For Exercises 28 and 29, consider the preference lists from the chair's paradox (reproduced here) and assume that everyone knows the administration will vote for the J-Plan, but that no one knows anything about how the faculty will vote.
| Administration | Students | Faculty | |
|---|---|---|---|
| First choice | J-Plan | Terms | Semesters |
| Second choice | Terms | Semesters | J-Plan |
| Third choice | Semesters | J-Plan | Terms |
Question 10.59
29. In a sentence or two, explain why the students′ strategy to vote for Semesters does not weakly dominate their strategy to vote for Terms.
29.
If the faculty votes for Terms, then the students will get their first choice—Terms—by voting for Terms, but they will get their third choice—the J-plan—by voting for Semesters.
31. Consider what happens if the leftmost voter changes his or her ballot to , , , .
| Election 1 | ||||
| Rank | Number of voters (4) | |||
| 1 | 1 | 1 | 1 | |
| First | ||||
| Second | ||||
| Third | ||||
| Fourth | ||||
Because is the only candidate in the first election that either wins or ties each other candidate in a head-to-head match-up, by the weak Condorcet method, wins outright in the first election. However, the winner becomes if the voter on the left changes his or her ballot as follows:
| Election 2 | ||||
| Rank | Number of voters (4) | |||
| 1 | 1 | 1 | 1 | |
| First | ||||
| Second | ||||
| Third | ||||
| Fourth | ||||
wins, thus showing that the weak Condorcet method is manipulable.
A-27