This activity presents another method for choosing among 3 or more choices when none wins a majority: instant runoff voting. In this voting system, voters again rank their choices. Each choice is given points, with 0 for the last choice, 1 for the next to last, and so on. The choice with the most total points wins, and no runoff elections are needed. Students use quantitative reasoning when analyzing the number of people satisfied by each voting method (MP2). They model with mathematics by comparing the voting methods and deciding what quantities are important (MP4).

The purpose of this discussion is to compare instant runoff voting with plurality, runoff, and ranked voting. Here are some questions for discussion:

• "How do the 4 voting methods we have seen compare?" (All 4 methods let voters show their top choice. Runoff, ranked, and instant runoff also allow voters to consider choices beyond their top choice.)
• “Which voting method would be best for a large election, for example, at the state or country level?” (Plurality or instant runoff would be best for a large election because they take only one round of voting.)
• "Which method should we use the next time our class has to make a decision? Why?" (We should use instant runoff to make sure everyone’s preferences are included.)

We have seen several methods for fairly deciding between more than two choices. There is no single fairest method. Different voting systems are used by different local, state, and federal governments as well as different countries.

In this activity, students make sense of how 5 friends voted on 3 choices of weekend activities. They also compare the results of some of the voting systems from the previous activities: plurality, runoff, and instant runoff. Students reason abstractly and quantitatively when calculating and interpreting the results of each voting method (MP2). They model with mathematics by evaluating the effectiveness of each voting method (MP4).

• “Based on their votes, which activity should they do this weekend?” (They should go hiking because everyone was at least a little interested in that.)
• “Why are the results the same for a runoff or a plurality?” (Both runoff and plurality start with everyone voting for their first choice. In a plurality, the choice with the most votes wins. In a runoff, if an option gets a majority of the votes, then there is only one round of voting. In this case, cooking has a majority of the first choice votes, so only one round happens.)
• “Why are the results different for an instant runoff and a runoff?” (Instant runoff takes everyone’s rankings into account, not just their first choice. This means the fact that some people did not want cooking but everyone had some interest in hiking changed the total points and the winner.)