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# 2.2: Preference Schedules


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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