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2.3: Plurality

Last updated

Dec 29, 2022
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- 2.2: Preference Schedules
- 2.4: What’s Wrong with Plurality?

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

Plurality Method

In this method, the choice with the most first-preference votes is declared the winner. Ties are possible, and would have to be settled through some sort of run-off vote.

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 2

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

$\begin{array}{|l|l|l|l|l|} \hline & 1 & 3 & 3 & 3 \\ \hline 1^{\text {st }} \text { choice } & \text { A } & \text { A } & \text { O } & \text { H } \\ \hline 2^{\text {nd }} \text { choice } & \text { O } & \text { H } & \text { H } & \text { A } \\ \hline 3^{\text {rd }} \text { choice } & \text { H } & \text { O } & \text { A } & \text { O } \\ \hline \end{array}$

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.

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?

$\begin{array}{|l|l|l|l|l|} \hline & 44 & 14 & 20 & 70 & 22 & 80 & 39 \\ \hline 1^{\text {st }} \text { choice } & \text { G } & \text { G } & \text { G } & \text { M } & \text { M } & \text { B } & \text { B } \\ \hline 2^{\text {nd }} \text { choice } & \text { M } & \text { B } & \text { } & \text { G } & \text { B } & \text { M } & \text { } \\ \hline 3^{\text {rd }} \text { choice } & \text { B } & \text { M } & \text { } & \text { B } & \text { G } & \text { G } & \text { } \\ \hline \end{array}$

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

Plurality Method

Example 2

Solution

Try it Now 1

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