This activity compares plurality voting with a different method for deciding the winner of an election that has more than two choices: runoff voting. If no choice has a majority of votes, then the choice or choices with the fewest votes are eliminated, and another vote is held between the remaining choices. This process is repeated until one choice gets a majority of the votes.

Students learn the technique of analyzing the results by holding their own vote. A fictitious story (choosing a field trip) is provided for students to vote on a situation with four choices, each of which may have some positive and negative aspects. They follow two different systems of voting rules to see how results can differ depending on the rule system used. Students use quantitative reasoning to analyze and compare two different voting rules (MP2).

Note: This activity includes a lot of teacher-directed voting activity. Students periodically stop to record information and determine the winner, or the need to do another round of voting, or reflect on the results.

The goal of this discussion is to compare the two voting methods. Here are some questions for discussion:

• “Which voting system seems more fair, plurality or runoff?” (The plurality system accounts for voters’ first choice only, but the runoff system allows people to pick their next favorite choice if their first choice is eliminated.)
• “Which voting system would be easier to implement on a large scale, like for a presidential election?” (The runoff system can take multiple voting sessions, so it takes more time than does the plurality system, in which only one voting session takes place.)

In this activity students revisit the situation from the previous activity, but they analyze the votes of a different class. In this case, the members of different student clubs all voted for the same field trip option. Students analyze a ranked-choice voting system using the provided data and compare it to a plurality voting system using the same data. They use quantitative reasoning to analyze and compare the two different voting systems (MP2).

Students must think through the voting process and determine which choice is eliminated at each round, and what vote totals the club presidents will turn in at every round of voting.

The goal of this discussion is to compare multiple voting systems and how using different methods of voting affects voter satisfaction with the result. Notice that after the first round, baseball seemed to be winning. After the second round, baseball was still winning, but museum's votes almost doubled. Only after 3 rounds of voting did museum overtake baseball to win the vote.

Ask students: 

• How did the results of this class compare to our own class?
• In this situation, everyone ranked their choices before the voting began. How does this impact the voting process? (In the runoff system, people could change their votes between each round, but in the ranked-voting system, everyone's choices are locked in before any rounds of voting begin.)
• What are some advantages and disadvantages of plurality, runoff, and ranked voting? (Plurality takes less effort but could be less fair. Runoff can be influenced between rounds of voting but allows people to vote beyond their first choice. Ranked voting locks in choices at the beginning but allows people to vote beyond their first choice.)
• If this class used plurality voting, what percentage of the class would be satisfied with the result? If this class used ranked voting, what percentage of the class would be satisfied with the result? (42% are satisfied with plurality voting, 58% are satisfied with ranked voting)
• Which system seems more fair—plurality, runoff, or ranked?