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Mathematics LibreTexts

2.2: Preference Schedules

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    34177
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    To begin, we’re going to want more information than a traditional ballot normally provides. A traditional ballot usually asks you to pick your favorite from a list of choices. This ballot fails to provide any information on how a voter would rank the alternatives if their first choice was unsuccessful.

    Preference ballot

    A preference ballot is a ballot in which the voter ranks the choices in order of preference.

    Example 1

    A vacation club is trying to decide which destination to visit this year: Hawaii (H), Orlando (O), or Anaheim (A). Their votes are shown below:

    \(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}
    \hline & \text { Bob } & \text { Ann } & \text { Marv } & \text { Alice } & \text { Eve } & \text { Omar } & \text { Lupe } & \text { Dave } & \text { Tish } & \text { Jim } \\
    \hline 1^{\text {st }} \text { choice } & \mathrm{A} & \mathrm{A} & \mathrm{O} & \mathrm{H} & \mathrm{A} & \mathrm{O} & \mathrm{H} & \mathrm{O} & \mathrm{H} & \mathrm{A} \\
    \hline 2^{\mathrm{nd}} \text { choice } & \mathrm{O} & \mathrm{H} & \mathrm{H} & \mathrm{A} & \mathrm{H} & \mathrm{H} & \mathrm{A} & \mathrm{H} & \mathrm{A} & \mathrm{H} \\
    \hline 3^{\mathrm{rd}} \text { choice } & \mathrm{H} & \mathrm{O} & \mathrm{A} & \mathrm{O} & \mathrm{O} & \mathrm{A} & \mathrm{O} & \mathrm{A} & \mathrm{O} & \mathrm{O} \\
    \hline
    \end{array}\)

    Solution

    These individual ballots are typically combined into one preference schedule, which shows the number of voters in the top row that voted for each option:

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

    Notice that by totaling the vote counts across the top of the preference schedule we can recover the total number of votes cast: \(1+3+3+3 = 10\) total votes.


    2.2: Preference Schedules 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.

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