2.3 Plurality

The voting method we’re most familiar with in the United States is the plurality method.

This method is sometimes mistakenly called the majority method, or “majority rules”, but it is not necessary for a choice to have gained a majority of votes to win. A majority is over 50%; it is possible for a winner to have a plurality without having a majority.

Example 1

In our election from previous pages, we had the preference table:

	1	3	3	3
$1^{\text {st }} \text { choice }$	A	A	O	H
$2^{\text {nd }} \text { choice }$	O	H	H	A
$3^{\text {rd }} \text { choice }$	H	O	A	O

Show solution

For the plurality method, we only care about the first choice options. Totaling them up:

Anaheim: 1+3 = 4 first-choice votes

Orlando: 3 first-choice votes

Hawaii: 3 first-choice votes

Anaheim is the winner using the plurality voting method.

Notice that Anaheim won with 4 out of 10 votes, 40% of the votes, which is a plurality of the votes, but not a majority.

Your Turn

Try it Now 1

Three candidates are running in an election for County Executive: Goings (G), McCarthy (M), and Bunney (B)[1]. The voting schedule is shown below. Which candidate wins under the plurality method?

	44	14	20	70	22	80	39
$1^{\text {st }} \text { choice }$	G	G	G	M	M	B	B
$2^{\text {nd }} \text { choice }$	M	B		G	B	M
$3^{\text {rd }} \text { choice }$	B	M		B	G	G

Note: In the third column and last column, those voters only recorded a first-place vote, so we don’t know who their second and third choices would have been.

Answer

Using plurality method:

G gets $44+14+20 = 78$ first-choice votes

M gets $70+22 = 92$ first-choice votes

B gets $80+39 = 119$ first-choice votes

Bunney (B) wins under plurality method.

[1] This data is loosely based on the 2008 County Executive election in Pierce County, Washington. See www.co.pierce.wa.us/xml/abtus...ec/summary.pdf

Adapted from Math in Society by David Lippman, hosted on LibreTexts (math.libretexts.org) and licensed under CC BY-SA 3.0. Changes were made. License: CC-BY-SA-3.0.