EXAMPLE 12 Approval Voting
To illustrate approval voting, suppose that we have nine members of a mathematics department who are trying to choose among five finalists for an open faculty position. They decide to use approval voting—the ballots are indicated in the following table. An X indicates an approval vote. For example, Voter 1, in the first column, approves of Candidates , and .
| Voter (department member) | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Candidate | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| X | X | X | X | X | X | ||||
| X | X | X | X | X | X | X | |||
| X | X | X | X | ||||||
| X | X | X | X | X | |||||
| X | X | X | X | X | |||||
Counting the Xs in each row shows that six department members (1, 2, 4, 6, 7, and 8) approved of Candidate , seven approved of Candidate , four approved of Candidate , and five approved of and . Thus, Candidate wins, with seven approval votes.