Section 7.2: Plurality Method
- Page ID
- 219574
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As stated in the previous section, when an election includes more than two candidates, different methods can be used to determine a winner. These methods are called voting methods, and each one uses a distinct rule for counting votes and declaring a result. The choice of voting method can significantly affect the outcome of an election. Here is the first of the four major voting methods.
The plurality method (also called first-past-the-post or simple plurality) is the most common and straightforward voting system used around the world. It's likely the method you're most familiar with because it's used in most U.S. elections.
Each voter ranks the candidates. The candidate who receives the most first place votes wins even if they don't receive a majority (more than 50%) of the votes.
Consider the following preference table with Candidates A, B, & C:
| Number of Voters | 11 | 10 | 8 | 6 |
|---|---|---|---|---|
| First Choice | A | D | B | D |
| Second Choice | C | B | A | C |
| Third Choice | D | C | C | B |
| Fourth Choice | B | A | D | A |
Use the plurality method to determine a winner.
✅ Solution:
Looking at the First Choice row,
Candidate A = 11 first place votes
Candidate B = 8 first place votes
Candidate C = 0 first place votes
Candidate D = 10 + 6 = 16 first place votes
Thus, Candidate D is the winner by the plurality method.
A survey of 23 customers was conducted asking them to rank which protein they prefer at a local Chipotle restaurant. The results are listed below:
| Number of Voters | 8 | 7 | 5 | 3 |
|---|---|---|---|---|
| First Choice | Steak | Carnitas | Chicken | Steak |
| Second Choice | Chicken | Barbacoa | Carnitas | Barbacoa |
| Third Choice | Barbacoa | Chicken | Steak | Chicken |
| Fourth Choice | Carnitas | Steak | Barbacoa | Carnitas |
Use the plurality method to determine which protein is the winner.
✅ Solution:
Looking at the First Choice row,
Steak = 8 + 3 = 11 first place votes
Carnitas = 7 first place votes
Chicken = 5 first place votes
Barbacoa = 0 first place votes
Thus, Steak is the winner by the plurality method.
City council members need to choose a new location for the city's community center. Four sites are being considered:
| Number of Voters | 35 | 30 | 20 | 15 |
|---|---|---|---|---|
| First Choice | Downtown | Northside | Eastside | Westside |
| Second Choice | Northside | Eastside | Westside | Eastside |
| Third Choice | Eastside | Westside | Northside | Northside |
| Fourth Choice | Westside | Downtown | Downtown | Downtown |
- Use the plurality method to determine which new location is the winner.
- How many voters put Westside and Eastside in their top two?
- How many people voted?
✅ Solution:
- Looking at the First Choice row,
- Downtown = 35 first place votes
- Northside = 30 first place votes
- Eastside = 20 first place votes
- Westside = 15 first place votes
Thus, Downtown is the winner by the plurality method.
- Looking at the First Choice and Second Choice rows: 20 + 15 = 35
- Looking at the top row: 35 + 30 + 20 + 15 = 100
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Consider the following preference table with Candidates A, B, & C:
Number of Voters 7 6 6 5 3 First Choice C B A B A Second Choice A A B C C Third Choice B C C A B Use the plurality method to determine a winner.
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A group of 41 people is choosing where to eat lunch during their meeting. The four fast food delivery options are: Board & Brew, Naugles, T.K. Burgers, or In-N-Out Burgers. Each voter ranks the restaurants from most preferred to least preferred.
Number of Voters 11 9 8 6 4 3 First Choice In-N-Out T.K. Burgers Naugles Board & Brew T.K.Burgers In-N-Out Second Choice Naugles Naugles T.K.Burgers T.K. Burgers In-N-Out T.K. Burgers Third Choice T.K. Burgers Board & Brew In-N-Out In-N-Out Naugles Board & Brew Fourth Choice Board & Brew In-N-Out Board & Brew Naugles Board & Brew Naugles Use the plurality method to determine a winner.
- Answers
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- Candidate B (11 votes)
- In-N-Out (14 votes)