# Selected topics in finite mathematics/Voting/Plurality

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## Objectives

Plurality is used find to find the winner by determining who has the most first place votes if there is one.

## Details

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

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.

## Homework

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

1. According to plurality A wins with the most votes

```     A= 3 votes
B= 2 votes
C= 1 vote
```