Selected topics in finite mathematics/Voting/Plurality
Objectives
[edit | edit source]Plurality is used find to find the winner by determining who has the most first place votes if there is one.
Details
[edit | edit source]Plurality: a method of analyzing elections that declares the winner to be the candidate with the most first place votes (if there is a winner).
Examples
[edit | edit source]100 people vote for the 3 candidates for Best New Artist at the Grammies. The preference schedule is shown below.
| 1st Choice | A | B | C | C | A | B |
| 2nd Choice | B | C | A | B | C | A |
| 3rd Choice | C | A | B | A | B | C |
| Number of Ballots | 12 | 20 | 32 | 24 | 10 | 2 |
Find the winner for the Best New Artist award.
A: 12+10=22
B: 20+2=22
C: 32+24=56
Candidate C has the most first place votes. This means they are the winner.
Nonexamples
[edit | edit source]FAQ
[edit | edit source]Homework
[edit | edit source]1.
| 3 | 2 | 1 |
|---|---|---|
| A | B | C |
| C | C | A |
| B | A | B |
According to Plurality, who will win?
2.
| 5 | 4 | 4 | 2 |
|---|---|---|---|
| A | B | C | D |
| D | C | B | A |
| B | A | D | C |
| C | D | A | B |
According to Plurality, who will win?
Homework Solutions
[edit | edit source]1. According to plurality A wins with the most votes
A= 3 votes
B= 2 votes
C= 1 vote