Selected topics in finite mathematics/Voting/Plurality

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