EXAMPLE 7 Sequential Pairwise Voting (with a different agenda)

Assume we have the same ballots as in Example 6, but now let’s use sequential pairwise voting with the agenda $D$, $C$, $B$, $A$. The first one-on-one pits $D$ against $C$, and $D$ wins by a score of 2 to 1 (as only the third voter ranked $C$ over $D$). Thus, $C$ is eliminated and $D$ moves on to confront $B$. Because $B$ wins this one-on-one (by a score of 2 to 1), $D$ is eliminated. Finally, $B$ takes on $A$, and $A$ wins by a score of 2 to 1. Thus, $A$ is the winner.