third becomes treasurer and so on until all the positions are filled.

There are two different ways to rank candidates in an election: extended and recursive. For this lesson, we will be investigating each of these ranking methods. Both can be used with any form of voting; however, for ease of example, I will use the plurality method to demonstrate.

As a reminder, in plurality voting, voters indicate their top choice to win. The person that receives the most votes wins the election.

## Extended Ranking

Extended ranking is a ranking method that extends a voting method until all candidates are ranked based on their performance in a single vote. If you define the term extend as 'to lengthen,' you will have a good idea of the process of the extended ranking method. The extended ranking method takes a traditional voting method and just lengthens the process until every candidate has a rank.

Let's look at plurality voting as an example. The plurality method simply looks for the person with the highest number of votes and indicates that person as the winner. Extended plurality ranking takes the same results from the plurality election and extends the process to indicate the person with the second highest, third highest and so on.

If we ran a plurality vote with four candidates, we might get the following results:

 Smith 45 Jones 50 Abner 62 Scott 70

In this example, Scott has received the highest number of votes, so he would be indicated as the winner in a plurality vote. To extend the plurality method and rank all candidates, we would use the same results. Abner, the person with the next highest number of votes, would earn second place. Jones, the person with the third highest number of votes, would take third place. And, Smith, with the least number of votes, would take last (in this case, fourth) place. If there were more candidates, this pattern would continue until all the candidates were ranked.

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