23. Consider the voting system in which the winner is determined by the total number of first- and second- place votes, with ties broken (when possible) according to the number of first-place votes. Thus, a candidate with no first-place votes and three second-place votes would defeat a candidate with two first-place votes and no second-place votes, but a candidate with two first-place votes and three second-place votes would defeat a candidate with one first-place vote and four second-place votes. Given Election 1 below, find a change in Voter 1's ballot that shows that this voting system is manipulable.
| Election 1 | |||
|---|---|---|---|
| Rank | Number of Voters (3) | ||
| First choice | |||
| Second choice | |||
| Third choice | |||
| Fourth choice | |||
| Fifth choice | |||
23.
If the first voter changes his preference so that is in first place and is still in third, fourth, or fifth place, then Candidate will be the winner since the candidate has 2 first- or second-place votes and has a first-place vote, whereas Candidate does not.
| Example of Election 2 | |||
| Rank | Number of voters (3) | ||
| First | |||
| Second | |||
| Third | |||
| Fourth | |||
| Fifth | |||