Review Vocabulary

Agenda manipulation The ability to control who wins an election with sequential pairwise voting by a choice of the agenda—that is, a choice of the order in which the one-on-one contests will be held. (p. 448)

Chair's paradox The fact that with three voters and three candidates, the voter with tie-breaking power (the "chair") can end up with his or her least-preferred candidate as the election winner, if all three voters act rationally in their own self-interest. (pp. p. 452 p. 453)

Disingenuous ballot Any ballot that does not represent a voter's true preferences. Also called an insincere ballot. (p. 439)

Gibbard-Satterthwaite (GS) theorem Alan Gibbard and Mark Satterthwaite's independent discovery that every voting system for three or more alternatives and any number of voters that satisfies the Pareto condition, that always produces a unique winner, and that is not a dictatorship can be manipulated. (p. 451)

Group manipulability A voting system is group manipulable if there exists at least one election in which a group of voters can change their ballots (with the ballots of voters not in the group left unchanged) in such a way that they all prefer the winner of the new election to the winner of the old election, assuming that the original ballots represent the true preferences of these voters. (p. 450)

Manipulation A voting system is manipulable if there exists at least one election in which a voter can change his or her ballot (with the ballots of all other voters left unchanged) in such a way that he or she prefers the winner of the new election to the winner of the old election, assuming that the original ballots represent the true preferences of the voters. (p. 439)

May's theorem for manipulability Kenneth May's discovery that for two candidates and an odd number of voters, majority rule is the only voting system that treats both candidates equally, treats all voters equally, and is nonmanipulable. (p. 444)

Strategy In the chair's paradox, a choice of which candidate (calendar, in our presentation) to vote for. This is a special case of the use of the term strategy in general game-theoretic situations. (p. 452)

Tie-breaking power The aspect of the voting rule used in the chair's paradox that says that the winner will be whichever candidate the chair votes for if there is a tie (which happens only if each candidate gets exactly one vote). (p. 452)

Unilateral change A change (in ballot) by one voter, while every other voter keeps his or her ballot exactly as it was. (p. 442)

Weak dominance One strategy (e.g., a choice of whom to vote for) weakly dominates another if it yields an outcome that is at least as good, and sometimes better, than the other. (p. 452)