19. Prove that for three alternatives, an odd number of voters, and an arbitrary sequence of individual preference lists, there is no Con- dorcet loser if and only if for each alternative there is an agenda under which that alternative wins in sequential pairwise voting. (Your proof should not involve producing three particular preference lists.) 20. Modify the individual preference lists from the voting paradox to show that an alternative that loses in sequential pairwise voting for every agenda need not be a Condorcet loser. (Notice that this does not contradict Exercise 19). Modify the individual preference lists from the voting paradox to show that an alternative that loses in sequential pairwise voting for every agenda need not be a Condorcet loser. (Notice that this does not contradict Exercise 19). 19. Prove that for three alternatives, an odd number of voters, and an arbitrary sequence of individual preference lists, there is no Con- dorcet loser if and only if for each alternative there is an agenda under which that alternative wins in sequential pairwise voting. (Your proof should not involve producing three particular preference lists.) 20. Modify the individual preference lists from the voting paradox to show that an alternative that loses in sequential pairwise voting for every agenda need not be a Condorcet loser. (Notice that this does not contradict Exercise 19). Modify the individual preference lists from the voting paradox to show that an alternative that loses in sequential pairwise voting for every agenda need not be a Condorcet loser. (Notice that this does not contradict Exercise 19)