Selected topics in finite mathematics/Voting/Plurality

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Objectives[edit]

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

Details[edit]

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]

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]

FAQ[edit]

Homework[edit]

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]

1. According to plurality A wins with the most votes

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