EXAMPLE 6 Sequential Pairwise Voting
Assume we have four candidates and that the agenda is , , , . Consider the following sequence of three preference list ballots:
| Rank | Number of Voters (3) | ||
|---|---|---|---|
| First | |||
| Second | |||
| Third | |||
| Fourth | |||
419
The first one-on-one pits against , and wins by a score of 2 to 1 (meaning that two of the voters—the two not in the middle—prefer to , and one of the voters prefers to ). Thus, is eliminated and A moves on to confront . Because wins this one on one (by a score of 3 to 0), A is eliminated. Finally, takes on , and wins by a score of 2 to 1. Thus, is the winner.