Review Vocabulary

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Agenda An ordering of the candidates to be considered, which is often used in sequential pairwise voting. (p. 418)

Approval voting A method of electing one or more candidates from a field of several in which each voter submits a ballot that indicates which candidates he or she approves of. Winning is determined by the total number of approvals that a candidate obtains. (pp. p. 428 p. 429)

Arrow’s impossibility theorem Kenneth J. Arrow’s discovery that any voting system can give undesirable outcomes. (p. 424)

Borda count A voting system for elections with several candidates in which points are assigned to voters’ preferences; these points are summed for each candidate to determine a winner. The actual point totals are referred to as a candidate’s Borda score. (p. 414)

Condorcet’s method A voting system for elections with several candidates in which a candidate is a winner precisely when he or she would, on the basis of the ballots cast, defeat every other candidate in a one-on-one contest. (p. 408)

Condorcet winner A candidate in an election who, based on the ballots, would have defeated every other candidate in a one-on-one contest. (p. 412)

Condorcet winner criterion (CWC) A voting system satisfies the Condorcet winner criterion if, for every election in which there is a Condorcet winner, that candidate wins the election when that voting system is used. (p. 413)

Condorcet’s voting paradox The observation that there are elections in which Condorcet’s method yields no winner. (p. 411)

Hare system A voting system for elections with several candidates in which candidates are successively eliminated in an order based on the number of first-place votes. (p. 420)

Independence of irrelevant alternatives (IIA) A voting system satisfies independence of irrelevant alternatives if the only way a candidate (called ) can go from losing one election to being among the winners of a new election (with the same set of candidates and voters) is for at least one voter to reverse his or her ranking of and the previous winner. (pp. p. 416 p. 417)

Manipulability A voting system is subject to manipulability (or is manipulable) if there are elections in which it is to a voter’s advantage to submit a ballot that misrepresents his or her true preferences. (p. 414)

Majority rule A voting system for elections with two candidates (and an odd number of voters) in which the candidate preferred by more than half the voters is the winner. (p. 407)

May’s theorem Kenneth May’s discovery that, for two alternatives and an odd number of voters, majority rule is the only voting system satisfying three natural properties. (p. 408)

Monotonicity A voting system satisfies monotonicity provided that ballot changes favorable to one candidate (and not favorable to any other candidate) can never hurt that candidate. (p. 422)

Pareto condition A voting system satisfies the Pareto condition provided that every voter’s ranking of one candidate higher than another precludes the possibility of this latter candidate winning. (p. 419)

Plurality runoff A voting system for elections with several candidates in which, assuming there are no ties, there is a runoff between the two candidates receiving the most first-place votes. (p. 423)

Plurality voting A voting system for elections with several candidates in which the candidate with the most first- place votes wins. (p. 412)

Preference list ballot A ballot that ranks the candidates from most preferred to least preferred, with no ties. (p. 406)

Sequential pairwise voting A voting system for elections with several candidates in which one starts with an agenda and pits the candidates against each other in one-on-one contests (based on preference list ballots), with losers being eliminated as one moves along the agenda. (p. 418)