# Selected topics in finite mathematics/Voting/Plurality

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## 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 votesB= 2 votes C= 1 vote