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