Self Check Answers

1. In the original election, Voter 2's most-preferred candidate () won. If Voter 2 were to move to the bottom of his ballot, Voter 2 would then get a (much!) less preferred candidate as the winner. Doing something to get an outcome you like less is really pointless.
2. Voter 1 had a ballot with over over over . If Voter 2 were to change from having over over over to a ballot having over over over , then would become the winner. Again, this is pointless because Voter 2 prefers the result of the original election ( being the winner) to the result obtained by her disingenuous ballot.
3. Switch the first two to get , , , . The trivial change of switching the order of the first two in the agenda never has an effect on which one-on-ones take place.
4. Yes. There are only two agendas with first and last, and wins with both of them.
5. If is first in the agenda, then one of two things must happen. Either loses to some alternative in the agenda between and , or defeats all of these and then loses to .