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Mathematics LibreTexts

2.3: 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


    2.3: Plurality is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.