4. There are at least two voting systems for two candidates (A and B) and three voters that are nonmanipulable and that treat all voters the same (meaning that if two voters were to exchange ballots, then the election outcome would be unchanged). (a) What does May's theorem tell us about such a voting system? (b) In one sentence, give an example of such a voting system (that is, produce the rule that determines which of the two candidates, A or B, wins an election). (c) In one sentence, give another example that is different from the example you gave in part (b) in that it produces a different winner for at least one election.

4. There are at least two voting systems for two candidates (A and B) and three voters that are nonmanipulable and that treat all voters the same (meaning that if two voters were to exchange ballots, then the election outcome would be unchanged). (a) What does May's theorem tell us about such a voting system? (b) In one sentence, give an example of such a voting system (that is, produce the rule that determines which of the two candidates, A or B, wins an election). (c) In one sentence, give another example that is different from the example you gave in part (b) in that it produces a different winner for at least one election.