Section 11.1 Preference Schedules
Objectives
Use preference schedules to organize ballots
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.
Definition 11.1.1. Preference Ballot.
A preference ballot is a ballot in which the voter ranks the choices in order of preference.
Example 11.1.2.
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:
| Bob | Ann | Mary | Alice | Eve | Omar | Lupe | Dave | Tish | Jim | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1st Choice | A | A | O | H | A | O | H | O | H | A |
| 2nd Choice | O | H | H | A | H | H | A | H | A | H |
| 3rd Choice | H | O | A | O | O | A | O | A | O | O |
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:
| 1 | 3 | 3 | 3 | |
|---|---|---|---|---|
| 1st choice | A | A | O | H |
| 2nd choice | O | H | H | A |
| 3rd choice | H | O | A | O |
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.