11. Assume the following ballots give the true preferences of the voters and that the Borda count is being used. Show that at least one of the voters can improve the election outcome from her point of view by a unilateral change in her ballot.
11.
| Election 1 | ||||
| Rank | Number of voters (5) | |||
| 1 | 1 | 1 | 1 | |
| First | ||||
| Second | ||||
| Third | ||||
| Fourth | ||||
A-26
has the highest Borda score and is the winner. But the winner becomes if the leftmost voter changes his or her ballot to , , , . Thus, has the highest Borda score and is declared the winner.
| Election 1 | |||||
| Rank | Number of voters (5) | ||||
| 1 | 1 | 1 | 1 | 1 | |
| First | |||||
| Second | |||||
| Third | |||||
| Fourth | |||||
, , and have the fewest first-place votes and are thus eliminated, leaving as the winner using the Hare system. But the winner becomes if the leftmost voter changes his or her ballot to , , , .